Nov 21, 2005 - I am particularly pleased to be able to thank my colleagues. ... Hans Wilschut, for reviewing the text of this thesis. I am ...... Glück, F.: 1998, Nucl.
KATHOLIEKE UNIVERSITEIT
WITCH, a Penning trap for weak interaction studies
21/11/2005
CERN-THESIS-2006-009
Instituut voor Kern- en Stralingsfysica Departement Natuurkunde Faculteit Wetenschappen
Promotor:
Proefschrift ingediend tot
Prof. Dr. N. Severijns
het behalen van de graad van doctor in de wetenschappen door
Valentin Yu. Kozlov
Leuven 2005
To my rst and major teachers of life, to my parents. With love and gratitude.
Acknowledgment I would like to thank everybody connected with the realization of this thesis. For the last four years, these people have inspired and helped me to complete this work within framework of the WITCH project. Even though the physics goal of the experiment was already attractive, they were able to provoked my interest still further as well as helping me avoid any pitfalls. First of all, it is a great pleasure to acknowledge the contribution of my supervisor, Prof. Nathal Severijns, for his friendly guidance and support. During the last four years, discussions with him were always highly valuable and I very much appreciate his willingness to help, his good advice and ability to negotiate with people in order to reach the best solution. I am particularly pleased to be able to thank my colleagues. Marcus Beck, for his expertise, knowledge of physics and general life discussions. His alien power was inspiring not only for good work, but also for fun outside of work. Bavo Delauré, for excellent example of a student being able to take initiative and be creative, as well as someone who was always ready to help. Axel Lindroth, for occasionally heated discussions but out of which, the truth was usually born. Sam Coeck, for his willing assistance while working on the set-up and also for very useful discussions about MCP detectors and Penning traps. Stefan Kopecky, whose expertise in Penning traps came at the right moment and was extremely helpful and eective. Mustapha Herbane, he only recently joined the group but has already provided valuable input. I would also like to express my gratitude to the colleagues and friends from the Nuclear Orientation part of the group: Victor Golovko, Ilya Kraev, Titia Phalet and Stefan Versyck. I wish to thank all the people involved in the WITCH experiment, those working at ISOLDE (CERN) and at other places around the world.
I am
particularly grateful to Dietrich Beck, Klaus Blaum, Frank Herfurth, Friedhelm Ames, Pierre Delahaye and Fredrik Wenander. I am indebted to the sta of the Mechanical and Electronics workshops at I
Contents
II
K.U.Leuven headed by Eddy De Wyngaert and Maurice Elskens with a special mention to Rony Heylen and Guido Claes. I also want to say a word of thanks to Jacques Pier-Amory, a design engineer at ISOLDE and a real professional at what he does, and Willy Schoovaerts, engineer at IKS. Without the people mentioned, the installation of the set-up would not have been completed. I would like to express my gratitude to the IT team of IKS, especially Luc Verwilst, for help in ghting with the computers.
Also thanks to the
administrative sta of IKS: Josee Pierre, Katia Cools and Sally Vetters for their guidance and help with all formalities. I also want to thank everybody at IKS for the pleasant times spent together. I am especially grateful to the members of jury: Dr. Klaus Blaum, Prof. Mark Huyse, Prof. Peter Lievens, Prof. Oscar Naviliat-Cuncic, Prof. Nathal Severijns and Prof. Hans Wilschut, for reviewing the text of this thesis. I am also obliged to my friends all over the world, in particular to Alexey Dobrynin, Ashot Gasparyan, Ilya Seluzhenkov and Cedric Cerna, for their support, friendship and pleasant chats.
I also cannot forget to thank my dear
girlfriend, Natalia Egorova, who supported me a lot during the nal stages of my thesis. Of course, I reserve my warmest and highest gratitude for my parents: my father, Yuri V. Kozlov, and my mother, Lubov' A. Kozlova.
Thank you so
much for your advice and support you provided during my life.
Katholieke Universiteit Leuven Instituut voor Kern- en Stralingsfysica Leuven, Belgium November 2005
Valentin Kozlov
Contents
Acknowledgment
I
Introduction
1
1
Physics context 1.1 1.2
2
3
3
Development of weak interaction theory Standard Model and
β -decay
. . . . . . . . . . . . .
3
. . . . . . . . . . . . . . . . . . .
7
1.2.1
The Hamiltonian for beta decay
1.2.2
β−ν
1.2.3
Beyond Standard Model
angular correlation
. . . . . . . . . . . . .
7
. . . . . . . . . . . . . . . . .
9
. . . . . . . . . . . . . . . . .
11
Review of small a experiments 6
He
Oak Ridge
2.2
32
2.3
TRIUMF-ISAC
2.4
Berkeley
2.5
TRIµP plans
. . . . . . . . . . . . . . . . . . . . . . . . . . . .
18
2.6
LPC-Caen set-up . . . . . . . . . . . . . . . . . . . . . . . . . .
18
2.7
WITCH set-up
18
Ar
experiment
13
2.1
. . . . . . . . . . . . . . . . . . . .
13
. . . . . . . . . . . . . . . . . . . . . . . . . . 38m K measurements . . . . . . . . . . . . . . .
15
experiment . . . . . . . . . . . . . . . . . . . . .
16
experiment
21
Na
. . . . . . . . . . . . . . . . . . . . . . . . . . .
Trap technique
16
21
3.1
Principle of a Penning trap
. . . . . . . . . . . . . . . . . . . .
21
3.2
Processes in a Penning trap . . . . . . . . . . . . . . . . . . . .
22
3.2.1
Ion motion in an ideal trap
22
3.2.2
Motion in the presence of additional forces
3.2.3
Ion cooling
3.2.4
Charge exchange . . . . . . . . . . . . . . . . . . . . . .
31
3.2.5
Many ions in a trap
31
. . . . . . . . . . . . . . . . . . . . . . .
25
. . . . . . . . . . . . . . . . . . . . . . . . .
29
. . . . . . . . . . . . . . . . . . . . III
Contents
IV
4
WITCH set-up 4.1
33
Overview of the experiment . . . . . . . . . . . . . . . . . . . . Principle of the experiment
. . . . . . . . . . . . . . . .
33
4.1.2
Overview of the WITCH set-up . . . . . . . . . . . . . .
38
4.2
Choice of isotopes
. . . . . . . . . . . . . . . . . . . . . . . . .
38
4.3
ISOLDE separator
. . . . . . . . . . . . . . . . . . . . . . . . .
41
4.4
REXTRAP
4.5
Beamline
. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
43
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
43
4.5.1
Horizontal beamline
4.5.2
Vertical beamline . . . . . . . . . . . . . . . . . . . . . .
46
4.6
WITCH traps . . . . . . . . . . . . . . . . . . . . . . . . . . . .
48
4.7
Retardation spectrometer
4.8
WITCH magnet system
4.9
Normalization . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.10 Ion-detection
. . . . . . . . . . . . . . . . . . . .
45
. . . . . . . . . . . . . . . . . . . . .
49
. . . . . . . . . . . . . . . . . . . . . .
51 52
. . . . . . . . . . . . . . . . . . . . . . . . . . . .
53
4.11 Experimental cycle . . . . . . . . . . . . . . . . . . . . . . . . .
55
4.12 Diagnostic system
. . . . . . . . . . . . . . . . . . . . . . . . .
57
4.13 Vacuum system . . . . . . . . . . . . . . . . . . . . . . . . . . .
57
4.13.1 Cleaning for vacuum . . . . . . . . . . . . . . . . . . . .
59
4.13.2 Pumping system
5
33
4.1.1
. . . . . . . . . . . . . . . . . . . . . .
61
4.14 O-line ion sources . . . . . . . . . . . . . . . . . . . . . . . . .
61
4.14.1 REXTRAP ion source . . . . . . . . . . . . . . . . . . .
62
4.14.2 WITCH ion source . . . . . . . . . . . . . . . . . . . . .
63
4.15 WITCH control system & DAQ . . . . . . . . . . . . . . . . . .
64
4.15.1 Choice of hardware . . . . . . . . . . . . . . . . . . . . .
64
4.15.2 Software developed . . . . . . . . . . . . . . . . . . . . .
68
Simulations 5.1
5.2
71
Beam transport . . . . . . . . . . . . . . . . . . . . . . . . . . .
71
5.1.1
PDT section
71
5.1.2
Injection into high magnetic eld . . . . . . . . . . . . .
Response function
. . . . . . . . . . . . . . . . . . . . . . . .
72
. . . . . . . . . . . . . . . . . . . . . . . . .
73
5.2.1
Ideal response for mono-energetic ions . . . . . . . . . .
73
5.2.2
In uence of residual gas . . . . . . . . . . . . . . . . . .
74
5.2.3
Doppler broadening
75
5.2.4
Cut-o angle
. . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . .
76
5.3
Recoil spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . .
78
5.4
Achievable precision
79
5.5
Procedure to analyse experimental data
5.6
β -particle
5.7
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
simulations in a simple approach
82
. . . . . . . . . . .
83
GEANT4
β -particle simulations β -spectrum . . . . . . .
. . . . . . . . . . . . . . . . . .
83
5.7.1
. . . . . . . . . . . . . . . . . .
83
5.7.2
WITCH set-up in the GEANT4 program
. . . . . . . .
86
V
5.7.3
6
88
Very rst tests of WITCH
95
6.1
HBL tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
95
6.2
VBL tests
6.3
6.4
7
Results of the simulations . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2.1
Pulsed Drift Tube tests
. . . . . . . . . . . . . . . . . .
6.2.2
E ciency of the vertical beamline
. . . . . . . . . . . .
101
Trap tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
102
6.3.1
Box trapping
102
6.3.2
Buer gas cooling
6.3.3
Excitations
6.3.4
Estimate of the buer gas pressure . . . . . . . . . . . .
117
6.3.5
Magnetic eld in the center of the cooler trap . . . . . .
124
6.3.6
Discussion on the frequency measurement . . . . . . . .
128
More tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
128
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
104
. . . . . . . . . . . . . . . . . . . . . . . . .
114
6.4.1
First radioactive ions in WITCH
6.4.2
Preliminary spectrometer tests
. . . . . . . . . . . . .
128
. . . . . . . . . . . . . .
130
6.4.3
MCP regime
. . . . . . . . . . . . . . . . . . . . . . . .
131
Perspectives 7.1
7.2
7.3
97 97
137
Possible improvements . . . . . . . . . . . . . . . . . . . . . . .
137
7.1.1
Beamline
137
7.1.2
HV switch . . . . . . . . . . . . . . . . . . . . . . . . . .
140
7.1.3
Traps
142
7.1.4
60 kV ion source
. . . . . . . . . . . . . . . . . . . . . .
143
7.1.5
Spectrometer . . . . . . . . . . . . . . . . . . . . . . . .
143
7.1.6
Vacuum . . . . . . . . . . . . . . . . . . . . . . . . . . .
143
Additional tests . . . . . . . . . . . . . . . . . . . . . . . . . . .
144
. . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.2.1
REXTRAP tuning . . . . . . . . . . . . . . . . . . . . .
144
7.2.2
The excitation frequencies . . . . . . . . . . . . . . . . .
144
7.2.3
The ion species in the rest gas and buer gas . . . . . .
148
7.2.4
Buer gas pressure . . . . . . . . . . . . . . . . . . . . .
148
7.2.5
Cooling time
. . . . . . . . . . . . . . . . . . . . . . . .
150
7.2.6
Temperature of the ion cloud . . . . . . . . . . . . . . .
151
7.2.7
Space charge studies . . . . . . . . . . . . . . . . . . . .
152
7.2.8
Spectrometer investigation
7.2.9
β
measurements
. . . . . . . . . . . . . . . .
152
. . . . . . . . . . . . . . . . . . . . . .
154
More physics with WITCH
. . . . . . . . . . . . . . . . . . . .
157
. . . . . . . . . . . . . . . . . . . . .
157
7.3.1
Tensor interaction
7.3.2
F/GT mixing ratio . . . . . . . . . . . . . . . . . . . . .
157
7.3.3
Q -value measurement +
158
. . . . . . . . . . . . . . . . . . .
7.3.4
EC/β
7.3.5
Charge state distribution
branching ratio
. . . . . . . . . . . . . . . . . .
159
. . . . . . . . . . . . . . . . .
159
Contents
VI
7.3.6
Search for heavy neutrinos . . . . . . . . . . . . . . . . .
160
7.3.7
More... . . . . . . . . . . . . . . . . . . . . . . . . . . . .
160
Conclusion
161
A Dipole excitation in the presence of a damping force
163
B Measurement time in case of
165
β -background
B.1
No
B.2
In the presence of the
β -background
. . . . . . . . . . . . . . . . . . . . . . . . . .
β -background
. . . . . . . . . . . . . . .
C Tuning of the WITCH beamline
165 165
169
C.1
REXTRAP
. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
170
C.2
HBL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
170
C.3
VBL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
171
Samenvatting
175
Bibliography
187
List of Figures
1.1
The
β -decay
process in the gauge theory and for four-fermion
contact interaction
. . . . . . . . . . . . . . . . . . . . . . . . .
β -decay.
7
1.2
Possible leptoquark interactions contributing to nuclear
2.1
Experimental apparatus of the Oak Ridge
2.2
Scheme of the TRIUMF experimental set-up
. . . . . . . . . .
17
2.3
Experimental arrangement of Berkeley set-up . . . . . . . . . .
17
2.4
Set-up with the transparent Paul trap from LPC-Caen . . . . .
19
3.1
6
He
experiment . . .
11 15
Most common types of Penning traps: hyperbolic trap and simple cylindrical trap . . . . . . . . . . . . . . . . . . . . . . . . .
22
3.2
The ion motion in an ideal Penning trap . . . . . . . . . . . . .
24
3.3
Con guration of electrodes in order to generate an azimuthal electric dipole or quadrupole RF eld
3.4
. . . . . . . . . . . . . .
reduced cyclotron motion by a quadrupole excitation at 3.5
27
Conversion of an initially pure magnetron motion into a pure
ωq = ωc
29
Trajectory of a particle in a Penning trap in case of a damping force only and when an additional azimuthal quadrupole excitation a is applied . . . . . . . . . . . . . . . . . . . . . . . . . . .
a=1
and
a = −1
30
4.1
Dierential recoil energy spectrum for
4.2
Schematic overview of the WITCH set-up
. . . .
34
. . . . . . . . . . . .
35
4.3
WITCH set-up presently installed in the ISOLDE hall, at CERN
36
4.4
Schematic overview of the ISOLDE hall
42
4.5
REXTRAP set-up: the trap electrode structure, buer gas dis-
. . . . . . . . . . . . .
tribution and potential along the trap axis . . . . . . . . . . . .
44
4.6
Schematic view of the horizontal beamline of the WITCH set-up
45
4.7
Vertical beamline of the WITCH set-up
4.8
The principle of PDT.
4.9
Geometry of the WITCH Penning traps
. . . . . . . . . . . . .
47
. . . . . . . . . . . . . . . . . . . . . . .
48
. . . . . . . . . . . . .
49
4.10 Scheme of the retardation spectrometer. . . . . . . . . . . . . .
50
VII
List of Figures
VIII
4.11 Magnetic and electric elds on the axis of the spectrometer
. .
52
. . . . . . . . . . . . . . . . . . . . . .
53
4.13 Scheme and photo of the LPC position sensitive MCP assembly
54
4.14 Operation cycle of the WITCH experiment
56
4.12 MCP working principle
. . . . . . . . . . .
4.15 General schematic view of the WITCH set-up with the diagnostics indicated
. . . . . . . . . . . . . . . . . . . . . . . . . . . .
58
4.16 Picture of the diagnostic based on the system with two cylindri. .
59
4.17 Scheme of the WITCH pumping system. . . . . . . . . . . . . .
cal bearings and the collimator strip in front (HBDIAG03).
60
4.18 REXTRAP ion source . . . . . . . . . . . . . . . . . . . . . . .
62
4.19 WITCH ion source
. . . . . . . . . . . . . . . . . . . . . . . .
63
4.20 Electrical scheme of the HV switch system for 60 kV. . . . . . .
65
4.21 Layout of the present version of the HV switch system for 30 kV.
65
4.22 Generic software architecture of the WITCH control system . .
69
4.23 HV control program for all WITCH electrodes connected to computer controllable power supplies. . . . . . . . . . . . . . . . . .
69
5.1
E ciency of the PDT as a function of HV . . . . . . . . . . . .
72
5.2
The response function of the WITCH spectrometer for a monoenergetic peak . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3
tion of the WITCH spectrometer . . . . . . . . . . . . . . . . . 5.4
Cut-o angle as a function of the recoil energy charged ion
Ekin
. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Eect of the cut-o angle on the response function (∆U
5.7
Dierential recoil spectrum calculated for the Estimated precision on the coe cient of
76
of a singly
5.6 5.8
75
Doppler broadening of the response function of the WITCH spectrometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.5
73
In uence of rest gas at dierent pressures on the response func-
= 10 V) 38 m of K
β + -decay β − ν angular correla-
77 77 79
tion, a depending on the total number of events N in the dier. . . . . . . . . . . . . . . . . . . . . . .
80
5.9
ential recoil spectrum
Results of the simple beta particle simulation . . . . . . . . . .
84
5.10
β -spectrum
generated for
35
Ar
. . . . . . . . . . . . . . . . . .
5.11 WITCH set-up in the GEANT4 simulation program 5.12 Trajectories of
β -particles
of 3 MeV energy in the WITCH set-up
5.13 3D plot of the points where time
85 87 88
β -particles hit the set-up for the rst
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.14 Plot showing the elements of the set-up which the rst
. . . . . .
89
β -particles hit
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
93
β -particles . . . . . the cases a = 1 and
93
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
94
5.15 Energy left in the pseudo-MCP detector by 5.16 Integral spectrum calculated for
a = 0.5
26m
Al
for
IX
5.17 Dierential spectrum calculated for and
a = 0.5
26m
Al
for the cases
6.1
Slit scans of the beam pro le with the HBL diagnostics
6.2
E ciency of the beam transfer through the HBL
6.3
a = 1
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
96
. . . . . . . .
96
TOF spectra (VBDIAG03 MCP detector) of ions coming from the REXTRAP set-up (no switching was performed) . . . . . .
6.4
6.6
TOF spectra of
39
K
after the PDT (VBDIAG03 MCP detector)
Simulated TOF spectra for dierent time constants (10
τP DT < 0.4µs), 6.7
98 99
µs < 99
TOF spectrum for dierent ion species/masses measured with except for
6.9
−5
compared to the measured spectrum . . . . . .
the VBDIAG03 MCP detector. 6.8
98
Schematic showing the behaviour of dierent parts of an ion bunch during the PDT HV switching . . . . . . . . . . . . . . .
6.5
94
39
K
(24 kV).
The PDT v oltage was 22 kV,
. . . . . . . . . . . . . . . . . . . . . .
100
First ions trapped in WITCH . . . . . . . . . . . . . . . . . . .
103
MCP signal for dierent storage times (simple box trapping in the cooler trap and no buer gas cooling)
. . . . . . . . . . . .
105
6.10 Trap voltages originally applied in order to capture ions in the cooler trap, get them in the quadrupole potential, transfer then into the decay trap and keep them there . . . . . . . . . . . . .
106
6.11 E ciencies of the ion ejection from the cooler trap (shoot through the decay trap) as a function of the decay trap voltages
. . . .
107
6.12 Oscilloscope pictures of the MCP signal corresponding to dierent cooling times
. . . . . . . . . . . . . . . . . . . . . . . . . .
109
6.13 Oscilloscope signal for a buer gas pressure of 9 mbar and 25 ms cooling time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.14 Time-of- ight values for
39
K
109
ions as a function of the cooling
time for dierent estimators and buer gas pressures of 5 mbar and 3 mbar. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.15 Width of the TOF signal for
39
K
112
as a function of the cooling
time for dierent estimators at buer gas pressures of 5 mbar and 3 mbar. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
112
6.16 MCP signal (SPMCPD01) for dierent cooling times (100..900 ms)113 6.18 Mass selective cooling of 6.19 Fitting the of
39
K
Ekin (tcool )
39
K
ν+
39
K
115
. . . . . . . . . . . . . . . . . . .
116
6.17 Dipole excitation at the reduced cyclotron frequency
of
spectra converted from the TOF spectra
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.20 Time of ight values for
39
K
122
ions as a function of the cooling
time. The corresponding ts are shown as well
. . . . . . . . .
122
6.21 Identi cation of dierent peaks based on the dipole excitation at the reduced cyclotron frequency
. . . . . . . . . . . . . . . .
126
List of Figures
X
6.22 Calculated radius of the ion motion under the 6.23
ν+
excitation as
a function of the frequency shift . . . . . . . . . . . . . . . . . .
129
35
130
Ar
half-life measurement on the VBDIAG01 MCP detector. .
6.24 Integral spectrum measured with the SPMCPD01 detector for dierent ion source acceleration voltages . . . . . . . . . . . . .
131
6.25 Summed MCP signal as a function of the number of incident particles (per bunch) . . . . . . . . . . . . . . . . . . . . . . . .
132
6.26 MCP signal shapes in the case of a double ion bunch . . . . . .
133
6.27 Change of MCP signal shape with the applied MCP HV and the saturation eect (VBDIAG03 detector).
. . . . . . . . . . . . .
135
6.28 Eect of the WITCH beam gate on the MCP signal (VBDIAG01, MCP HV=1.6 kV): removing early arriving ions with the beam gate increases the MCP signal of later arriving ions. 7.1 7.2 7.3
Time-of- ight spectrum on the detection MCP (oscilloscope pic138
Split anode of the new diagnostic MCP.
139
. . . . . . . . . . . . .
HV of the PDT as a function of time in case of a standard
. . . . . . . . .
7.8
νdipole (magnetron
excitation)
. . . . . . .
145
νdipole (reduced cyclotron) . . . Rb and 87 Rb ions measured in the prepa-
146
ration trap of the ISOLTRAP set-up . . . . . . . . . . . . . . .
147
Cooling resonance for
85
Cyclotron resonance for
85
of the ISOLTRAP set-up 7.9
141
The number of ions ejected from REXTRAP as function of the shift of the excitation frequency
7.7
141
The number of ions ejected from REXTRAP as function of the excitation frequency
7.6
. . . . . . . . .
Improved HV switch circuit scheme, modi ed by adding the clamping diode to improve the switching speed
7.5
135
ture) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
exponential decrease and using clamping diode 7.4
. . . . . .
Rb ions measured in the precision trap . . . . . . . . . . . . . . . . . . . . .
147
The number of ions ejected from the ISOLTRAP preparation trap as a function of the delay between the end of cooling by means of RF - eld and the extraction . . . . . . . . . . . . . . .
150
7.10 The width of the ejected ion signal as a function of storage time in the RFQ trap of ISOLTRAP . . . . . . . . . . . . . . . . . .
151
7.11 The number of ejected ions as a function of the buer gas pressure/voltage of the buer gas control unit for the REXTRAP set-up
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.12 Energy deposited by hind the MCP
β -particles
151
in the scintillator detector be-
. . . . . . . . . . . . . . . . . . . . . . . . . . .
156
7.13 Precision on Fermi to Gamow-Teller ratio measurement as a function of
β−ν
angular correlation parameter . . . . . . . . .
157
7.14 Achievable precision for the determination of the Q-value from the EC peak position . . . . . . . . . . . . . . . . . . . . . . . .
159
XI
S.1
Schematische voorstelling van de WITCH-opstelling
S.2
TOF spectra van
S.3
Gesommeerd MCP signaal als functie van het aantal invallende deeltjes per puls
39
K
. . . . . .
177
na de PDT . . . . . . . . . . . . . . . . .
179
. . . . . . . . . . . . . . . . . . . . . . . . . .
183
List of Tables
1.1
Conditions for violation of the discrete symmetries. . . . . . . .
9
2.1
Overview of small a experiments. . . . . . . . . . . . . . . . .
14
3.1
Example of the dierent
ω+, c, z, −
frequencies for the WITCH
Penning trap. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2
25
Time scale of an increase (decrease) of the magnetron (reduced cyclotron) radius in the case of WITCH cooler trap . . . . . . .
27
4.1
Candidate isotopes . . . . . . . . . . . . . . . . . . . . . . . . .
40
4.2
Vacuum in the WITCH set-up (no buer gas used).
. . . . . .
61
5.1
Total e ciency of optimized WITCH set-up.
. . . . . . . . . .
81
5.2
Increase of the total measurement time in the case of to the
6.1
β -background
26m
Al
due
. . . . . . . . . . . . . . . . . . . . . . . .
E ciency of box trapping of
39
K
ions in the cooler trap. No
buer gas is used . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2
Estimation of the buer gas pressure in the cooler trap. calculation is based on the dipole excitation of the
6.4
39
K
ions . .
6.7 B.1
120
Evaluation of the buer gas pressure in the cooler trap based on Cyclotron frequencies calculated for various isotopes for
9 6.6
108
The
the TOF measurement . . . . . . . . . . . . . . . . . . . . . . . 6.5
105
Trapping e ciencies as a ratio to the number of ions shot through the traps (without capturing) . . . . . . . . . . . . . . . . . . .
6.3
90
T and
Bestim. = (9.018 ± 0.004)
123
Btheor =
T in the center of the cooler
trap. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
125
ν+ ν+
frequencies calculated for frequencies calculated for
B = 9.018(4) B = 8.997(3)
T.
. . . . . . . . . .
127
T.
. . . . . . . . . .
127
Increase of the measurement time for the channel near the endpoint energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . XIII
167
List of Tables
XIV
C.1
Positions of the detectors and the collimator diaphragms in HBL and VBL
S.1
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
173
E ciënties voor een volledig geoptimaliseerde WITCH-opstelling en de op dit egenblik bereikte waarden . . . . . . . . . . . . . .
185
Introduction Despite the fact that the
β -decay
process was discovered already at the end
of 19th century, our understanding of weak interactions has developed only gradually.
Nuclear beta decay has played a crucial role in the development
of weak interaction theory.
For instance, such experimental foundations of
the present standard electroweak model (which is the uni ed theory of the electromagnetic and weak interactions) as a) the assumption of maximal parity
violation; b) the assumption of massless neutrinos and c) the vector axialvector (V-A) form of the weak interaction have their origin in the detailed analysis of nuclear beta decay process. Although the standard model of the electroweak interaction was shown to be very successful in describing existing experimental data both qualitatively and quantitatively, a number of parameters have to be determined experimentally and several important properties of the interaction are not well understood. One of these is that from the ve possible types of weak interactions vector (V ), axial-vector (A), scalar (S ), tensor (T ) and pseudoscalar interaction (P ) just V and A interactions are present at a fundamental level. This assumption is based on experimental results only and the presence of scalar and tensor types of weak interaction is today ruled out only to the level of about 8% (combining the results of several experiments) of the V - and A-interactions [Severijns et al., 2006]. The main aim of the WITCH (acronym for Weak Interaction Trap for Charged particles) experiment is to study the structure of the electroweak interaction by determining the
β−ν
angular correlation from the shape of the
recoil ion energy spectrum. The primary goal is to concentrate on the possible scalar component in the interaction.
A cloud of radioactive ions stored in
a Penning trap serves as the source for the experiment, thus leading to the minimization of scattering and energy loss of the decay products. The energy spectrum of the recoiling daughter ions from
β -decays
be measured with a retardation spectrometer.
in this ion cloud will
This recoil energy spectrum
can be measured for a wide variety of isotopes, independent from their speci c 1
2
LIST OF TABLES
properties. The set-up is installed at the ISOLDE (CERN) facility, which provides a wide range of radioactive beams with good intensities, giving access to many isotopes of interest. The construction of WITCH was completed and the experiment is presently in the commissioning stage. First tests with stable beams as well as with radioactive ones were done already. The work presented here will focus on the development of the set-up, its present status, the results of the rst tests and possible improvements. The rst chapter gives an overview of the physics of weak interactions with emphasis on the
β -decay process and the β − ν
angular correlation. The second
chapter gives an overview the main experiments which determined the
β−ν
angular correlation parameter a. Since the WITCH experiment uses a Penning trap, the basics of the Penning trap theory with some examples for the WITCH case are given in the third chapter. Chapter 4 provides a detailed overview of the set-up, starting from the physics principle of the experiment and continuing with the technical aspects to ful l the primary goal of the experiment. Chapter 5 is dedicated to the calculations and simulations done in order to ensure a good understanding of the set-up.
Chapter 6 describes the very rst tests
performed, discusses the results of these tests and highlights several problems experienced during this commissioning.
Finally, Chapter 7 suggests possible
solutions, technical modi cations and more tests that should lead to an even better understanding of the set-up and to further optimize it. overview of extended physics goals is given in this last chapter 7.
Also a brief
Chapter 1 Physics context The WITCH experiment is aiming to probe physics beyond the Standard Model of electroweak interactions. The corresponding physics background is given in this chapter.
1.1 Development of weak interaction theory One can somewhat arbitrarily divide a development of weak interaction theory into dierent periods, each one associated with speci c concepts and framework.
The Fermi theory The rst theoretical description of the weak interaction was formulated by Fermi [Fermi, 1934]. Fermi's theory was a very important key to our understanding of weak interaction physics. Numerous eorts to test predictions of this theory and some of its extensions were made in order to determine the nature of the interaction. Applying this theory made it possible to describe both at that time known beta processes (β
−
and
β+
decays), to explain electron and
positron spectra, to classify the beta decaying nuclei by their decay probability (allowed and forbidden transitions) and to estimate the weak interaction coupling constant
GF ,
but also to predict new phenomena such as inverse beta
decay, electron capture and
νe
scattering on
e−
[Mukhin et al., 1997]. Fermi's
theory also played an important role in neutrino physics:
the electron neu-
trino was nally discovered in a nuclear reactor experiment [Reines and Cowan, 1953a,b] based on the idea that a neutrino capture process may induce a detectable radioactivity. Fermi's theory of nuclear beta decay incorporated the neutrino hypothesis in a formalism similar to quantum electrodynamics. Fermi's Hamiltonian 3
HF
CHAPTER 1 Physics context
4
involves a local four fermion vector type interaction:
GF HF = gF Jµ · j µ = √ (¯ pγµ n)(¯ eγ µ νe ) 2 where
γµ
Jµ
and
jµ
refer to the hadronic and leptonic vector currents respectively,
are the Dirac
γ -matrices
(mass)−2 ,
γ5 = γ1 γ√ ¯ = e† γ4 . The interaction 2 γ3 γ4 and e gF = GF / 2. However, this coupling has the
with
is characterized by a strength, dimension of
(1.1)
i.e. can not correspond to a fundamental interaction
strength. It is remarkable that the simple Fermi theory is still useful today for the phenomenological description of low energy decay processes.
V-A extension of the Fermi theory Fermi's vector type interaction theory alone could not explain all experimental data (for instance, the so-called decay of
6
He).
”θ − τ puzzle”
or the high probability of beta
In 1956 Lee and Yang suggested that parity conservation could
be violated in weak interactions [Lee and Yang, 1956]. Several tests were then proposed to verify this hypothesis.
The rst clear evidence came from the
celebrated measurement of the electron decay asymmetry from polarized
60
Co
nuclei [Wu et al., 1957] which also indicated that the magnitude of the violation is very high. Finally, a set of experimental results and theoretical work led to the modi cation of Fermi's assumption and to the formulation [Feynman and Gell-Mann, 1958, Sudarshan and Marshak, 1958] of a universal theory in which the interaction is described by an eective Hamiltonian density in terms of a self-coupling universal current
Jµ :
In today's terms, the
GF HV −A = √ Jµ† · Jµ + h.c. 2 charged current Jµ for weak interactions
(1.2) is
Jµ = Jµhadronic + Jµleptonic = u ¯γµ (1 − γ5 )d0 + ν¯e γµ (1 − γ5 )e
(1.3)
This formulation can be extended to incorporate several generations of fermions by adding more terms into the current. The main statements of this theory are the following:
•
it assumes only the (V-A) variant of the interaction
•
the weak vector current is conserved
•
maximal parity (P ) violation and violation of charge conjugation (C )
•
massless neutrinos
1.1 Development of weak interaction theory
5
•
all leptons are left-handed while anti-leptons are right-handed
•
conservation of lepton number (leptons are always produced in pairs, or when one lepton is annihilated another lepton is produced)
Following Cabibbo [Cabibbo, 1963] the relative strength of the purely leptonic, semi-leptonic and strange purely hadronic processes do not have to be identical. In terms of the quark states this can be incorporated into the theory via the relation
d0 ≈ cos θC · d = Vud d where angle
d0 (resp. d) denotes the weak (resp. mass) and Vud is one element of the so-called
quark mixing matrix (see Eq.(1.7)).
(1.4)
eigenstate,
θC
is the Cabibbo
Cabibbo-Kobayashi-Maskawa
The (V-A) theory completed by the
Cabibbo hypothesis provides a good approximation for phenomenology of weak interactions at low energy.
Theory of electroweak interaction In analogy with quantum electrodynamics it was proposed that the weak interaction mechanism is also due to the exchange of an intermediate boson with a mass
MW
[Lee and Yang, 1960].
The vertex coupling of this boson to the
fermions is characterized by a dimensionless constant g. In the limit of low momentum transfer one can derive a simple relation between the Fermi coupling of the (V-A) theory and that of the intermediate vector boson theory:
g2 GF √ = 2 8MW 2
(1.5)
However, the intermediate boson does not arise from a gauge symmetry principle. Therefore, this suggestion can not be considered as a fundamental theory but rather as an eective approximation only valid for processes at energies below the W mass threshold. The uni cation of the electromagnetic and weak interactions relies on a set of elaborated concepts and on the guiding principle of gauge invariance [Salam and Ward, 1961]. gauge group
The electroweak uni cation theory is based on the
SU (2)L ⊗ U (1)Y
[Glashow, 1961, Weinberg, 1967, Salam, 1968]
and contains four vector bosons:
W +, W −, Z 0
and
γ
. Three of them (W
±
, Z 0)
correspond to weak interaction and have mass. The latter can be explained by the symmetry breaking or Higgs mechanism. The fundamental strengths of the weak interaction g and of the electromagnetic interaction e are related by
e = g sin θW
(1.6)
CHAPTER 1 Physics context
6
where
θW
is the Weinberg angle. Theory successfully predicted the existence
of the c -quark (Bc
= 1/3, qc = (+2/3)|e|)
and neutral weak currents.
The
measurement of the ratio between neutral current and charged current events provided an estimate of the Weinberg angle, and Eqs.(1.5),(1.6) also an estimate of
MW ±
θW and from knowledge of GF MZ 0 (MZ 0 = MW ± / cos θW ).
and
Today the uni ed theory of electroweak interactions together with a description of the strong interaction forms the Standard Model of elementary particles.
As far as currently known there are 12 elementary particles (i.e.
which make up all the other particles found in Nature, and do not themselves
1
have any internal structure) : six leptons and six quarks which can be grouped in doublets:
leptons
e− νe
quarks
u d
µ− τ− , , νµ ντ c t , , s b
The upper part in each quark doublet has a charge charge of
−1/3.
+2/3,
the lower one a
The weak eigenstates of the quarks of charge
−1/3
dier
from the eigenstates of these quarks with respect to the electromagnetic and strong interaction for which the quarks were de ned. For d - and s -quark this is expressed as the Cabibbo-mixing (Eq.(1.4)). In the case of the three presently known quark families the quark mixing is expressed by the Cabibbo-KobayashiMaskawa matrix [Cabibbo, 1963, Kobayashi and Maskawa, 1972]:
d0 Vud s0 = Vcd b0 Vtd
Vus Vcs Vts
Vub d Vcb s Vtb b
(1.7)
where the prime denotes the weak eigenstates. The normalization of the particle wave-function requires that the CKM-matrix is unitary. At present the Standard Model of the electroweak interaction is very successful in describing the interaction both qualitatively and quantitatively. However, we already know that it has to be extended to account for the non-zero neutrino mass. Also the theory contains many free parameters and ad-hoc assumptions and many open questions still remain. Therefore, it is necessary to search for the existence of new physics or new phenomena beyond the Standard Model. The role of beta decay experiments in this branch of weak interaction studies is quite high (see e.g. [Deutsch and Quin, 1995, Herczeg, 2001,
1 there are also mediator bosons (gluon, W ± , Z 0 , γ ) which are also considered elementary in a sense that they are not themselves made up of smaller particles
1.2 Standard Model and
β -decay
W+
u
e
e
e+
e+
d
Figure 1.1:
The
β -decay
7
u
d
process in the gauge theory (left) and for four-fermion
contact interaction (right) (from [Severijns et al., 2006]).
Severijns et al., 2006]). One can even say that nuclear
β -decay
has become a
precision tool to test some underlying symmetries of the Standard Model. As the current work is directly related to
β -decay
studies in search for
β -decay
physics beyond the present theory, a closer view on the theory of
and
possible extensions of the Standard Model is given in the next paragraph.
1.2 Standard Model and β -decay The symmetries of the underlying gauge group determine the properties of a fundamental interaction and its gauge bosons. In low-energy processes like
β-
decay, in which the energies involved in the process are much smaller than the mass of the gauge boson, the interaction is equally well described by a fourfermion contact interaction. This kind of description preserves the symmetries of the gauge interaction.
Fig. 1.1 shows the scheme of
β -decay
for both a
description in terms of the exchange of gauge bosons and a four-fermion contact interaction.
1.2.1 The Hamiltonian for beta decay The standard (V-A) Hamiltonian for nuclear
β -decay
resulting from a four-
fermion contact interaction follows from Eqs.(1.2),(1.3) and (1.7):
GF uγµ (1 + γ5 )d) (¯ eγ µ (1 + γ5 )νe ) + h.c. H = √ Vud (¯ 2
(1.8)
Only a non-strange interaction is considered. This Hamiltonian assumes maximal parity violation and only vector and axial-vector interactions. The most general interaction Hamiltonian describing nuclear
β -decay
that
includes all possible interaction types consistent with Lorentz-invariance is given by [Lee and Yang, 1956, Jackson et al., 1957a, Jackson, 1958]
CHAPTER 1 Physics context
8
Hβ
=
(¯ pn) (¯ e (CS + CS0 γ5 ) ν) + (¯ pγµ n) (¯ eγ µ (CV + CV0 γ5 ) ν) 1 + (¯ pσλµ n) e¯σ λµ (CT + CT0 γ5 ) ν 2 0 − (¯ pγµ γ5 n) (¯ eγ µ γ5 (CA + CA γ5 ) ν) 0 + (¯ pγ5 n) (¯ eγ5 (CP + CP γ5 ) ν) + h.c.
(1.9)
with
1 σλµ = − i(γλ γµ − γµ γλ ) 2 The interacting particles are now leptons and nucleons.
(1.10)
The interactions
Oi , i ∈ {S, V, T, A, P }, with OS = 1, OV = γµ , OP = γ5 . The ve dierent terms in Eq.(1.9) are
are described by their operators
√1 σλµ , OA = −iγµ γ5 , 2 called Scalar (S ), Vector (V ), Tensor (T ), Axial-Vector (A) and Pseudoscalar
OT =
(P ) contributions because of the transformation properties of the corresponding operators. The coe cients
Ci
and
Ci0
are the coupling constants. The nucleon
current is now given by
X
p¯Oi n
(1.11)
e¯Oi (Ci + Ci0 γ5 )ν
(1.12)
i and the lepton current by
X i
This description does not take into account eects due to nucleon or nuclear structure. The C -coe cients determine the properties of the Hamiltonian in Eq.(1.9), and hence of the interaction, with respect to space inversion (P ), charge conju-
Ci 6= 0 and Ci0 6= 0, 0 while it is preserved for either Ci = 0 or Ci = 0. Maximum parity violation 0 corresponds to |Ci | = |Ci |. Other relations between the C -coe cients and the gation (C ) and time reversal (T ). Parity is violated if both
symmetry properties of the interactions are given in Table 1.1.
1.2 Standard Model and
β -decay
Symmetry
9
Condition for violation
6 0 and ReC 0 6= 0) or = 0 (ImC 6= 0 and ImC 6= 0 ) 0 C 6= 0 and C 6= 0 ImC 6= 0 or ImC 0 6= 0
(ReC
C P T
Table 1.1: Conditions for violation of the discrete symmetries.
The beta transitions are traditionally divided into allowed and forbidden transitions.
Allowed transitions correspond to processes in which no orbital
angular momentum is carried away by the pair of leptons. Their selection rules are:
∆J = Ji − Jf πi πf where
Ji
and
πi
(resp.
Jf
and
πf )
= 0, ±1 = +1
(1.13)
designate the spin and parity of the initial
(resp. nal) state. The allowed transitions can then be subdivided into singlet and triplet components depending on whether the lepton spins are anti-parallel (S = 0) or parallel (S = 1). In allowed transitions the singlet state can only
∆J = 0 (Fermi selection rule) whereas the triplet state corresponds ∆J = 0, ±1 (Gamow-Teller selection rule). In this last case, transitions between states of zero angular momentum (0 → 0) are excluded since it is ~i = J ~ f = ~0. The dierent transitions impossible to generate a triplet state for J arise when to
are described by dierent interaction terms of Hamiltonian (1.9).
It can be
shown [Wu and Moszkowski, 1966] that the S and V interactions lead to Fermi transitions (F), the A and T interactions to Gamow-Teller transitions (GT). In the minimal Standard Model of the weak interaction only V interactions are present (CV
CT = CT0 = CP = CP0 = 0).
1.2.2
β−ν
and A
0 = CV0 = 1, CA = CA ≈ −1.27 CV , CS = CS0 =
angular correlation
Since the present work is dedicated to an experiment to probe the existence of a Scalar charged current weak interaction, it is necessary to see how the
Ci /Ci0 -coe cients are related to observables. It was shown by Jackson, Treiman and Wyld [Jackson et al., 1957b] that the β − ν angular correlation, which is de ned by the relative direction of the momenta of the two leptons, i.e. pβ and pν , depends on the coupling constants Ci /Ci0 , i ∈ {S, V, T, A, P } and at the same time on the nuclear matrix elements. For pure β transitions, however, the correlation becomes independent of the matrix elements, allowing one to
CHAPTER 1 Physics context
10
study the value of the non-Standard Model coupling constants independently of nuclear structure.
For allowed
β -decay
of non-oriented nuclei the above
authors calculated for the general Lorenz invariant interaction of Eq.(1.9) the distribution in electron and neutrino direction and electron polarization:
ω( σ|Ee , Ωe , Ων )dEe dΩe dΩν = F (±Z, Ee ) pe Ee (E0 − Ee )2 dEe dΩe dΩν × (2π)5 1 pe · pν m p p ξ 1+a +b +σ· G e +H ν 2 Ee E ν Ee Ee Eν pe pe · pν pe × pν +K +L Ee + m E e Eν Ee Eν
(1.14)
Ω denote the total energy, momentum and angular β -particle and the neutrino; E0 is the total β -particle energy at the spectrum endpoint; m is the rest mass of the electron; F (±Z, Ee ) is the Fermi-function which corrects for the Coulomb interaction between the β particle and the nuclear charge; σ is the spin vector of the β -particle; ξ is a The symbols E, p and coordinates of the
normalization factor which is proportional to the decay rate and contains the nuclear matrix elements
ξ
MF
and
MGT :
= |MF |2 (|CS |2 + |CS0 |2 + |CV |2 + |CV0 |2 ) 0 2 + |MGT |2 (|CA |2 + |CA | + |CT |2 + |CT0 |2 )
The upper (lower) sign refers to
β − (β + )-decay.
(1.15)
Expressions for all correlation
coe cients a, b, c, G, H, K and L can be found in the literature [Jackson et al., 1957a, Severijns et al., 2006].
Although G, H, K and L also can be used to
search for exotic interactions (S,T ), they are of no practical relevance at present [Severijns et al., 2006]. They are hard to measure since one has to determine the polarization of the
β -particle
with high precision. Including Coulomb cor-
rections, the coe cients a and b can be calculated from (the upper (lower) sign refers to
aξ +
β − (β + )-decay)
αZme ∗ 0 0∗ 2 0 2 2 0 2 2Im(CS CV + CS CV ) = |MF | |CV | + |CV | − |CS | − |CS | ∓ pβ αZme |MGT |2 0 2 ∗ 0∗ |CT |2 + |CT0 |2 − |CA |2 − |CA | ± 2Im(CT CA + CT0 CA ) 3 pβ 2
(1.16)
bξ
∗ 0∗ = ±2ΓRe |MF |2 (CS CV∗ + CS0 CV0 ∗ ) + |MGT |2 (CT CA + CT0 CA ) with
Γ = (1 − α2 Z 2 )1/2
(1.17)
1.2 Standard Model and
β -decay
11
The parameter b in Eq.(1.14), known as the Fierz interference term, is not linked to any product of the observable quantities and will thus contribute to any correlation measurement. Looking at Eqs.(1.16,1.17) one notices that the rst has a quadratic dependence while the second depends linearly on the
Ci /Ci0
coupling constants. However, the b term has the disadvantage that it depends on the parity properties of the interaction (i.e. the two terms of Eq.(1.17) will be trivially equal to zero for
CS = −CS0
or
CT = −CT0 ).
This makes a measure-
ment of the a -parameter more favorable, even though a higher experimental precision is needed to get stringent limits for the coupling constants.
1.2.3 Beyond Standard Model In the Standard Model a number of parameters as well as several important properties of the interaction are determined empirically. One of these is that from ve possible types of interactions: vector, axial-vector, scalar, tensor and
pseudoscalar (see Eq.(1.9)) only the V and A interactions are present at a fundamental level. A wide range of theoretical extensions of the Standard Model are available (for instance, to account for nite neutrino mass, for a possible magnetic moment of the neutrino [Voloshin et al., 1986], left-right symmetric models [Beg et al., 1977], ...). Here we will brie y extend on models with leptoquarks as related to scalar interactions.
Leptoquark extensions derive from Grand Uni ed Theories (GUTs). Here the gauge bosons couple to both quarks and leptons and have lepton number as well as color and baryon number. They are called leptoquarks. Their Feynman diagrams relevant for
β -decay
are shown in Fig. 1.2.
d
X (1=3)
u
/
Y (1=3)
e
X (2=3)
e+
u
/
Y (2=3)
Figure 1.2: Possible leptoquark interactions contributing to nuclear
intermediate leptoquark can be a vector (X) or scalar (Y) particle.
β -decay.
d e+
e The
The absolute
value of the charge is given between the brackets (from [Severijns et al., 2006]).
Leptoquarks have a fractional charge
Q = 2/3
or Q =-1/3 . They can have
spin 1 (vector leptoquarks) or spin 0 (scalar leptoquarks). Their interaction at low energy can also be described in the form of a contact interaction [Herczeg, 1995, 2001]. The Hamiltonian for leptoquark interactions at low energy con-
12
CHAPTER 1 Physics context
serves lepton and baryon numbers and couples leptons of the rst generation to quarks of the rst generation. Thus no baryon or lepton number violation or generation mixing interactions are considered. Notably, both scalar and vector leptoquarks can lead to V, A, S and T interactions. Thus, a limit on e.g. vector leptoquarks not only yields a limit on the V interaction but also on e.g. a
S interaction, if just leptoquark exchange is considered. Conversely, a limit on e.g. S interaction yields always a limit on both scalar and vector leptoquarks. However, a limit on S or T interactions derived by assuming the exchange of leptoquark does not constrain S or T interactions caused by processes dierent from leptoquark exchange [Herczeg, 1995].
Chapter 2 Review of small a experiments The interest to measure the
β − ν angular correlation parameter a raised in β -decay interaction. It was established that
order to determine the form of the
the weak interaction is dominated by V and A currents [Allen et al., 1959]. Nevertheless, scalar and tensor interactions are today ruled out only to the level of about 10% of the V - and A-interaction [Severijns et al., 2006]. This means that a sizable contribution of exotic scalar and tensor interactions is not excluded and present constraints should be improved. Table 2.1 summarizes the main results obtained in dierent measurements of the
β−ν
angular correlation parameter a. The best limit for tensor inter-
TRIUMF-ISAC tion. Berkeley by about
6
He
32
Ar experiment and K measurements yield the best limits for scalar contribu21 N a experiment gives a result on a -parameter which deviates
action is obtained in Oak Ridge
experiment, while
38m
3σ from the value calculated within the Standard Model.
Two planned
1 and WITCH) are listed as well. These set-ups and
experiments (LPC-Caen
techniques used are brie y described in this chapter.
2.1 Oak Ridge 6He experiment In this experiment the energy spectrum of recoil ions from the
He was produced in a reactor by the 6 He to 6 removed and He was left to decay in a
was observed [Johnson et al., 1963]. The
9
Be(n, α) 6 He
β − -decay of 6 He
6
reaction. A continuous stream of water vapor brought
the laboratory where the vapor was
conical volume (Fig. 2.1). To check the source activity a proportional counter
1
Laboratoire de Physique Corpusculaire de Caen, IN2P3-ENSI, France 13
CHAPTER 2 Review of small a experiments 14
(place)
(type of decay)
Isotope
68% C.L.
a ± ∆a,
a)
−0.3343 ± 0.0030, 0.9989 ± 0.0052(stat) ± 0.0039(syst),
a)
(GT) (F)
0.9978 ± 0.0030(stat) ± 0.0037(syst)
He Ar (F)
32
K
b)
38m
δa < 1%
0.5243 ± 0.0091
(GT)
(mixed)
He
Na
6
Paper/experiment
(Oak Ridge)
[Johnson et al., 1963]
(ISOLDE)
[Adelberger et al., 1999]
21
6
a experiments.
35 [Beck et al., 2003a] δa < 1% Ar (mixed), 26m WITCH Al (F) 46 (ISOLDE) V (F) Assuming the Fierz coe cient b = 0, otherwise the limit is for a˜ (see Eq.(2.1)) This result deviates by 3σ from the Standard Model calculation.
(LPC-Caen)
[Ban et al., 2004]
(Berkley)
[Scielzo et al., 2004]
(TRIUMF)
[Gorelov et al., 2005]
a) b)
Table 2.1: Overview of small
Status
published published published published
commissioning
commissioning
2.2
32
Ar
Figure
experiment
2.1:
15
Experimental apparatus of Oak Ridge
6
He
experiment (from
[Johnson et al., 1963]).
detector (the monitor counter) was installed. The energy of the recoil
6
Li
ions
was analyzed by a tandem of stigmatic-focusing magnetic and electrostatic de ectors. At the last stage the ions were accelerated and then detected by a secondary-electron multiplier [Johnson et al., 1963]. Although this experiment was carried out in the early 60's it provides the best limit on a tensor interaction till now.
Note that in this experiment the direct measurement of the recoil
energy spectrum was used.
2.2
32
Ar
experiment
Another technique to extract the recoil information is based on measuring the delayed proton (p ) or gamma (γ ) radiation.
If the daughter nucleus is
particle unstable, the daughter momentum can be determined from the decay products due to the Doppler eect. In principle it is possible to measure either a shift of the peak of a secondary radiation or the broadening of the peak. In the rst approach one has to determine a coincidence with the
β -particle.
In
the experiment described in [Adelberger et al., 1999] the second method was used because it seemed di cult to determine the su cient precision.
β -particle's
kinematics with
CHAPTER 2 Review of small a experiments
16
A 60 keV
32
a carbon foil.
32
Ar
Ar
beam from the ISOLDE facility (CERN) was implanted in
Delayed protons after the super-allowed
0+ → 0+ β -decay
of
(i.e. a pure Fermi decay, so that a test for scalar interaction is performed)
were detected in a pair of p-i-n diodes. To avoid possible beta background the detection apparatus was placed inside a 3.5 T superconducting magnet. The experimental data were tted to a single parameter
a ˜
which includes both the
a -parameter and the Fierz term b (see Eqs.(1.16, 1.17)):
a ˜=
a 1 + (me /Eβ ) · b
A total precision of about 0.9% on the parameter
(2.1)
a ˜(a ) was obtained (Table 2.1).
One more comment about this experiment: the systematic error of 0.0039 (Table 2.1) comes from the fact that the Q -value of
32
Ar
was estimated from
the isospin-multiplet mass equation (IMME). This was necessary because of the
±50
keV uncertainty in the
32
cently a new mass measurement of value [Blaum et al., 2003].
Ar mass [Audi et al., 1997]. However, re32 Ar was preformed, yielding an improved
Thus, the systematic uncertainty will be reduced
and a nal value will be given after a re-analysis.
2.3 TRIUMF-ISAC 38mK measurements This experiment deduces the
β −ν
correlation from the
β+
momentum and the
recoiling nucleus momentum obtained in a coincidence measurement [Gorelov et al., 2005].
The recoil momentum is detected via a time-of- ight
(TOF) measurement, where the
β -particle
event serves as a start trigger. A
magneto-optical trap (MOT) is used to provide a cooled, backing-free source of atoms. The ion beam of
38m
K
is produced at TRIUMF's ISAC facility and then
neutralized and captured in a rst MOT. To avoid background from untrapped atoms of both beam to a 2
nd
38
K
and
38m
K,
the trapped atoms are transfered by a push
MOT equipped with the detectors (Fig. 2.2). The
β -telescope
is a position-sensitive Si-strip detector backed by a plastic scintillator.
Ar recoils are detected by an MCP detector
readout. Two independent analyses of the data set report the value of shown in Table 2.1. Since the
β -decay
of
38m
The
2 with a resistive anode position
K
a ˜
(a )
is of pure Fermi type, it sets a
limit for a scalar interaction.
2.4 Berkeley 21N a experiment Similar to the TRIUMF experiment, at Berkeley a MOT and a coincidence measurement are used to study the
2
MCP - Microchannel Plate detector
β−ν
β − recoil atom
correlation in the mixed
2.4 Berkeley
Figure 2.2:
21
Na
experiment
17
Scheme of the TRIUMF experimental set-up (from [Gorelov et al.,
2005]). Not to scale.
Figure 2.3: Experimental arrangement of the Berkeley set-up (from [Scielzo, 2003]).
The scheme is not to scale.
CHAPTER 2 Review of small a experiments
18
decay of the mirror nucleus
21
N a.
A
21
Na
beam is produced by bombarding a
target with protons from the 88-inch cyclotron at Lawrence Berkeley National Laboratory [Scielzo et al., 2004]. When the atoms are captured in the trap, a trigger in either portion of the
β
telescope opens a
3 µs
coincidence window,
providing the time for the recoils to reach the MCP detector. Fig. 2.3 shows the experimental set-up. The a -parameter is deduced from the time-of- ight spectra of the recoiling
21
Ne
ions. The result deviates by about
value calculated within the Standard Model (Table 2.1).
3σ
from the
Further analysis is
necessary to understand this dierence, which is probably caused by a systematic error in the branching ratio used (several disagreeing values of the branching ratio exist [Achouri et al., 2004]). A new precision measurement of the branching ratio of the pure Gamow-Teller transition in
21
N a-decay
was
recently performed at the TRIµP facility at KVI Groningen [Achouri et al., 2004] and is being analysed now.
2.5 TRIµP plans Measurements of beta decay correlations with
21
Na
trapped in a MOT are
also planned at TRIµP facility. The rst aim is to repeat the Berkeley
β−ν
correlation experiment with an independent set-up but later also searches for Time-Reversal Invariance Violation are planned, i.e. a measurement of the Dcorrelation coe cient in
21
N a decay and a search for an electric dipole moment
in the Ra atom [Wilschut et al., 1999, Berg et al., 2003].
2.6 LPC-Caen set-up The goal of this experiment is to improve the precision on the a -parameter measured in the pure GT-decay of than 40 years ago.
The
6
He
6
He
and performed at Oak Ridge more
nuclei are produced at the SPIRAL facility of
GANIL. In order to increase the injection e ciency of the ions into the set-up, the radioactive ion beam is cooled and bunched by means of a Radio Frequency Quadrupole buncher [Ban et al., 2004]. The open geometry Paul trap constitutes the radioactive source of the experiment (Fig. 2.4). Similar to the two previous experiments the
β −ν
correlation will be deduced from a time-of- ight
measurement and the coincidence between the To detect the
β -particles
β -particle and 300 µm
a telescope consisting of a
the recoiling ion.
Si -strip detector
(SSD) and a thick plastic scintillator is used while the recoil ions will be counted with a position sensitive micro-channel plate. The set-up is now complete and under commissioning.
2.7 WITCH set-up
Figure
19
Set-up with the transparent Paul trap from LPC-Caen (from
2.4:
[Severijns et al., 2006]).
2.7 WITCH set-up The WITCH experiment aims to study a possible admixture of a scalar type interaction in
β -decay
by determining the
β−ν
angular correlation from the
shape of the recoil energy spectrum [Beck et al., 2003a, Kozlov et al., 2004], i.e. to use the similar method of measuring a -parameter as in the successful Oak Ridge
6
He
experiment.
3
The set-up combines a double Penning trap
structure to form the scattering-free radioactive source of the experiment and a retardation spectrometer for a direct measurement of the recoil ion energy. An MCP detector is used to count the recoil ions.
The set-up was installed
at the ISOLDE facility at CERN and commissioning has started at the end of 2004. The primary goal is to measure the a -parameter with a precision of
δa ' 0.5%
and hopefully later to be able to optimize the set-up in order to
push the limits down to
δa ' 0.2%.
This work gives an overview of the present commissioning stage of the experiment, the mathematical simulations that were performed, the rst tests with the set-up, suggestions for improvements and nally a number of tests that are required for a better understanding of the behaviour of the set-up and to achieve the nal goal.
3
The theory of Penning traps is reviewed in chapter 3.
Chapter 3 Trap technique Ion traps have gained increasing importance in the eld of experimental nuclear physics and play now an important role in many elds:
nuclear structure,
astrophysics, as well as weak interaction studies [Herfurth, 2001, Kluge et al., 2003]. Since two Penning ion traps are at the heart of the WITCH experiment, this chapter is dedicated to a description of the main properties and operating principles of this type of traps.
3.1 Principle of a Penning trap A Penning trap [Brown and Gabrielse, 1986] is a three dimensional device which uses a combination of a strong axial magnetic eld and an electrostatic potential to store ions. A homogeneous magnetic eld
ˆz B = B·e
is used to
con ne ions in radial direction while a quadrupole electrical potential assures con nement in the longitudinal direction:
U (r, z) = with
U0
U0 (2z 2 − ρ2 ) 4d2
(3.1)
ρ the radial distance of the stored particle from the x2 + y 2 ) and d the characteristic trap dimension. The two
the trap p potential,
trap center (ρ
=
most common possibilities to produce this potential are shown in Fig. 3.1. Since a quadrupole potential has a hyperbolic shaped equipotential surface, the most trivial way to build a Penning trap is to combine a ring electrode and two end-caps of hyperbolic form (see Fig. 3.1(left )).
In this case the
characteristic trap parameter d is given by:
s 1 2 ρ20 z + d= 2 0 2 21
(3.2)
CHAPTER 3 Trap technique
22
Figure 3.1: Most common types of Penning traps: hyperbolic trap (left) and simple
cylindrical trap (right).
where
ρ0
and
z0
are the distances of the ring electrode and end-caps from the
trap center, respectively (Fig. 3.1). The potential of Eq.(3.1) can also be de ned by a superposition of the potentials of a set of cylindrical electrodes. This structure is named cylindrical Penning trap.
The parameter d now looses its meaning as representation of
the trap dimension. However,
U0 /d2
still serves to describe the depth of the
potential well.
3.2 Processes in a Penning trap 3.2.1 Ion motion in an ideal trap The equation of motion for a particle with charge q and mass m in an axial magnetic eld
B and an electrical potential described by Eq.(3.1) is given by: r¨
=
q (r˙ × B − 5U ) m
or
x ¨ y¨ z¨
−
x˙ 0 x 2 y˙ × 0 − ωz y = 0 2 z˙ ωc −2z
(3.3)
3.2 Processes in a Penning trap
with The mass dependence
23
r q qU0 ωc = B and ωz = m md2 of ωc and ωz is widely used for precision
(3.4) mass mea-
surements. One can easily see that the axial and radial motion are decoupled in an ideal Penning trap. The axial part is a simple harmonic oscillation with frequency
ωz
along the z-axis:
z¨ + ωz2 z = 0 For the radial motion of a particle Eq.(3.3) can be rewritten as ([Brown and Gabrielse, 1986]):
1 ¨ − ωc ρ˙ × e ˆz − ωz2 ρ = 0 ρ 2 where
ρ=
p
x2 + y 2
is the radial coordinate. In case of
(3.5)
ωz → 0 this reduces to ωc . The
the equation for a uniform circular motion with cyclotron frequency
1 2 2 ωz ρ comes from the repulsive radial term in the electrostatic potential of Eq.(3.1). Two consequences of this repulsive radial potential can additional term
be considered: rst, the frequency of the cyclotron rotation will be reduced because this potential reduces the centrifugal force; second, the fast cyclotron orbit will be superimposed upon a much slower, circular magnetron orbit. The equation for the radial motion can be solved by introducing two velocity vectors
V (+)
and
V (−)
([Brown and Gabrielse, 1986]), de ned as
V (±)
ˆz = ρ˙ − ω∓ ρ × e h i p 1 = ωc ± ωc2 − 2ωz2 2
ω±
where
(3.6) (3.7)
If now one takes the time derivative of Eq.(3.6) and also uses Eq.(3.5) the equations of motion for
V±
can be obtained:
(±) ˆz V˙ = ω± V ± × e Taking the dierence
(V + − V − )
(3.8)
the radial equation of motion can be found
to be
ρ=−
ˆz V (+) − V (−) × e ω+ − ω−
(3.9)
Dierentiating this equation and taking into account Eq.(3.8) leads to the velocity dependence
ρ˙ =
ω+ V (+) − ω− V − ω+ − ω−
(3.10)
CHAPTER 3 Trap technique
24
Figure 3.2: The ion motion in an ideal Penning trap is a superposition of the re-
duced cyclotron motion (ω+ ), the magnetron motion (ω− ) and a harmonic oscillation (ωz ) in the direction of the magnetic eld.
Since a uniform circular motion with angular frequency described by
ˆz , ωc ρ = −v × e
ˆz ωc e
and velocity
v
is
it follows from Eq.(3.9) that the radial motion
of a particle in a Penning trap is the epicyclic superposition of two uniform circular motions.
They are named magnetron and reduced cyclotron motion
and characterised by the magnetron frequency frequency
ω+
ω−
and the reduced cyclotron
(Eq.(3.7)). Therefore, the complete motion of a particle is the su-
perposition of three independent eigenmotions: two epicycles and the harmonic axial oscillation, as is shown in Fig. 3.2. From Eq.(3.7) the following frequency relations can be obtained:
ω+ + ω− = ωc ,
2 2 ω+ + ω− + ωz2 = ωc2 ,
ω + ω− =
1 2 ω 2 z
Under the usual operating conditions for a Penning trap the frequencies and
ωz
(3.11)
ω+ , ω − ,
dier by several orders of magnitude. One can assume
ω+ ≈ ωc ωz ω−
(3.12)
2 = 1.817 · 104 V/m2 , 26 35 122 + 9 T eld) and its choice of isotopes ( Al , Ar, In; 1 charge state) [Delauré,
Typical frequencies for the WITCH Penning trap (U0 /d 2004] is shown in Table 3.1.
3.2 Processes in a Penning trap
Isotope
26
Al 35 Ar 122 In
ω+
[kHz]
25
ωc
ωz
[kHz]
[kHz]
ω−
[kHz]
33414
33415
260
1.01
24827
24828
224
1.01
7122
7123
120
1.01
Table 3.1: Example of the dierent
ω+, c, z, −
frequencies for the WITCH Penning
trap.
The Hamiltonian for the radial motion
Hρ
is the sum of the kinetic energy
and the repulsive electrostatic potential energy:
1 1 2 2 2 Hρ = m ρ˙ − ωz ρ 2 2
(3.13)
Using Eqs.(3.9)(3.10) and the relations (3.11) this radial Hamiltonian can be expressed as
Hρ =
1 ω+ V (+)2 − ω− V (−)2 m 2 ω+ − ω−
(3.14)
It is important to note in this respect that the magnetron motion has negative energy, i.e. it is unstable such that the magnetron radius increases when the magnetron motion loses energy. For example, simply removing energy from the magnetron motion by buer gas collisions will cause the particle to move down the magnetron energy hill to a larger radius until the ion is lost on the electrodes of the trap. This property of the magnetron motion needs particular attention in view of ion cooling in a Penning trap. The magnetron motion has another `speciality': unlike the other frequencies (see Eq.(3.4)) to rst approximation it does not depend on the mass of a particle:
ω− =
U0 2 Bd2
(3.15)
3.2.2 Motion in the presence of additional forces Some of the main features of Penning traps are the possibility to store ions in a very well localized space in vacuum and their mass selectivity. However, to achieve these one needs to adopt the ion motion in the proper way. The most common cases applicable for WITCH at present are brie y reviewed below. Details can be found in [Savard et al., 1991, Forstner, 2001, Kellerbauer, 2002]
Frictional damping Using buer gas in a Penning trap allows to decrease the ion kinetic energy by collisions with the atoms of the gas. The damping of the ion motion can be
CHAPTER 3 Trap technique
26
described to good approximation by a viscous damping force:
F D = −δ r˙ where
δ
is the damping coe cient which is given by
δ= Here
(3.16)
Kmob
q Kmob
p/pN T /TN
(3.17)
is the reduced ion mobility which is tabulated for dierent gases and
species (viz. [Ellis et al., 1976, 1978, 1984, Viehland and Mason, 1995]), while
p/pN
T /TN
and
are the gas pressure and temperature relative to normal pres-
sure/temperature, respectively. Taking into account this additional damping force, the equation of motion Eq.(3.3) will now look like:
x ˙ x x ¨ y˙ ωc 2 y¨ − −x˙ ωc + δ y˙ − ωz y = 0 m 2 z˙ −2z 0 z¨
(3.18)
Apparently, the axial motion is still decoupled from the radial one. However, it is now described by a damping harmonic oscillator.
It can be shown also
that the radial motion is still the superposition of two circular motions but the frequencies dier from the undamped case
0
ω = ω± ± ∆ω, On the other hand,
∆ω
1 ∆ω = 16
δ m
2
δ 2 8ωz + m (ωc2 − 2ωz2 )3/2
is quite small and can be neglected in many cases.
It is also important to note that the sum of the frequencies equal to
ωc .
(3.19)
ω+
and
ω−
is still
Another essential consequence is a time dependence of the radius
of the particle motion [Savard et al., 1991]
ρ± (t) = ρ± (0) exp(α± · t)
where
α± = ∓
ω± δ m ω+ − ω−
(3.20)
(3.21)
ω+ ω− the reduced cyclotron motion shrinks with a constant α+ ≈ −δ/m while the magnetron radius increases much slower because α− ≈ (δ/m) · (ω− /ω+ ). This means that the ion can still be lost because of the permanent Because
increase of the radius of its magnetron motion if it is kept in the trap long enough.
An example of the time scale of the change of the radius for the
−1
magnetron and reduced cyclotron motion (α± ) for the case of the WITCH set-up is given in Table 3.2.
3.2 Processes in a Penning trap
Kmob 2 /Vs
B=6 T
−1 α−
m
35
Ar K
39
27
−1 α+
B=9 T
−1 α−
−1 α+
0.00207
83 s
7.6 ms
187 s
7.6 ms
0.00215
86 s
8.8 ms
194 s
8.8 ms
Table 3.2: Time scale of the increase (decrease) of the magnetron (reduced cy2 clotron) radius due to frictional damping for the WITCH cooler trap (U0 /d = 4 2 −4 1.817 · 10 V/m ) and He buer gas at 10 mbar pressure.
Figure 3.3: Con guration of electrodes in order to generate an azimuthal electric
dipole (left diagram) or quadrupole (right diagram) RF eld in the center of a Penning trap in order to excite the radial ion motion.
Dipole excitation Applying an additional time-varying electric eld can in uence the motion of particles in a Penning trap.
The two most common possibilities are dipole
and quadrupole excitations. An appropriate electrode con guration is shown in Fig. 3.3. The ring electrode has to be segmented into four pieces to allow both schemes (cuts are made along the azimuthal axis). Fig. 3.3 (left) shows how to connect an RF source in the case of dipole excitation of the trapped ions. The dipole potential is given by:
Φd = a where
a
Ud cos (ωd t − φd ) · x , ρ0
(3.22)
is a geometrical parameter which takes into account the deviation of
the electrodes shape from the ideal dipole con guration and
Ud is the amplitude
of the dipole excitation. Eq.(3.3) for ion motion now contains an inhomogeneous part:
CHAPTER 3 Trap technique
28
x ¨ y˙ ωc x −k cos(ω t − φ ) 2 0 d d d y¨ − −x˙ ωc − ωz y = 0 2 z¨ 0 −2z 0
k0
where
= a
q Ud · m ρ0
(3.23)
(3.24)
One can clearly see that the axial motion is not changed by the dipole excitation. For the radial motion an important dierence appears: the radii of the excited motion are not constant anymore but time-varying functions. dipole excitation frequency is
ω±
tween the excitation and corresponding motion exactly cyclotron motion) or
π/2
If the
∆φ = φd − φ± beequals 3π/2 (reduced
and the relative phase
(magnetron motion), the radius can be expressed as
ρ± (t) = ρ± (0) +
k0 · td 2(ω+ − ω− )
(3.25)
This means that the increase of radius of the excited motion is proportional to the duration
td
of the dipole excitation and to the amplitude
Ud .
This
property of the dipole excitation allows to drive ions out of the trap center. If one does it for the magnetron motion, all ions (of all masses) can be brought to a larger radius at the same time since
ω−
is to rst order mass independent
(see Eq.(3.15)). If this excitation is done at the reduced cyclotron frequency
ω+ ,
mass selectivity can be obtained.
Quadrupole excitation To achieve an azimuthal quadrupole eld one needs to connect a periodic voltage to a four-split ring-electrode (Fig. 3.3, right ). The corresponding potential is described by
Φd = a where
a
Uq cos(ωq t − φq ) · (x2 − y 2 ) , ρ20
(3.26)
is a geometrical factor which again corrects for the non-ideal shape of
the electrode segments. The Eq.(3.3) now transforms to
n 2 o ωz − 2k0 cos(ωq t − φq ) x 2 x ¨ y˙ ωc n o y¨ − −x˙ ωc − ωz2 − 2k cos(ω t − φ ) y =0 0 q q 2 z¨ 0 −ωz2 z
(3.27)
3.2 Processes in a Penning trap
29
Figure 3.4: Conversion of an initially pure magnetron motion (shown by a circle)
into a pure reduced cyclotron motion (right) by a quadrupole excitation at On the left graph the rst half of a period is indicated (0 the right is a continuation of the left one until
where
t ≤ Tq
k0 = a
< t ≤ Tq /2).
ωq = ωc
.
The graph at
(from [Delauré, 2004]).
q Uq · m ρ20
(3.28)
Again, the axial motion is not aected, while the radii
ρ± (t)
of the radial
motion are again time-varying functions. If the RF frequency of the quadrupole excitation
ωq = ω+ + ω− = ωc and the phase shift between the excitation and (φq − φ+ − φ− ) = π , the expression for the radius looks like ω ω conv conv ρ± (t) = ρ± (0) cos t ± ρ∓ (0) sin t (3.29) 2 2
the radial motions
with
ωconv =
k0 2(ω+ − ω− )
(3.30)
This leads to an important property of the quadrupole excitation: the two radial motions now become coupled and at RF frequency
ωq = ωc they are conTq = π/ωconv .
tinuously converted one into another with the conversion period
The trajectory of an ion under such excitation is shown on Fig. 3.4. This type of resonant excitation is also called sideband excitation.
3.2.3 Ion cooling As was shown above Penning traps give quite some possibilities to manipulate ions. This feature becomes important if one talks about a precision experiment like WITCH. The recoil energy spectrum can be in uenced by dierent ion species that are present in the original beam, by the spatial size of the ion
CHAPTER 3 Trap technique
30
. Figure 3.5: Trajectory of a particle in a Penning trap in case of a damping force
only (left ) and when an additional azimuthal quadrupole excitation at the cyclotron frequency
ωc
is applied (right ) (from [Savard et al., 1991]).
cloud but also by the energy of the ions in the cloud.
The last one has to
be su ciently small since it can not be separated from the recoil energy after nuclear
β -decay.
One of the simple, relatively fast and widely used techniques
to `cool' ions in the sense of energy dissipation is based on ion collisions with buer gas atoms [Savard et al., 1991].
This method is applicable for a wide
range of isotopes and is used in the WITCH experiment as well.
However,
as was discussed on page 25, the disadvantage of this technique is that the magnetron motion is increased in radius and with time ions are thus lost on the electrodes of the trap. The evolution of the radial motion when only buergas cooling is used is shown in Fig. 3.5(left ). On the other hand, the radius of the reduced cyclotron motion decreases much faster than the increase of the magnetron radius (see on page 26). Now, as we know, the quadrupole excitation at frequency
ωc
causes continuous con-
version of the magnetron motion into the reduced cyclotron motion. So, using this excitation together with buer-gas leads to an overall cooling of ions in a sense of centering of the trajectories and dissipation of energy [Savard et al., 1991].
The corresponding ion motion is illustrated in Fig. 3.5 (right ).
One
should note here that the ions can be cooled only to the temperature of the buer gas. Typical pressures which are used for this buer gas are in the range
10−2 ÷ 10−5
mbar and the cooling time is in order of
10 ÷ 20
ms.
This technique has still another advantage. Since the cyclotron frequency depends on the mass of the particle (Eq.(3.3)), this fact makes it possible to remove impurities from the trap. However, rst the dipole excitation has to be applied. Because such excitation is mass-independent (see Eq.3.15) it will bring all ions on a larger magnetron radius. Next, the quadrupole excitation at the frequency
ωc
corresponding to the mass of interest has to be used, so
3.2 Processes in a Penning trap
31
that only the proper species will be re-centered.
3.2.4 Charge exchange As we have seen, the ion motion in a Penning trap is meta-stable but still ions can stay con ned for a long time.
However, they can be in uenced by the
interaction with rest gas particles. This can lead to a charge exchange, so that the ions become neutralized, which means they will be lost. This eect is more pronounced for elements with a large ionization potential, like noble gases, and much less for alkalis. As an example, for the REXTRAP set-up
20
∼100 ms when N e is used 10−3 ÷10−4 mbar [Delahaye, 2004]. after
35
Ar ion losses become signi cant
as buer-gas at a pressure of the order of Some tests in this respect which were made
with the WITCH Penning trap set-up are described in Section 6.3.
3.2.5 Many ions in a trap In fact, the formalism described in the previous subsections is only valid for a single particle in a Penning trap. If two or more ions are present, the Coulomb interaction between them has to be taken into account.
This will certainly
change the ion behavior in the trap. Two eects show up when the Coulomb interaction is considered:
•
the electric potential produced by the trap electrodes is in uenced by the electric eld of the ions (space-charge), and
•
the motion of the particles is aected but also the ion cloud is enlarged due to the Coulomb repulsion force.
The observable consequence of the Coulomb repulsion is a shift of the resonant frequency from the one derived for a single ion.
Experiments performed at
REXTRAP have shown deviations from single particle theory beginning with
4
10
ions [Forstner, 2001]. Since the WITCH experiment is going to deal with
∼ 106
ions this kind of phenomena needs to be taken into account.
How-
ever, the attempts to calculate this phenomenon meet some problems.
An
analytical solution exists only for two particles and without buer-gas or RF excitation [Baumann, 1993], while numerical computer simulations for the real
6
situation (viz. 10
ions and more) exceed usable computer time [Forstner, 2001].
Nevertheless, several experimental studies of space charge eects in a Penning trap were made (see [Ames et al., 2001, Paasche et al., 2002]).
A numerical
simulation to overcome the computer limit was made by D.Beck [Beck et al., 2001]. At ion densities larger than a certain limit (which is, however, probably not reached with the WITCH set-up [Delauré, 2004]) the ion cloud can be described as a non-neutral plasma [Dubin and O'Neil, 1999]. In this regime one
CHAPTER 3 Trap technique
32
can treat the ion cloud as a collective phenomenon rather than looking on the scale of single particles. An application of this description for the WITCH case is discussed in [Delauré, 2004]. The importance for WITCH is stimulated by the following reasons:
•
Since for REXTRAP it was shown that the e ciency of buer-gas cooling
6
decreases signi cantly for more than 10
ions [Ames et al., 2001], corre-
sponding studies have to be made also for the WITCH set-up.
•
The response function of the WITCH spectrometer depends on the position of the recoil ion, i.e. because Coulomb repulsion enlarges the ion cloud in the trap it will induce systematic uncertainties for the experiment.
•
It might be that the Coulomb repulsion also changes the ion energy distribution in the trap which can again lead to an additional uncertainty in the measurements [Delauré, 2004].
The response function of the WITCH spectrometer will be discussed in detail in Section 5.2.
Chapter 4 WITCH set-up Since the WITCH experiment aims to search for a Scalar admixture in weak interactions and the possible eect of this is expected to be small, many aspects have to be taken into account in order to render the experiment as precise as possible. In this chapter rst the physics principle of the experiment and a short overview of the set-up are described. Thereafter, and then the experimental conditions and the technical specialities of the set-up are reviewed in more detail.
4.1 Overview of the experiment 4.1.1 Principle of the experiment Using Eq.(1.14) one can write the following expression for the correlation in nuclear
β -decay
W (θβν ) ≈ 1 + a · where
θβν
β−ν
angular
for unpolarized nuclei:
is the angle between the
β
h vβ m i cos θβν 1 − b c E
(4.1)
particle and the neutrino, E,
vβ /c
and m
are the total energy, the velocity relative to the speed of light and the rest mass of the
β
particle, b is the Fierz interference term (Eqs.(1.17 and 1.15)) which
has experimentally been shown to be small (e.g.
|bF | < 0.0044
at C.L.=90%
[Hardy and Towner, 2005]) and can as a rst approximation be assumed to be zero, and a is the
β−ν
angular correlation coe cient, which can be deduced
from Eqs.(1.15 and 1.16). Since the Scalar (S ) and Vector (V ) interactions lead to Fermi transitions (F) and the Axial-Vector (A) and Tensor (T ) interactions to Gamow-Teller transitions (GT) (see Sec. 1.2.1 and [Wu and Moszkowski, 1966]), the
β−ν
angular correlation coe cient a can be approximated as 33
CHAPTER 4 WITCH set-up
34
Figure 4.1:
Dierential recoil energy spectrum for
a = 1
and
a = −1
(from
[Kozlov et al., 2004]).
2
2
' 1−
aF
'
aGT
In the Standard Model, i.e.
aF = 1
and
aGT = −1/3.
|CS | + |CS0 | 2
|CV |
,
" # 2 2 1 |CT | + |CT0 | − 1− 2 3 |CA |
(4.2)
in the absence of S - and T -type interactions,
Any admixture of S to V (T to A) interaction in
such a pure Fermi (Gamow-Teller) decay would result in
a < 1 (a > −1/3).
A
measurement of a therefore yields information about the interactions involved. However, the neutrino cannot be detected directly and the
β−ν
angular cor-
relation thus has to be inferred from other observables. From properties of the general Hamiltonian of the weak interaction [Wu and Moszkowski, 1966] and of the Dirac
γ -matrices
it can be shown that a V interaction only takes place
between a particle and antiparticle with opposite helicities and an S interaction only between a particle and antiparticle with the same helicities. Therefore in super-allowed
0+ → 0+
Fermi decay, where the
β-
and neutrino spins have
to be coupled to zero, the particle and antiparticle will be emitted preferably into the same direction for a V interaction and into opposite directions for an S interaction. This will lead to a relatively large energy of the recoil ion for a V interaction and a relatively small recoil energy for an S interaction (Fig. 4.1). The WITCH experiment aims to measure the shape of the recoil energy spectrum with high precision to determine the
β −ν
angular correlation
4.1 Overview of the experiment
35
parameter a and from this deduce a limit on a possible scalar admixture in weak interactions. An experiment to measure the recoil energy spectrum has two di culties: 1. the
β -emitter
is usually embedded in matter, which causes a distortion
of the recoil ion spectrum due to ion scattering in the source which leads to energy losses, and 2. the recoil ions have very low kinetic energy making a precise energy measurement di cult. In order to avoid the rst problem and to be as independent as possible from the properties of the isotopes to be used, the WITCH experiment uses a double Penning trap structure to store radioactive ions (see Sec. 4.6). The ion cloud in the second trap, the decay trap, constitutes the source for the experiment, where the ions are kept for several half-lives, i.e., of the order of 1 to 10 s for the cases of interest [Beck et al., 2003a]. To solve the second problem and measure the recoil energy spectrum a retardation spectrometer is used. The working principle of such a device is similar to the
β -spectrometers
used for the determination of the neutrino rest-mass in
Mainz [Picard et al., 1992] and Troitsk [Lobashev and Spivak, 1985]. The spec-
Bmax = 9 T, Bmin = 0.1 T, and an electrostatic retardation system
trometer consists of two magnets: the rst one providing a eld the second one providing
(see Sec. 4.7). Recoil ions are created in the strong magnetic eld region (i.e. in the Penning trap) and pass on their way to the detector the region with low magnetic eld (i.e. the retardation section of the spectrometer). Provided that the elds change su ciently slow along the path of the ions, their motion can be considered as adiabatic. According to the principle of adiabatic invariance of the magnetic ux [Jackson, 1975]:
p2⊥ = const B where
p⊥ is
(4.3)
the momentum projection perpendicular to the magnetic eld
B.
From Eq.(4.3) it follows that the radial kinetic energies of the ion in the trap
trap
retard
(Ekin, ⊥ ) and in the retardation section (Ekin, ⊥ ) are related as:
retard Ekin, ⊥ trap Ekin, ⊥ Thus a fraction
=
Bmin 0.1T = Bmax 9T
1 − Bmin /Bmax ≈ 98.9%
(4.4)
of the energy of the ion motion per-
pendicular to the magnetic eld lines will then be converted into energy of the ion motion along the magnetic eld lines. The total kinetic energy of the recoil ions can be probed in the homogeneous region of low magnetic eld retarding them with a well-de ned electrostatic potential.
Bmin
by
By counting how
36
CHAPTER 4 WITCH set-up
Figure 4.2: Schematic overview of the WITCH set-up (from [Delauré, 2004]).
4.1 Overview of the experiment
Figure 4.3:
37
The WITCH set-up as presently installed in the ISOLDE hall, at
CERN. At the right side one can see the high voltage cage of the REX-EBIS (top) and REXTRAP (ground oor) set-ups.
CHAPTER 4 WITCH set-up
38
many ions pass the analysis plane for dierent retardation voltages, the cumulative recoil energy spectrum can be measured [Kozlov et al., 2004, Beck et al., 2003a].
4.1.2 Overview of the WITCH set-up The general scheme of the set-up can be seen in Fig. 4.2 (a more technical layout is shown in Fig. 4.15). Fig. 4.3 shows the set-up as installed in the ISOLDE hall. In a rst step the ions produced by the ISOLDE facility (Sec. 4.3) get trapped and cooled by REXTRAP (Sec. 4.4). As soon as a su cient amount
6
of ions (10
to
107
ions) has been collected by REXTRAP they are ejected as a
60 keV (optionally 30 keV) bunch and are transmitted through the horizontal beamline (Sec. 4.5.1) of WITCH and a into the vertical beamline (Sec. 4.5.2). decelerated from 60 keV to
∼50
90◦ -bender
with spherical electrodes,
There the ions are electrostatically
eV in several steps before they enter the cooler
trap, the rst Penning trap of the WITCH set-up (Sec. 4.6).
In this cooler
trap the ion cloud is prepared for ejection through the dierential pumping barrier into the second Penning trap, the decay trap. The latter is placed at the entrance of the retardation spectrometer (Sec. 4.7). After
β -decay the recoil
ions emitted into the direction of the spectrometer spiral from the trap placed in the strong magnetic eld into the weak eld region.
In the homogeneous
low- eld region the kinetic energy of the ions is then probed by the retardation potential. The ions that pass this analysis region are re-accelerated to
∼10
keV
to get o the magnetic eld lines. The re-acceleration also ensures a constant detection e ciency for all recoil energies. Finally, the ions are focused with an Einzellens onto an MCP detector (see Sec. 4.10). For normalization purposes several
β -detectors
are also installed in the spectrometer section (Sec. 4.9).
4.2 Choice of isotopes The following criteria are applied to choose the right isotopes for
β−decay
experiments with WITCH:
Fermi decay: A Scalar admixture can be present only in Fermi transitions. The best candidates are pure Fermi decays since in this case the
β−ν
correlation coe cient is independent of nuclear matrix elements. Apart from pure Fermi transitions, mirror transitions with a major contribution from the Fermi type can also be interesting. However, in this case the
ft -value has to be known to determine the ratio of the Fermi and GamowTeller matrix elements.
Half-life: In order to have a reasonable time available for the measurement, decays with a half-life of the order of seconds or less are needed.
4.2 Choice of isotopes
39
Long lived daughter: To exclude a distortion of the recoil spectrum by the decay of a radioactive daughter nucleus and to avoid the background created by such a nucleus, the lifetime of the daughter nucleus has to be su ciently long or preferably these nuclei are stable.
Characteristics of other branches: To have a clean recoil spectrum other decay branches have to be avoided. However, as it will be discussed later (Sec. 5.3), only the upper half of the spectrum will be analysed, therefore other branches, if present, should have an endpoint energy that is at least twice lower than that of the main branch.
Production yield: As shown in Sec. 5.3, the WITCH experiment needs high statistics.
This means that the
β -emitters
with higher production rate
are preferable. From superallowed
0+ → 0+
decays the requirement on the lifetime of the
daughter nucleus leads to the candidates listed in the upper part of Table 4.1. In this table the main characteristics of the candidates are shown, including
1 [ISOLDE, 2005]. If there are
their production yield at the ISOLDE facility additional
β -decay branches, the one with the highest energy is used to estimate
the part of the recoil spectrum to be tted. The maximum energy of the recoil ion is calculated using the expression:
(max)
Erecoil (β ± ) =
∆E(∆E ∓ 2me ) 2(Mat (A, Z ∓ 1) ± me )
(4.5)
β + (β − )-decay, ∆E is the energy dierence between the initial and nal nuclear state, me is the electron mass, Mat (A, Z ∓ 1) is the atomic mass, i.e. Mat (A, Z ∓ 1) = A · u + mexcess , where u = 931494043 eV [Eidelman et al., 2004] is the uni ed atomic mass unit, A is the number of nucleons, mexcess is the mass excess (tabulated, for instance in where the upper(lower) sign corresponds to
[Audi et al., 1997]). For the energy of the recoil ion from electron capture one has:
EC Erecoil =
(∆E)2 2 Mat (A, Z − 1)
(4.6)
As can be seen from Table 4.1, the candidate isotope with the highest yield at ISOLDE is
38m
K.
However, the ground state of
one of the branches is very close in energy to the
38
K is also a β -emitter and β -decay of 38m K . However,
because of its very small probability and long half-life while the measurement cycle of WITCH is rather short, the ratio of decays from ground over isomeric state is of the order of
1
5 · 10−5 ,
for an equal initial population, at the end of
measured yields are normalized to a proton beam of 1 µA, while an average intensity for ISOLDE is about 2 µA and may a few days per year be even up to 4 µA [ISOLDE, 2005]
CHAPTER 4 WITCH set-up 40
moth.
Al
Cl
nucl. 26
34
K
Sc
38
42
46 V Mn
50
54 Co
Cl
Ar
33
35
122 In
Table 4.1:
state
T1/2
gs
1920 s
1.525 s
7.4 · 105 y
6.3452 s
gs
iso
iso
458 s
0.6813 s
0.923 s
gs 61.7 s
gs
iso 0.283 s
0.42237 s
iso
gs
105 s
gs iso
daugh.
Mg
nucl. 26
S
Ca
Ar
34
38
42
46 Ti Cr
50
PEC
EC Erecoil
yield
(max)
∆E
Erecoil
BR
T1/2
53.2
state
4.232
[MeV]
387.9
3.95 · 104
%
2.195
138.1
4.6983
185.6
7.6 · 105 2.9 · 105
1.5 · 103
1.26 · 103 2.24 · 105 3.4 · 107 1.4 · 109
[atoms/s]
100
5.492
429.1
[eV]
97.3
3.511
144.2
370.0
100
6.0435
%
stable
28.5
3.7456
408.9
0.083
gs 476 fs
100
444.2
580.8
[eV]
exc
325 fs
stable
99.8
6.426
5.9131
626.2
280.6
gs
1.8 · 1017
gs
1.25 ps
592.3
gs exc
8.24309
35
Cl 122 Sn
β−ν
correlation measurements with WITCH. Lifetimes, atomic masses, decay energies PEC from [Hardy et al., 1990] (except for 33 Cl and 35 Ar which
676.2
100
0.104
stable
1.41 · 102
gs
507.4
4.1 · 107
54 Fe
0.074
546.3
2.5 · 108
0.193 s
0.072
gs
287.2
244.4
452.7
414.5 4.742
271.3
1.6 · 107
5.583
5.9653
207.3
5.49289
0.48
4.7459
143.9
100
98.1
6.370
98.6
1.23
5.2295
stable
stable
1.17 ps
69
97.7
1.215 ns
150 fs
16
86.0
gs
gs
exc
stable
4.2279
exc
exc
0.76 ps
3.9369
S
gs
3.9
11.6
33
exc
??
1.56 ps
88.8 s
exc
2.511 s
1.5 s
exc
gs
10.3 s
iso
gs
10.8 s
1.775 s
iso
gs
iso
Candidate isotopes for
and branching ratio's (BR) are taken from [Firestone, 1996],
are from [Naviliat-Cuncic et al., 1991]) and yield information from [ISOLDE, 2005].
4.3 ISOLDE separator
the cycle (viz.
∼ 2
41
s) [Delauré, 2004].
However, Table 4.1 shows that this
population is not equal and the ISOLDE yield of
38
larger by two orders of magnitude than the yield of
38m
K in its ground state is K . On the other hand,
this ratio depends on the target and can be smaller. It should thus be possible to develop a target that produces enough does not aect the measurement on
38m
38m
K
ions while the presence of
38
K
K.
Apart from pure Fermi decays, the mirror transitions in isospin
T = 1/2
odd-even nuclei can also be interesting since for these decays the eect of nuclear structure is minimized [Delauré, 2004]. However, the sensitivity of the angular correlation parameter a on the coupling constants
CS , CS0
β−ν
in this case
depends on the Fermi to Gamow-Teller mixing ratio y : the sensitivity being higher if the mixing ratio is larger. This limits the candidates to two transitions:
33
Cl →33 S
and
35
Ar →35 Cl [Delauré, 2004], which are also listed in Table 4.1.
For these two decays the uncertainty on the parameter a due to the mixed character of the decays can be determined from the experimental log ft value [Naviliat-Cuncic et al., 1991] and turns out to be in the order of 0.3% [Delauré, 2004]. The disadvantage of
β+
decays is that the probability of the shake-o eect,
on which one has to rely (see Sec. 5.3) to be able to measure the recoil spectrum, is only in the order of 10%, such that the measurement statistics is reduced by one order of magnitude. Especially in the commissioning phase when the set-up is not yet fully optimized, one needs as high statistics as possible to understand the behaviour of the set-up and to test it.
For this reason the spectrometer
tests to see the rst recoil ion spectrum will be performed with the
122
In
(Table 4.1).
β−
emitter
Another advantage of this isotope is that the production
β + candidate. The measurement plan of WITCH is thus to rst use In, mainly to test 35 and optimize the set-up and then to investigate either Ar or 38m K for a scalar + interaction study, since these isotopes are among the β emitters of interest the yield is by one order of magnitude higher than for any other
122
ones that are most abundantly produced at ISOLDE . The best suited isotopes would be while
46
V
26m
Al
and
46
V
but the yield at ISOLDE for the rst is still to low,
is currently not yet available at all.
4.3 ISOLDE separator In order to reach the required high precision WITCH needs high intensity radioactive beams.
The world leading facility regarding the production of
most radioactive nuclei is the on-line isotope separator facility ISOLDE at CERN [Kugler et al., 1992, Kugler, 2000, ISOLDE, 2005]. The target group of ISOLDE is permanently working to improve and extend the ISOLDE targets, in order to increase the beam intensities and enlarge the variety of available isotopes. That is why ISOLDE was chosen for the installation of the WITCH
CHAPTER 4 WITCH set-up 42
Figure 4.4: Schematic overview of the ISOLDE hall. The two separators (GPS and HRS) are shown. The WITCH experiment
and REXTRAP set-up are also indicated.
4.4 REXTRAP
43
set-up. ISOLDE produces a large variety of radioactive nuclei (more than 60 elements have been produced over the last 30 years). the facility is shown in Fig. 4.4 .
The schematic layout of
CERN's Proton Synchrotron Booster (PS
Booster) delivers a pulsed proton beam with an energy of 1 to 1.4 GeV that is sent onto the ISOLDE target. Radioactive isotopes are produced by spallation, fragmentation or ssion reactions in the target material. The reaction products diuse out of the target into the ion source. Depending on the desired species they are singly charge ionized either by surface ionization, electron impact in a hot plasma or by resonant laser ionization. Then the ions are extracted from the ion source and accelerated to 60 keV (optionally 30 keV). There are two mass separator magnets which are used for a mass selection of the beam. The general-purpose separator (GPS ) has a mass resolving power of about 2400 and can provide radioactive ions to three dierent beamlines simultaneously (one mass to one beamline).
The high resolution separator (HRS ) has bet-
ter resolving power of about 6000 which can be reached in high resolution mode [Kugler, 2000]. After mass separation the DC beam is delivered to the users via an extensive electrostatic beamline system. The WITCH experiment takes the ISOLDE beam behind the REXTRAP set-up, which is discussed in the following section.
4.4 REXTRAP REXTRAP [Ames et al., 2005] is a 1 m large cylindrical gas- lled Penning trap which serves as the rst stage of the ion preparation for the REX-ISOLDE postaccelerator [Habs et al., 2000].
Similar to REX-ISOLDE, REXTRAP is also
used by WITCH as a beam cooler and buncher of the incoming continuous ISOLDE ion beam. The beam ejected from the REXTRAP has a better emittance than the original ISOLDE beam: mm · mrad (at 30 keV, for less than
105
it was measured to be about
10 π ·
ions and sideband cooling [Ames et al.,
2005]), while the typical ISOLDE beam emittance is
35 π· mm · mrad (at 60 keV)
[Schmidt, 2001]. To be able to capture the 60 keV ion beam of ISOLDE, the complete REXTRAP set-up is located on a high voltage (HV) platform at 60 kV. The magnetic eld for the Penning trap operation is provided by a superconducting magnet of 3 T maximum eld. Since REXTRAP was designed to handle large amounts
5
of ions (10
÷ 107 )
it has relatively large dimensions (Fig. 4.5).
The central
part of REXTRAP is split into two parts. The stopping part has a high buer gas pressure of about
10−3
mbar of Ne or Ar to make sure that the ions loose
su cient energy in order to be captured in the potential minimum of the trapping part (Fig. 4.5).
When the ions are in this potential minimum they are
exposed to the RF -sideband cooling for typically 20 ms in a buer gas pressure
CHAPTER 4 WITCH set-up
44
Figure 4.5: REXTRAP set-up: the trap electrode structure, buer gas distribution
and potential along the trap axis are shown (from [Schmidt, 2001]).
of about
10−4
mbar [Ames et al., 2005]. After the end of the cooling, the ions
are accelerated towards the trap exit. The typical repetition rate of REXTRAP for REX-ISOLDE purposes is 50 Hz while the WITCH experiment requires at present only 1 Hz repetition.
4.5 Beamline The purpose of the WITCH beamline is to guide and prepare the ion bunch coming from REXTRAP for injection into the WITCH Penning traps.
The
beamline is divided in two sections: the Horizontal beamline (HBL) and the Vertical beamline (VBL). Both sections serve dierent purposes.
4.5.1 Horizontal beamline After the ISOLDE ion beam is cooled and released in bunched mode from the REXTRAP, it is injected into the HBL part of the WITCH set-up. The function of the HBL is to transfer the ion beam from the REXTRAP set-up into the WITCH vertical beamline (Sec. 4.5.2) as e cient as possible. The general
4.5 Beamline
45
Figure 4.6: Schematic view of the horizontal beamline of the WITCH set-up
overview of this is given in Fig. 4.6.
The HBL primarily contains dierent
electrodes to guide the ion bunch into the VBL. Only static voltages are used for this. The essential components of the HBL are two systems of kicker-bender electrodes and an einzellens. The two electrostatic benders each consist out of two spherical electrodes.
The spherical shape ensures that the beam is also
focused in the direction perpendicular to the de ection plane [Delauré, 2004]. The construction of these kicker-bender combinations is based on the design made for the REX-ISOLDE beamline. Between the kicker-bender systems the einzellens is installed in order to better focus the beam. In order to be able to also correct the beam direction, steerer plates are used in the HBL (Fig. 4.6). Three beam diagnostic systems are foreseen to monitor the beam while tuning it (see Sec. 4.12). The horizontal beamline is one single vacuum section.
4.5.2 Vertical beamline An overview of the VBL is shown in Fig. 4.7. It contains primarily cylindrical electrodes (inner diameter 59.5 mm) and steerer plates. The VBL can be divided in two sections by its function. In the rst section a special long electrode, named Pulsed Drift Tube (PDT ), is installed (see below). This electrode serves to shift the potential energy of the ions down over the range corresponding to the original beam energy (i.e. 30 kV or 60 kV for typical ISOLDE operation). The second part of the VBL contains a set of electrodes to create a drift section in order to inject the ion bunch into the magnetic eld. Instead of having
46
CHAPTER 4 WITCH set-up
Figure 4.7: Vertical beamline of the WITCH set-up (from [Delauré, 2004]).
4.5 Beamline
47
Figure 4.8:
The principle of PDT.
one long electrode the drift region is split into dierent shorter components to provide exibility during beam tuning [Delauré, 2004]. The two dierent sections of the VBL are also separated vacuum sections: the rst part, containing the PDT, can be separated by a valve from the second one, the drift section, which is part of the spectrometer vacuum (see Sec. 4.13). The PDT vacuum chamber, together with part of the drift section, can be taken out in order to free space for loading/unloading the traps.
Pulsed drift tube section The ISOLDE beam has 60 keV or 30 keV kinetic energy. Ions at such energy can not be injected into the Penning traps, meaning the beam has to be retarded before injection. One possibility is to put the trap structure on a high voltage platform. However, this means that also the magnet, the corresponding electronics etc. have to be on the same platform. This is too di cult to realize in the case of the WITCH experiment because of the vertical orientation of this part of the set-up. Another solution is to use a pulsed cavity as described in [Herfurth et al., 2001]. The principle of such a cavity
2 as used at WITCH is
illustrated in Fig. 4.8. When the ion pulse is inside the PDT the potential of the cavity is switched down over the range of 60 kV (30 kV) from 52 kV (26 kV) down to -8 kV (-4 kV). In this way the kinetic energy of the ions is not changed while the potential energy is shifted to -8 kV (-4 kV), so that the total energy becomes zero (Fig. 4.8). This means that the ions can now be captured in the Penning traps at ground potential. In reality one has to take into account the
2
named Pulsed
Drift Tube in the case of WITCH, or in short PDT
CHAPTER 4 WITCH set-up
48
Figure 4.9:
Geometry of the Penning traps.
The cooler trap (left ) is separated
from the decay trap (right ) by a dierential pumping barrier.
The total length of
the two traps is 42.8 cm. EE denotes the End-cap Electrodes, CE the Correction Electrodes and RE the central Ring Electrode of the traps. Also the buer gas inlet is shown.
energy spread and the ripple of the power supplies. All these cause the ions to have an energy slightly higher than the ground level. To trap the ions in the WITCH cooler trap a voltage in the order of 100 V therefore has to be applied to the end-cap electrodes (Sec. 4.6). The corresponding electronics to perform the operation of the PDT is described is Sec. 4.15.1.
4.6 WITCH traps When the ion beam is decelerated in the VBL and injected in the region of the high magnetic eld, it is ready to be captured in the WITCH Penning traps. The purpose of the traps is to capture, cool, center and store the ions. To separate these functions in the WITCH set-up two Penning traps are used, a cooler trap and a decay trap (Fig. 4.9). First, the ions get trapped in the cooler trap, where they are buer gas cooled to room temperature and then centered. For this purpose helium gas is injected into the trap as a buer gas (see Sec. 3.2.3). After this the ions are ejected through a dierential pumping barrier into the decay trap where they are kept for a couple of half-lives, i.e. of the order of 1 s to 10 s for the nuclides of interest. The pumping barrier serves to limit the ow of buer gas (He ) into the decay trap, since the ion cloud in the decay trap constitutes the source for the experiment and ultra-high vacuum is required in the spectrometer behind the traps so as to exclude scattering of the recoil ions on rest gas or buer gas atoms. The WITCH traps are of the cylindrical type since this allows to inject more ions and have better pumping due to the more open structure, compared
4.7 Retardation spectrometer
49
to the hyperbolic Penning traps that are used for high-accuracy mass measurements. The design of both WITCH traps is similar to the ISOLTRAP cooler trap [Bollen et al., 1996, Raimbault-Hartmann et al., 1997]. The central ring electrode is divided into eight sections along the axis to allow to apply dierent
RF excitation schemes (Sec. 3.2.2). The decay trap has a shortened end-cap electrode but is otherwise similar to the cooler trap. More details can be found in [Delauré, 2004].
4.7 Retardation spectrometer As can be seen from Fig. 4.1 and Table 4.1 the recoil ions have very small energy, in the order of a few hundreds of eV. This energy is su cient to leave the trap but is di cult to measure. To analyze the recoil energy of ions produced in
β-
decay the WITCH experiment uses a retardation spectrometer (Fig. 4.10). The principle is based on applying a retardation potential, so that only ions with energy above the retardation potential can reach the detector. This detector is an MCP detector, which is just a counter with no energy sensitivity. When a certain retardation voltage is set, the corresponding number of ions is counted on the detector.
If now the voltage is changed, a dierent number of ions
reaches the detector. One can thus scan the whole recoil energy spectrum (in fact, the integral recoil energy spectrum is measured). However, the retardation potential probes only the component of the ion energy parallel to the axis of the electrical eld, while ions escaping from the trap also have a radial component of motion.
Conversion of the radial component of kinetic energy
into the longitudinal one is thus needed. The principle to do this is based on the adiabatic invariance of the magnetic ux, also known as inverse magnetic mirror. In this case the energy conversion is de ned by the ratio of the magnetic elds [Jackson, 1975]. This is why the double Penning trap structure is placed in a strong magnetic eld of 9 T while the analyzing region is in a weak magnetic eld of 0.1 T. Thus a fraction
1 − Bmin /Bmax ≈ 98.9% of the ion radial energy
is converted into axial energy while the ions spiral from the high eld to the low eld region. The requirement of adiabaticity means that over one cyclotron turn the change of the magnetic eld is small [Delauré, 2004]. The scheme of the designed retardation spectrometer is shown in Fig. 4.10. During the design several considerations were taken into account. First of all, the retarding electric eld is parallel to the magnetic eld in the volume occupied by the recoil ions. Next, to assure that the energy conversion is adiabatic it is preferable that the electrostatic retardation of the ions is performed as soon as possible after they leave the high magnetic eld region [Delauré, 2004] (Fig. 4.11). On the other hand it should not be too fast, as the ions can otherwise be re ected already in the intermediate zone because of incomplete energy conversion. The retardation potential therefore reaches its maximum in the re-
50
CHAPTER 4 WITCH set-up
Figure 4.10: Scheme of the retardation spectrometer.
4.8 WITCH magnet system
51
Figure 4.11: Magnetic eld pro le (solid line) and retardation electric eld (dashed
line) on the axis of the spectrometer (z-axis). The electric eld has been calculated for
Uret = 100
V. z=0 corresponds to the center of the 9 T magnet. The positions of
the traps and the detector are also indicated.
gion where the ions experience the full energy conversion (so called analysis
plane ). The ions that pass this analysis plane are re-accelerated to
∼10
keV
to get o the magnetic eld lines and are then focused with an Einzellens onto the MCP detector. This has two advantages: 1) it ensures a constant detection e ciency for all recoil energies; 2) the majority of the
β -particles
will miss the
ion detector since they are not focused by the einzellens but instead continue spiraling along the magnetic eld lines, so that most of them end up by hitting the wall. The disadvantage of this approach is that the ion beam gets large in radial dimensions, meaning a large detector is required [Delauré, 2004]. The response function of the spectrometer and how this is aected by different eects is discussed in Sec. 5.2.
4.8 WITCH magnet system As was mentioned before, the WITCH experiment needs two magnets for its operation. The magnet system built by Oxford Instruments
TM
contains both
superconducting magnets of 9 T and 0.2 T in one single cryostat. The double Penning trap structure is placed in the lower bore tube (internal diameter 13 cm) of the strong 9 T magnet while the spectrometer is in the top bore tube (internal diameter about 21 cm) of the weak 0.2 T magnet.
The eld along
the axis produced by the two magnets together (the 0.2 T magnet was scaled to 0.1 T) is shown in Fig. 4.11. The position of both trap centers, the analysis
CHAPTER 4 WITCH set-up
52
plane and the MCP detector are also indicated. The homogeneity of the 9 T magnet in the region of both trap centers is about a
5·10−5 , the homogeneity of
the 0.2 T magnet when the applied current is set to produce the 0.1 T plateau is about
10−3
at the plateau position [Superconductivity, 2002].
The cryostat system needs re lling of the liquid nitrogen once every 3 days and of the liquid helium once every 7 days. These periods are long enough to be convenient for the measurements (even re lling of the liquid nitrogen should not disturb the experiment). The system is equipped with magnet power supplies that allow to power up and down the system at any time and set any possible combination of the magnetic eld (0
< Bstrong ≤ 9
T and
0 < Bweak ≤ 0.2
T).
4.9 Normalization If only one retardation step is applied during one trap lling it is necessary to know how many ions are stored in the trap at every lling in order to measure the shape of the recoil spectrum precisely. This means that a precise normalization is required. This is e.g. possible by counting the are emitted after the nuclear
β -decay.
β -particles that
About half of the beta particles will
go in the direction of the spectrometer but they will not be disturbed by the electrostatic barriers of the spectrometer because of their much higher energies of O (MeV). In the spectrometer itself the trajectories as the ions.
β -particles
follow almost the same
It is therefore impossible to install the
β -detector
there, as it would then also block the ions and thus disturb the recoil ion measurement. However, higher up in the spectrometer, where the recoil ions get o the magnetic eld lines and are re-accelerated onto the MCP detector, while the betas continue along the eld lines, the trajectories of both particles are separated.
At present several p-i-n diode detectors are installed in the
electrode SPDRIF01 (Fig. 4.10 and Fig. 4.15). The simulations to determine the best place for these
β -detectors
and to calculate the trajectories of the
β-
particles will be discussed in Sec. 5.7. The present position of the detectors is meant for test purposes to check the simulations. An alternative possibility to measure the recoil spectrum is to scan all necessary retardation potentials during one single trap lling. normalization is required.
In this case no
However, a correction for the time-dependence of
the count rate due to the life-time of the trapped isotope has to be performed in this case. The corresponding electronics that was developed for this type of measurement is described in Sec. 4.15.1. In the current WITCH set-up both methods can be used.
4.10 Ion-detection
53
Figure 4.12: MCP working principle (from [DelMar, 2005]).
4.10 Ion-detection The detector to count the number of ions that passed the retardation barrier of the spectrometer is a microchannel plate detector (MCP). The working principle of an MCP is based on electron multiplication (Fig. 4.12). An MCP consists of a specially fabricated plate which has several million independent channels each of which acts as an independent electron multiplier. An incident particle (ion, electron, photon etc.) enters a channel, hits the wall and emits an electron. These secondary electrons are accelerated by the electric eld that is created by a voltage applied across both ends of the MCP. In principle, the e ciency of such a detector depends on the initial ion energy and incidence angle, but this can be overcome if the particles are accelerated to more than a few keV energy. This, together with the fact that the ions can be focused more easily when they are accelerated, are the two reasons why the ions are accelerated up to 10 keV after the retardation section. A more detailed description of the working principle of an MCP detector can be found, for instance in [Wiza, 1979, Gao et al., 1984, Brehm et al., 1995]. The original detection part of the set-up was designed for a Hamamatsu MCP detector with active area of 2 cm diameter and an e ciency of 30% (test detector) but it was also foreseen to use a larger detector. The test detector has a single anode and thus cannot give any spatial information about the ion envelope.
However, since the diameter of the ion beam at the detector
position is expected to be about
∼4
cm it is much more interesting to use a
larger detector and possibly also with position sensitivity (the latter is useful to study the properties of the set-up as well as a number of systematic eects). A group from LPC-Caen together with the company Roentdek [Roentdek, 2005] developed and tested two MCP position sensitive systems with active diameter of 47 mm (DLD40) and 83 mm (DLD80) (Fig. 4.13) [Roentdek, 2005,
54
Figure 4.13:
CHAPTER 4 WITCH set-up
Scheme of the assembly for MCP tests performed at LPC-CAEN
(top ) and photo of the LPC position sensitive MCP (bottom ) (from [Naviliat-Cuncic, 2005]).
4.11 Experimental cycle
55
Figure 4.14: Operation cycle of the WITCH experiment. The time axis is not to
scale.
Liénard et al., 2005].
The position encoding is done with the use of a delay
line anode, which is made from conducting wires rolled up in X and Y directions. The position in one direction is deduced from the propagation time dierence of the signals to reach two opposite ends of the corresponding wires [Liénard et al., 2005]. The detection e ciency was found to be 52.3(3)% and the position resolution of this detector has been estimated to be 110(26) µm. Acceleration of the ions in a potential of about 4000 V ensures a maximal e ciency, whatever the incident ion energy, and avoids a loss of e ciency due the ion incident angle [Liénard et al., 2005]. In the present WITCH set-up the detector of 47 mm diameter can be easily implemented while the larger detector requires a more serious modi cation of the detection part (see Sec. 7.1).
CHAPTER 4 WITCH set-up
56
4.11 Experimental cycle The experimental cycle of WITCH in principle depends on the isotope and its half-life. However, it cannot be smaller than
tmin = tprep ,
the ion preparation
time (Fig. 4.14), which is mainly de ned by the cooling time needed in the REXTRAP and in the WITCH cooler trap. In addition it is also limited by the used electronics. For instance, at present the HV switch system to pulse down the PDT cannot operate at a rate higher than 1 Hz (see Sec. 4.15.1). The WITCH experimental cycle begins when the REXTRAP starts to accumulate the almost continuous ISOLDE beam during
taccum (Fig.
4.14). At
the same time the cooling process in REXTRAP by means of buer gas collisions starts.
Then the RF sideband cooling is applied (Sec. 3.2.3).
Next,
the ions are ejected from the REXTRAP and injected into the WITCH beamline. There they are pulsed down in the PDT during
tP DT
and injected into
the cooler trap, where similarly to the REXTRAP the ion bunch is cooled via buer gas collisions and sideband cooling. Thereafter the ions are transfered to the decay trap. At this moment the preparation time tprep ends and the real measurement period tmeas starts. During this period the recoil ions which pass the retardation barrier are counted with the MCP detector. After the end of the measurement the decay trap is emptied in order to be reloaded again with the next ion bunch (Fig. 4.14). One should note that the preparation cycle can take place during the time of measurement
tmeas ,
i.e. that just after the end of the measurement period
a new ion bunch is already prepared and ready to be injected into the decay trap.
4.12 Diagnostic system To monitor the beam and study the properties of the WITCH set-up (for instance, its e ciency) diagnostic detectors are located at several places (Fig. 4.15), approximately in focal planes according to the beam transport simulations. In the VBL and HBL the diagnostic systems include both a Faraday Cup (for beam intensities of O (pA)) and an MCP (for a beam intensity lower than pA). However, at present the MCP detectors (DelMar
TM
MCP-MA25, diameter of
the sensitive area 18 mm [DelMar, 2005]) are only installed in the VBL. In the spectrometer part there is only one diagnostic detector, SPMCPD01 (Fig. 4.15). The VBL and HBL diagnostic systems consist of a linear feedthrough (CaburnMDC E-BLM-275-6) and a movable plate on which the detectors are mounted. The originally designed system was found to be not reliable enough and to cause occasional blocking of the diagnostics. It was therefore re-designed and two systems of bearings were implemented to support the weight of the detector plate and to guarantee the necessary motion. One is based on two cylindrical
4.12 Diagnostic system
Figure 4.15:
57
General schematic view of the WITCH set-up with the diagnostics
indicated (HBDIAGxx, VBDIAGxx, SPMCPDxx, where xx is the corresponding number. SPMCPD02 is the detection MCP). The abbreviations used are: HB is horizontal beamline, VB is vertical beamline, SP is spectrometer, DIAG is diagnostic and D is ◦ detector. The HBL is 90 rotated (i.e. the top view of the HBL is shown).
CHAPTER 4 WITCH set-up
58
Figure 4.16:
Picture of the diagnostic based on the system with two cylindrical
bearings and the collimator strip in front (HBDIAG03).
stainless steel bearings (Caburn-MDC ALMB-1), the second one makes use of four stainless steel wheels (HEPCO SSLJ13CNS/ENS). To scan the position and size of the beam, several collimator systems are used.
A rotation cube,
which allows to vary the collimator opening continuously, is installed in front of the HBDIAG02 and VBDIAG01 diagnostics. At all other places a stainless steel collimator strip with holes of dierent diameter (3, 5, 8, 20 mm) can be placed in front of the detector. The same strip has also a slit of
20 × 1 mm2
to
scan the beam pro le (Fig. 4.16). In the HBL the strip installed has one slit which allows to scan the beam pro le only in the direction de ned by the strip
◦
motion while in the VBL an angular (45 ) slit is added instead of the 20 mm hole. The combination of these two slits permits to obtain information about the beam pro le in two directions: along the strip motion and perpendicular to it [Delauré, 2004].
The SPMCPD01 MCP detector is installed on a long
rotating arm and does not have any collimator system in front.
4.13 Vacuum system As was already mentioned in the beginning of this chapter, to measure a precise recoil spectrum scattering of ions has to be avoided. The eect of the rest gas on the response function of the set-up will be discussed in Sec. 5.2 but it can already be stated here that the WITCH experiment requires ultra high vacuum (UHV) conditions. The special care here that is required to achieve this goal is described in this section.
4.13 Vacuum system
Volume
HBL
Pressure, mbar
59
VBL
10−7 ÷ 10−8 a)
≤ 10−7
Spectrometer
Detection
bottom
top
∼ 5 · 10−8
∼ 10−8
∼ 5 · 10−8
the HBL vacuum is worse when the WITCH set-up is open to the REXTRAP beamline. a)
Table 4.2: Vacuum in the WITCH set-up (no buer gas used).
4.13.1 Cleaning for vacuum As far as vacuum is concerned, the world is a dirty place! This means that it is necessary to clean all vacuum vessels and components in some way [Reid, 1999]. Already during the design, care was taken to avoid any trapped volumes and to have as many open ways for pumping as possible.
Next, all compo-
nents of the WITCH set-up were cleaned either with pure ethanol or acetone before assembling. These cleaning agents are good solvents and evaporate easily with low residue. After this chemical cleaning the HBL and VBL with all
◦ The bore tube of ◦ the magnet system was vacuum baked at 150 C only because of construction
the components were vacuum baked at 200-250 C in-situ.
restrictions. After baking the bore tube, walls were in addition treated with the glow discharge method using Ar gas, which is an eective nal cleaning process to reduce out-gassing and desorption rates [Reid, 1999]. The spectrometer electrodes rst passed standard chemical cleaning and were then vacuum
◦
red at a temperature of 950 C in
10−6
mbar pressure in the TS-MME/CERN
vacuum ring furnace which has a useful working volume of 5.5 m height by 1 m diameter. Typical pressures for the WITCH set-up with all components mounted and no buer gas used are listed in Table 4.2 (see also Fig. 4.17).
4.13.2 Pumping system The WITCH pumping system is shown in Fig. 4.17. It is at present based on the
3 ATP400 or ATP900) and pre-vacuum
combination of turbo pumps (Alcatel
rotary pumps (Alcatel 2015SD or 2063SD). There are four dierent vacuum sections which are separated by means of VAT
TM
UHV valves: the HBL, the PDT
(or VBL), the spectrometer and the detector region. Every section, except the spectrometer, is evacuated by one ATP400 turbo pump. Since the spectrometer vacuum includes part of the vertical beamline, the Penning trap section (together with the cooler trap where the buer gas is injected) and the spec-
3 Alcatel Vacuum http://www.adixen.com
Technology
has
now
its
own
brand
name
Adixen:
60
CHAPTER 4 WITCH set-up
Figure 4.17: Scheme of the WITCH pumping system. The abbreviations used are:
HB: horizontal beamline, VB: vertical beamline, SP: spectrometer, DR: detection region, UHVV: UHV valve, PREV: Pre-Vacuum valve, TURP: Turbo pump, ROTP: Rotary pump, PIRA: Pirani gauge, PENN: Penning gauge, FULL: Full-range gauge [Delauré, 2004].
4.14 O-line ion sources
61
trometer itself, this region requires the highest pumping power. Two ATP900 (pumping speed 900 l/ sec) are installed for this section: one at the bottom of the cryostat and another one on top of it. Due to the fact that the spectrometer response function is in uenced by the pressure in the spectrometer itself (Sec. 5.2), it is of utmost importance to have very good vacuum in this region. The present spectrometer electrode structure is therefore designed in such way
4 material can still be installed in order to further improve
that so-called NEG
the vacuum in this section, possibly to the low
10−9
or even
10−10
mbar range.
To monitor the pressure every section is equipped with either a combination of Penning and Pirani vacuum gauges or a full-range vacuum gauge (Fig. 4.17).
4.14 O-line ion sources In order to perform the o-line commissioning of the WITCH set-up two ion sources are available. The rst one is the ion source of the REXTRAP set-up, which allows to test the entire line REXTRAP→WITCH beamline→WITCH traps→detector. The second ion source is part of the WITCH set-up itself and is located in the VBL just in front of the entrance to the magnetic eld and in the same vacuum chamber where also the VBDIAG03 diagnostics is installed (Fig. 4.15). Both o-line sources produce stable ions and are described in this section.
4.14.1 REXTRAP ion source The principle of the REXTRAP ion source (Fig. 4.18) is based on the concept described in [Dezfuli et al., 1996]. An alkali-zeolite is lled in a conically shaped cylindrical hollow heater made from graphite. The direct current going through this heater builds up a temperature gradient between the thinnest part in front and the thicker part at the end. This gradient causes a steady ow of alkali atoms from the back of the reservoir to the front. There the atoms are ionised with the aid of tungsten wires incorporated in the zeolite material. The ions are then accelerated in the electrostatic eld created between the ionizer at high voltage and an electrode at ground potential. The beam can additionally be in uenced by an extraction electrode [Schmidt, 2001]. The whole ion source assembly is electrically isolated from the beam-line and can be elevated up to 65 kV, the heating current is up to 75 A, providing a beam with intensities typically of a few nA. The ion source works very reliably and delivers ion beams of
133
Cs+ ,
zeolite [Forstner, 2001].
4
non-evaporable getter (Sec. 7.1.6)
39
K+
and
23
N a+
depending on the used
62
CHAPTER 4 WITCH set-up
Figure 4.18: REXTRAP ion source (from [Forstner, 2001]).
4.14 O-line ion sources
63
Figure 4.19: WITCH ion source (from [Pfeier, 2001]).
4.14.2 WITCH ion source Since the REXTRAP ion source is also used for the REX-ISOLDE facility this limits its application for WITCH. This is why a commercial cross beam ion source was bought from Pfeier company (type BN846481-T). The principle of this ion source is based on electron bombardment of gas atoms (Fig. 4.19). The electrons emitted by the tungsten cathode enter the ionization chamber through a gap. When the electron energy is su ciently high, a small portion of the gas in the ionization chamber is ionized. These ions are pulled out by the extraction electrode and then focused with an ion lens [Pfeier, 2001]. The standard ion source delivers a DC beam.
However, it was modi ed in such
way that the voltage of the lens (V3, see Fig. 4.19) can also be pulsed, thus providing a pulsed ion beam as well. Depending on the gas pressure and the cathode current the ion source intensity can be up to 100 nA [Coeck, 2003]. The ion energy is about 100 eV.
CHAPTER 4 WITCH set-up
64
4.15 WITCH control system & DAQ To control the whole WITCH set-up a dedicated system of electronics and software has been developed [Lindroth et al., 2004]. The dierent components of this specially designed hardware and software that was developed for the WITCH experiment are described in this section.
4.15.1 Choice of hardware The hardware used to operate the set-up is a combination of commercially available electronics and devices that were specially developed for WITCH.
Beamline The WITCH beamline is mainly lled with electrodes. All of them, except the
PDT, require static voltages. To control these voltages a set of power supplies was bought from ISEG company (CPx, EHQ series) and Spellman.
For the
steerer plates a bipolar power supply was built at IKS. This has 9 independent channels and both negative and positive polarity voltages can be set in the range of (-2 kV,+2 kV). The computer control is realized with a CAN eldbus for ISEG power supplies, with analog signals for Spellman and ISOBUS for steerer plate power supplies. Control via analog signals is not currently implemented into the developed software.
PDT For proper operation of the PDT the high voltage has to be switched over 60 kV (30 kV) while the ions travel inside the electrode (Sec. 4.5.2). In practice the pulse down process proceeds via an exponential decay of the voltages, with a time constant
τP DT .
This means that the ions leaving the PDT at dierent
times will have dierent energies. In order to get a reasonably low energy spread
tswitch ≈ several · τP DT . For the present HV τP DT = 0.186 µs and tswitch ∼ 1.3 µs (1.2 µs) beam, where tswitch is de ned such that ∆Eion
10
of
35
Ar
= 40%).
while the production of
35
Ar:
At present the 26m Al is not yet
it might be di cult
ions due to charge exchange losses in the
REXTRAP set-up.
5.5 Procedure to analyse experimental data The procedure that was developed to analyse the experimental data is as fol-
recoil Se(C) (Ekin ) is calculated taking estimated a is the β − ν angular correlation parameter, N 0
lows: rst, a recoil ion spectrum parameters
0
0
0
(a , N , σ )
where
is the number of events and
0
σ0
is the standard deviation of a Gaussian which is
taken for the response function. This spectrum is then compared to the experimental integral spectrum
recoil S(Ekin )
using the Maximum-Likelihood estimate,
which tells how much the calculated spectrum deviates from the data. Based on this deviation the estimated parameters are adjusted, so that the deviation of the calculated spectrum from the data gets smaller.
In order to nd the
better parameters the downhill simplex method is used [Beck, 2005b]. Another possible method to analyse the experimental data is described in [Delauré, 2004] and is based on a comparison of the randomly generated
recoil Se(R) (Ekin )
recoil S(Ekin ). The e(R) (E recoil ) has input parameters (N 0 , a0 , b0 ) where N 0 is random spectrum S kin 0 0 the number of events, a is the β − ν angular correlation parameter and b is spectrum and the measured integral spectrum
the Fierz term (see Sec. 1.2.2). The best tting sample spectrum gives the t parameters
af it
and
bf it .
The
χ2
method can be used to compare the simulated
sample with the measured spectrum. To calculate or generate the spectrum
recoil Se(C,R) (Ekin )
is not a trivial task
because this sample spectrum has to take into account: 1. All necessary corrections to the shape of the Coulomb interaction between the
β -particle
β -spectrum
such as the
and the nucleus, radiative
corrections, second order contributions (weak magnetism and induced tensor term) and recoil order contributions. rections and their in uence on the
Details about these cor-
β -spectrum
shape can be found in
[Wilkinson, 1989, 1990, 1993, 1995a], [Wilkinson, 1995b, 1997, 1998, Glück, 1998]; 2. The response of the set-up. The theoretical spectrum from item 1 has to be folded with the response function which takes into account all set-up related eects (part of them is described above in Sec. 5.2). 3. A possible
β -background
(see Sec. 5.7).
5.6
β -particle
simulations in a simple approach
83
At present the procedure for data analysis is still under development, i.e. more corrections to the
β -spectrum
shape still have to be included in the program
code, while the response function of the set-up as well as the real
β
background
have still to be investigated in detail.
5.6
β -particle
simulations in a simple approach
As was already discussed in Sec. 4.9 a normalization (counting
β -particles) may
be necessary for the precise measurement of the recoil spectrum. This means that a suited place to install one or more
β -detectors
has to be found in order
to provide enough statistics for the normalization. The original eld map provided by Oxford Instruments covers the volume of the set-up contained within
0 < R < 12
−102 cm < z < 190 cm in steps of 2 cm and (z = 0, R = 0) corresponds to the eld map was extrapolated for the case R = 0
cm in steps of 1 cm, where
center of the 9 T magnet. The with cubic spline up to
z = 260
cm in the form [Beck, 2005b]:
B(z) = with
z0 = 116.6 cm.
14570 (z − z0 )3
(5.7)
The radius of the particle motion at each position is calcu-
lated and it is checked whether this radius exceeds the radius of the electrode at this position. If it does, this is counted as a hit at the current Z -position. The results of these simulations done for three dierent energies and for three dierent starting points are presented in Fig. 5.9. The center of the coordinate system
(z = 0, R = 0) corresponds to the center of the 9 T magnet. According β -detectors were installed in the SPDRIF01 electrode. (see
to these results test
Fig. 5.9 and Fig. 5.11 and comments to these gures).
5.7 GEANT4 β -particle simulations Similar simulations as described in the previous section were also performed using the GEANT4
1 simulation package [Agostinelli et al., 2003, GEANT4, 2005].
GEANT4 is a toolkit for simulating the passage of particles through matter. It contains a complete range of functionality including tracking, geometry, physics models and hits [Agostinelli et al., 2003]. Using this package gives better exibility to control physics processes in the simulated set-up and provides realistic results.
β -particle simulations performed for WITCH using GEANT4 to de ne β -detector and to check the β -background on the main MCP
the position of a
are described in this section.
1
GEANT is an abbreviation for GEometry ANd Tracking.
CHAPTER 5 Simulations
84
Figure 5.9:
Results of the simple beta particle simulation.
(a ) is the electrode
structure in the program; (b ), (c ) and (d ) are the positions where the electrode if they start from
z = 0, r = 2
mm (d ).
z = 0, r = 0
The simulation is for
β -particles touch z = 0, r = 1 mm (c ), and mono-energetic β -particles of 3 MeV, mm (b );
5 MeV and 7 MeV which are emitted isotropically.
5.7 GEANT4
β -particle
simulations
85
Figure 5.10: β -spectrum generated for the branch with 35 of Ar.
E0β = 4943.3
keV (BR
=
98.02%)
5.7.1
β -spectrum
In principle it is possible to generate the
β -spectrum using the GEANT4 tools.
The disadvantage of this is that the spectrum will be produced during every run of the program, i.e. using a lot of CPU time, and the result will strongly depend on the used random generator and the computer architecture. In general it is also a good idea to separate the steps of the simulation: 1. description of the source of the experiment, i.e. generation of the initial event; 2. response of the set-up to this primary event; 3. reconstruction of the primary event using the output of item 2; In this way it is possible to split the tasks between dierent people/groups and cross-check the simulations, include non-standard model physics to generate primary events and test the reconstruction procedure of the primary events from the response of the set-up.
Based on this philosophy a separate pro-
β -spectrum
was written. In its rst version one has to
gram to generate the
β + /β − -decay, β to set the endpoint energy E0 and enter the number of events to be generated Nev , i.e. only one branch can be simulated. The output of the program specify as input information the charge Z, to choose between
is the energy of every
β -particle
and its direction
(px , py , pz ),
stored in one
ROOT Tree le [Brun et al., 2001]. At present only the Fermi function is implemented to account for the nuclear Coulomb interaction with the emitted
CHAPTER 5 Simulations
86
β -particle. β -spectra were generated for the most intensive branches for 35 Ar, 60 Co and 122 In. Fig. 5.10 shows an example for the branch of 35 Ar with β endpoint energy E0 = 4943.3 keV and branching ratio BR = 98.02%. The mean energy of 2.28 MeV for the produced spectrum is close to the average energy of the total spectrum (taking into account all branches) E β = 2.266 MeV [Firestone and Ekström, 2004].
This can be considered good enough in or-
der to nd the best place for a normalization
β -background
β -detector
and to check the
on the main detector.
5.7.2 WITCH set-up in the GEANT4 program The scheme of the simulated set-up is presented in Fig. 5.11. The double Penning trap structure is described as a set of two solid cylinders (inner diameter 40 mm) made from copper and a pumping diaphragm with opening of 4 mm diameter, also made from copper. All electrodes as well the walls of the lower and upper magnet bore tubes are made from stainless steel. detector a very simpli ed model is used, i.e.
For the MCP
a solid disk of quartz material
(SiO2 ), 80 mm diameter and 1 mm thick. Due to this primitive assumption it will further be called pseudo-MCP detector. the whole set-up and was set to be
10−7
The vacuum is the same in
mbar. Since the
β -particles
have a
much higher energy O (MeV) than the retardation barrier O (100 eV) the electric eld is not implemented in the description of the set-up.
The magnetic
eld map was extended by Oxford Instruments, so that it covers the range
−100 cm < z < 350 cm in steps of 1 cm 0.5 cm where (z = 0, R = 0) corresponds
and
0 < R < 21
cm in steps of
to the center of the 9 T magnet.
The original eld map is provided separately for the 9 T magnet and the 0.2 T magnet. The 0.2 T magnet was scaled to 0.1 T and the total eld map was calculated (Fig. 4.11). For the positions in between the eld map points, linear interpolation was used:
Bz (R, z) = az · zmap + bz , where az = Bz [iR , jz + 1] − Bz [iR , jz ] bz = Bz [iR , jz ] − az · zmap zmap = z/stepz and similar for the radial component of the eld
(5.8)
BR (R, z):
BR (R, z) = aR · Rmap + bR , where aR = BR [iR + 1, jz ] − BR [iR , jz ] bR = Bz [iR , jz ] − aR · Rmap Rmap = R/stepR
(5.9)
5.7 GEANT4
β -particle
simulations
87
Figure 5.11: WITCH set-up in the GEANT4 simulation program. The positions
are given as they are used in the program, i.e.
(z = 0, R = 0)
corresponds to the
place where the 9 T magnet bore tube merges with the 0.2 T magnet bore tube. This coordinate system is shifted by 428 mm with respect to the one that is used for the eld map, where the origin was taken at the 9 T magnet center. comparison the numbers given in brackets are for the system where corresponds to the center of the 9 T magnet.
To facilitate
(z = 0, R = 0)
CHAPTER 5 Simulations
88
Figure 5.12: Trajectories of
β -particles
of 3 MeV energy for an isotropic distribu-
tion. The center of the decay trap is at -32.3 cm.
In these Eqs.(5.8,5.9)
Bz [iR , jz ] (BR [iR , jz ])
are the tabulated values for the
axial (radial) component of the magnetic eld from the eld map le and
stepz (stepR )
is the step size of the eld map for the axial (radial) eld projec-
tion. The initial
β
event is either read from the le produced by the
β -spectrum
program (Sec. 5.7.1) or a mono-energetic event is generated for program test purposes. The spatial distribution is isotropic and ions are equally distributed in a sphere of 5 mm radius ( nal simulation), a 1 mm radius sphere or a disk of dierent radius (the disk is perpendicular to the axis of the magnetic eld) in the center of the decay trap.
5.7.3 Results of the simulations Simulations were rst done for certain xed energies to avoid arti cial eects of the programming. It was veri ed that GEANT4 calculates the right radius of the
β -particle
emitted perpendicular to the magnetic eld lines.
Correct
reading of the eld map was also checked at dierent points. The trajectories of the
β -particles were visualized (Fig. 5.12) and no strange eects were found.
Fig. 5.12 also shows that at the end of the spectrometer the trajectories of the
β -particles
diverge as they are following the magnetic eld lines.
Finally the program was run with the
35
Ar spectrum (Fig. 5.10), an isotropic
distribution and a cloud of ions of 5 mm radius in the center of the decay trap. The positions and elements of the set-up which the
β -particles
hit rst after
leaving the decay trap were detected. This is shown in Fig. 5.13 and Fig. 5.14.
hit the set-up for the rst time.
35
Ar
spectrum, 5 mm cloud, isotropic
simulations
distribution. The center of the decay trap is at -323 mm.
β -particles
β -particle
Figure 5.13: 3D plot of the points where
5.7 GEANT4 89
CHAPTER 5 Simulations
90
One can recognize the shape of certain electrodes and also the pumping diaphragm (at nearly -400 mm).
Numerically the amount of hits is shown in
Fig. 5.14. As can be seen, the largest number of hits is in the pumping barrier: nearly 80% of the betas going in this direction hit the barrier. The next volume that is actively bombarded by
β -particles
is the SPDRIF01 electrode, as
was also shown already in the rst simulations based on the simple approach (Sec. 5.6).
However, one has to note that Fig. 5.14 gives the absolute num-
ber of hits for the whole volume.
Taking into account that the size of the
pumping barrier is much smaller than the size of the SPDRIF01 electrode, one can conclude that the pumping barrier is the most e cient place to install the
β -detectors.
The technical possibility to implement this is discussed in Sec. 7.1.
Another important output of these simulations is the estimate for the background on the main detector.
β
As was mentioned, the MCP detector is
introduced in the program as a very primitive model. Nevertheless, this allows to check how many particles will arrive on the detector. Fig. 5.14 and Fig. 5.15 show that this amount is actually rather large: from a total of 250 000 simulated events 8608 betas arrive on the 8 cm diameter pseudo-MCP detector.
This
number has to be compared to the number of ions arriving on the same detector. From 250 000 events only half goes in direction of the spectrometer. Assuming
β + -decay is measured and that one thus has to rely on the shake-o eect + −1 get 1 recoil ions, gives an additional factor of ∼ 10 . Taking into account
that to
a cut-o angle one needs to additionally apply factor of 0.8 (see Sec. 5.2.4 and Table 5.1).
This means that about 10 000 ions will arrive as full recoil ion
spectrum on the MCP detector. It might be that an MCP of 4 cm diameter is su cient for the ion detection. Since the
β -background
events equally cover
the surface of the pseudo-MCP, a twice less diameter of the detector means a reduction of the background by a factor of 4, i.e.
corresponding to 2152
beta-particle events. This comparison of the
β -background
is not complete since one still has to
take into account the detection e ciency of the MCP for ions of O (10 keV) energy (the recoil ions are accelerated onto the MCP, see Sec. 4.10) and particles of O (MeV) energy.
β-
The model used for the MCP detector is too
primitive to give the answer on this question. The measurements performed by the TRIUMF and Berkeley groups [Behr, 2005, Scielzo, 2005] showed that this e ciency is very close to the one for ions (i.e. the absolute MCP detection e ciency is about 50÷75% for
β -particles of O (MeV) energy).
This means that
if one assumes the MCP registration e ciency for betas and ions to be 60%, the MCP detector will register
∼1290 β−particles
against 6 000 ion events in
the full recoil ion spectrum. However, the beta-background has to be compared to the number of events not for the total recoil ion spectrum but for every retardation step of the spectrometer. Since the
β -particles
have a much higher energy than the retar-
5.7 GEANT4
β -particle
simulations
91
βM CP = 0.06
MCP:
βM CP = 0.6
Ø=8cm
Ø=4cm
Ø=8cm
3.0
1.5
20.8
5.9
1.5
1.11
5.7
2.2
1.3
1.07
3.9
1.7
144 eV < E < 284 eV 144 eV < E < 277 eV 144 eV < E < 270 eV
Ø=4cm
with βs no βs Table 5.2: Increase (tmeas /tmeas ) of the total measurement time in the case of 26m Al due to the β -background. Two sizes of the detector and dierent sensitivities
of the MCP to
β -particles are considered.
Three energy regions to scan are presented,
the retardation scan step is in all cases is the same, i.e. 7 eV.
dation barrier, the number of
β
events on the MCP detector will be the same
for every retardation step, i.e. for any channel of the recoil ion spectrum. The spectrum which is measured with the retardation spectrometer is the integral one (Fig. 5.16). This means that near the endpoint energy the ion count rate is lowest and the in uence of the beta-background is the largest. However, a measurement of the integral spectrum also means that the number of ion counts is increasing if the retardation potential is decreased, so that the eect of the
β -background is respectively reduced. Fig. 5.16 shows the integral spectrum of 26m Al and three estimates of the β -background mentioned above, leading to very dierent results. Finally, it is necessary to estimate how long one has to measure in view of this background in order to achieve the precision discussed in Sec. 5.4. The corresponding mathematics is presented in Appendix B where Eq.(B.8) de nes the time increase for every retardation step in comparison with the no-beta background case. Table B.1 gives an example of how much the collection time should be increased in case of
26m
Al
for a measurement
close to the endpoint energy region. This part should experience the largest time increase, since there the ion counting rate is lowest. This means that the time of measurement of all other channels should be aected less. Table 5.2 shows estimates of the total time increase again for
26m
Al
(the recoil ion spec-
trum endpoint energy is 280.6 eV (Table 4.1)), when the part of the recoil ion spectrum with
144 eV < E < 284 eV
is considered and for a retardation step
of 7 eV. The rst row gives the values when all 20 channels are scanned, the second row when the last bin is skipped and the last row when the last 2 bins are skipped.
The calculations are done supposing that the e ciency of the
β = 0.6) and if it would β be ten times smaller (M CP = 0.06). As can be seen, when the last two bins (which contain only few counts; see Fig. 5.16) are not measured and the MCP MCP for
β -particles
is equal to the one for ions (M CP
detector has a diameter of 4 cm, the time increase is about factor of 1.7 for
βM CP = 0.6
and almost negligible for
βM CP = 0.06.
Fig. 5.16 and Fig. 5.17
show the part of the integral and dierential spectrum that are cut in this case (dash-dotted vertical line).
Of course, it is also necessary to check how the
CHAPTER 5 Simulations
92
nal precision of the a -parameter is in uenced by reducing the measurement window.
From comparison of the two cases
a = 1
and
a = 1/2
(shown in
Figs. 5.16 and 5.17) one might expect that the eect should not be too large. The important dierence between the original way of measurement (if there is no
β -background)
and the measurement discussed in this paragraph, is that
in the rst case every channel is measured during the same time, while in the presence of the
β -background
the channels closer to the endpoint energy are
measured much longer than the other channels. These simulations, for sure, have to be checked experimentally and the issue about the MCP detection e ciency for ions and betas also has to be investigated in practice, especially for the MCP detector dedicated for the WITCH experiment.
If one uses the output of the simulations presented in
N = 107 ions in the dierential spectrum is su cient to achieve a precision ∆a = 0.005, the time increase shown in Table 5.2 means that the required precision on the β − ν correlation might still be achieved in a realistic time period (e.g. 8.6 hours × 20.8 = 7.5 days for 35 Ar). Nevertheless, reducing the β -background will clearly Fig. 5.8 to estimate the total measurement time, i.e. that
be advantageous. Some ideas how one might avoid this background are given in Sec. 7.1.
5.7 GEANT4
β -particle
simulations
93
Figure 5.14: Plot showing the elements of the set-up which the β -particles hit 35 Ar spectrum, 5 mm cloud in center of the decay trap, isotropic distribution.
rst.
Figure 5.15:
Energy left in the pseudo-MCP detector by
spectrum is used; 5 mm cloud; isotropic distribution.
β -particles.
The
35
Ar
CHAPTER 5 Simulations
94
Figure 5.16: Integral spectrum calculated for
26m
Al for the cases a = 1 and a = 0.5. E = 270 eV is indicated.
The endpoint energy is 280.6 eV (Table 4.1); the position of
Three estimates of the beta background are shown (dotted lines) for the cases: (1) β β ions ions 8 cm MCP detector, M CP = M CP ; (2) 4 cm MCP detector, M CP = M CP ; (3) β ions 4 cm MCP detector, M CP = 0.1 · M CP
Figure 5.17:
a = 0.5.
Dierential spectrum calculated for
26m
Al
indicated.
a = 1 and E = 270 eV is
for the cases
The endpoint energy is 280.6 eV (Table 4.1); the position of
Chapter 6 Very rst tests of WITCH The installation of the WITCH set-up took several years and commissioning was started already during the last phase of the installation. In most of the tests the o-line REXTRAP ion source (delivering a
39
K ion beam) was used.
The tests performed are discussed in this chapter.
6.1 HBL tests The rst part of the WITCH set-up which the ions enter is the horizontal beamline (Sec. 4.5.1).
Since also the installation of WITCH has begun with
the HBL, it is logic that the rst tests of WITCH were performed at this part of the set-up. Since the ISOLDE facility (and respectively, REXTRAP) can operate basically at 60 keV or 30 keV, the tests were done using both high voltage settings. In most of the tests the o-line REXTRAP ion source (
39
K
ion beam) was
used. Ions were rst cooled in the REXTRAP for 20 ms in Ne buer gas and then injected into the WITCH set-up. The typical pressure in the HBL is in the range of
10−8 ÷ 10−7
mbar (the pressure being better if the HBL vacuum
section is separately pumped and worse if it is open/connected to other vacuum sections).
The REXTRAP set-up can operate at 50 Hz repetition rate
providing a beam that is intense enough to be measured in the Faraday cups of the WITCH diagnostics system. All Faraday cup measurements at WITCH are normalized to the current on the last REXTRAP diagnostic (BTS.FC20 ) which is about 1 m away from the rst WITCH electrodes. It is possible to scan the pro le of the beam in the HBL but at two dierent positions and each time only in one direction (horizontally at HBDIAG01 and vertically at HBDIAG03). The typical size of the beam is about 3.5 mm (FWHM) in both directions, see Fig. 6.1.
The tests performed showed that the tuning can be 95
CHAPTER 6 Very rst tests of WITCH
96
Figure 6.1: Slit scans of the beam pro le at two positions in the HBL diagnostics.
Left : HBDIAG01 (horizontal) scan, right : HBDIAG03 (vertical) scan. Plots are for a 30 keV
39
K
beam.
done in such a way that there is no signi cant loss of beam intensity through the HBL, i.e. nearly 100% transmission e ciency is obtained (see Fig. 6.2). To tune the voltages and monitor the beam the three diagnostics in the HBL and the rst one in the VBL are generally used (Fig. 6.2). However, because the quality of the beam in the HBL de nes how well it is injected into the VBL and also later into the magnetic eld and into the traps, it is necessary to check the injection of the ion beam from the HBL into the VBL also over a longer distance, i.e. using another diagnostics higher up (for instance, an MCP which is installed in the spectrometer), for ne tunning of the beam transport.
Figure 6.2:
E ciency of the beam transfer through the HBL (also see Fig. 4.6).
The upper number gives the transfer e ciency obtained in tests with a 60 keV ion beam while the lower number is for 30 keV ions.
6.2 VBL tests
97
6.2 VBL tests The next section of the WITCH set-up is the vertical beamline (VBL). This is a more complicated system than the HBL since it contains the pulsed drift tube electrode, PDT, (see Sec. 4.5.2) and is situated in the vicinity of the high magnetic eld. The main purpose of this part of WITCH is to shift the potential energy of the ions in the PDT and then guide and inject them into the magnetic eld and the cooler Penning trap. An additional speciality of the VBL (in fact of the PDT ) is the high voltage of 60 kV or 30 kV (depending on the ion beam energy). The vertical beamline was rst tested in the laboratory for vacuum conditions and high voltage sparking and then was installed at ISOLDE in May 2003. The typical vacuum in the VBL is of the order
6 · 10−8 ÷ 5 · 10−7
mbar.
The main purpose of the VBL tests that were performed till now was to prove the functionality of the PDT, check its e ciency and investigate and optimize the injection of the ion beam into the WITCH magnetic eld.
6.2.1 Pulsed Drift Tube tests Because the development of the necessary electronics to start PDT tests took more time than expected, the rst successful tests were performed only in July 2004.
Earlier, during the design phase of this part of the set-up, intensive
SIMION simulations had been performed. According to these simulations the travel time of 30 keV 4 kV) is
∼ 5 µs
39
K
ions in the PDT (for a combination of HV = +26/-
while the present electronics scheme of the HV switch box
provides a pulse down time of the PDT of about 1.2 µs (time constant
0.18 µs)
[Delauré et al., 2005].
This gives an
∼ 3.7 µs
τP DT =
time window to pulse
down the ion beam. However, the ion bunch ejected from the REXTRAP setup (see Fig. 6.3) has a time structure that is longer than this time window (the typical bunch length is
∼ 10 µs),
meaning it is not possible to pulse the
1 of it. So the original bunch can be
complete bunch but at best only about 43%
considered to consist of dierent parts: 1) ions which will pass through the PDT before the pulsing down starts, 2) an intermediate part containing partially bunched ions, 3) well bunched ions, 4) another intermediate part of partially pulsed down ions 5) ions which enter the PDT when it is already at low voltage (Fig. 6.4). For the cases 1) and 5) these ions will have
∼ 60
keV (30 keV) after
the PDT, i.e. they are much faster than the well-bunched ions. This leads to the time structure of the signal after the PDT as shown in Fig. 6.5 (a, b, c and d correspond to the transitions between dierent parts in Fig. 6.4). In this gure the simulated (using SIMION) and measured spectra are compared. One clearly sees that already at the position of the VBDIAG03 diagnostics the ions
1 43% is estimated as follows: the switching time window is ∼ 3.7 µs and the length of the incoming pulse is ∼ 10 µs (Fig. 6.3), meaning that at least 37% of the incident ions should be well bunched, but one also has to take into account an ion distribution in the bunch.
98
CHAPTER 6 Very rst tests of WITCH
Figure 6.3: TOF spectra (VBDIAG03 MCP detector) of ions coming from the 39 REXTRAP set-up (no switching was performed). The main component is K; 23 N a also comes from the ion source (but disappears a few days after re lling of 20 the source [Wenander, 2005]); N e+ appears due to ionization of the REXTRAP
buer gas.
Figure 6.4:
Schematic showing the behaviour of dierent parts of an ion bunch
during the PDT HV switching. Dierent parts of the initial bunch are in uenced in dierent ways.
6.2 VBL tests
99
Figure 6.5: TOF spectra of
MCP detector).
39
K
after the PDT (at the position of the VBDIAG03
The simulation is for a HV switch time constant = 0.2µs.
The
measured spectrum is the MCP signal inverted and scaled to the simulated spectrum. Measurement and simulation are both for HV PDT = 26 kV. The zero of the TOF-axis corresponds to the start of the HV switching.
−5 Figure 6.6: Simulated TOF spectra for dierent time constants (10 µs
0.4µs),
< τP DT
99.9997%), but the transfer line is not yet equipped with a cold trap or other puri cation system. The buer gas pressure measurement is done at a point after the gas dosing valve (Pfeier Vacuum, RME005 ) and before the transfer line enters into the vacuum chamber. With this installation the buer gas pressure is regulated via a feedback loop. The gas dosing valve was adjusted to 5 mbar
2 on the buer gas gauge (Balzers PKR251 ). This results
2 One has to remember that the read-out is dierent for dierent gases. Here and below the values for the buer gas are given at the measurement point (feeding line) and how they are displayed on the unit, i.e. without taking into account the type of the gas.
6.3 Trap tests
105
Storage
Number of ions
E ciency
time
(di.estimators)
(fraction to transfer) 1
0
5220±10
( Transfer)
2330±40
1
30µs
4500±200
0.86±0.04
2050±200
0.88±0.08
3900±400
0.75±0.08
1800±185
0.78±0.08
6200±200
1.18±0.04
2630
1.13±0.02
8.2 ms 19 ms 170 ms 530 ms 910 ms
7500±700
1.4±0.1
3100±200
1.34±0.09
7100±800
1.4±0.2
3300±500
1.4±0.2
6400±500
1.2±0.1
3070±255
1.3±0.1
Table 6.1: E ciency of box trapping of
39
K
ions in the cooler trap. No buer
gas is used. The rst row for each storage time lists the estimated number of ions via summing of the MCP signal, the second row by summing the absolute values. Errors correspond only to the standard deviations of the measured signal.
Figure 6.9:
MCP signal for dierent storage times. 39
cooler trap was used with no buer gas cooling.
K
Simple box trapping in the ions were produced in the
REXTRAP ion source and transfered into WITCH. The magnetic eld was 6 T.
CHAPTER 6 Very rst tests of WITCH
106
Figure 6.10: Trap voltages originally applied in order to rst capture ions in the
cooler trap (squares), get them in the quadrupole potential (crosses), transfer them into the decay trap (diamonds) and keep them there (circles). The lines connecting the points are introduced to guide the eye. The labels on the
x-axis refer to the electrodes
for the decay (D) and the cooler (C) trap. The labeling of the trap electrodes was explained already in Fig. 4.9. The centers of the cooler trap and decay trap correspond to respectively CRE1 and DRE8.
in a measured pressure at the top of the cryostat system of several
10−8
mbar.
Such a pressure, according to vacuum ow calculations for a simpli ed setup, results in a buer gas pressure inside the cooler trap in the required range of
10−3 ÷ 10−4
mbar. It is to be noted that these calculations did not take into
account several features of the set-up that reduce the pumping speed (such as the long connection between the turbo pump and the vacuum system and the presence of the electrode structure), but is expected to yield the right order of magnitude of the gas pressures.
The eect of the buer gas cooling can immediately be seen by checking if ions end up into the quadrupole potential in the center of the trap. The applied scheme is that the ions are rst trapped into the box potential of around 80 V formed by the end-cap electrodes and after
∼75
ms the end-cap electrode
voltages are reduced to zero (Fig. 6.10, curve 2.Cooling in quadrupole potential). If the ions are already signi cantly cooled by collisions with the buer gas atoms they have to stay into this quadrupole potential (with a depth of about 10 V) formed by the central ring electrode and the correction electrodes. This eect was clearly seen.
6.3 Trap tests
Figure 6.11:
107
E ciencies of the ion ejection from the cooler trap (shooting the
ions through the decay trap onto an MCP detector) as a function of the decay trap voltage. E ciencies are expressed as a ratio to the situation when the decay trap is at -10 V and when the ions are shot through all the traps. Two estimators are used (see p.103).
Trap voltages When ions are cooled in the cooler trap, they stay in the quadrupole potential. For a proper WITCH operation the cloud of ions has to be transfered into the decay trap since only the energy of ions decaying in this trap will be probed by the retardation spectrometer. A di culty with this is, however, that during the transfer the ions can regain some energy because of the dierence in the potentials and/or shape of the quadrupole wells. This eect has to be minimized because it brings an uncertainty in the recoil ion energy. The original scheme for capturing ions in the cooler trap, cooling them into the quadrupole potential and thereafter transferring them into the decay trap is presented in Fig. 6.10. One can clearly see that the dierence between the lowest point of the quadrupole potential and the potential of the decay trap is about 10 V (the voltages shown are applied voltages on the electrodes and not exactly the potentials which are seen by the ions). This means that the ion cloud can get 10 eV energy during the transfer. Tests were therefore carried out to probe the decay trap potential.
The
results are presented in Fig. 6.11. During the tests the ions were rst cooled in the cooler trap for 100 ms and then simply shot out of the cooler trap. The decay trap voltages were increased until a clear loss in the number of ions appeared, at which moment the decay trap is thus at a higher potential than the quadrupole potential in the cooler trap.
Following these tests the decay
trap voltage was chosen to be -8.5 V. At this potential a large fraction of ions
CHAPTER 6 Very rst tests of WITCH
108
still passes through (and during the rst trap tests one wants to have as many ions as possible) but the fact that it is less then 100% means that the value of 8.5 V is close to the depth of quadrupole potential of the cooler trap (Fig. 6.11). It is interesting to note that a SIMION calculation indicates that for a voltage of -10 V applied on the central ring electrode of the cooler trap (CRE) the potential in the cooler trap center is -8.4 V. One more result of these tests, which can be seen from Fig. 6.11, is that after 100 ms of cooling there is still a large spread in the ion energy (or also the space size of the cloud which results in the energy spread).
Trapping e ciencies From the test described above (Fig. 6.11) and an additional measurement of the extraction of the ions from the decay trap, the trapping e ciencies can be evaluated. For the situation where the cooling time is 100 ms and the buer gas pressure is 5 mbar, the end-cap electrodes of the decay trap are set to +10 V and -8.5 V is applied on all other decay trap electrodes (Table 6.2). A trapping e ciency of about 60% was found for the cooler trap, while the transfer into the decay trap and the trapping e ciency of the decay trap was found to be about 100%. However, during this test there was no ion species determination of the detected ions. Number of ions trapped compared to the number of ions shot through both traps
Ejected from the Cooler trap
Ejected from the Decay trap
0.59 ± 0.02
0.65 ± 0.05
Table 6.2: Trapping e ciencies determined by comparing the number of trapped
ions to the number of ions shot through both traps (without capturing). Only statistical errors are indicated here, which does not fully take into account the instability of the REXTRAP ion source (see page 104). The trap parameters are given in the text.
Dierent pressures It is also necessary of course to nd an optimum for the buer gas pressure that is used. In a simple approach, at higher buer gas pressures the ions should be cooled faster, which is important, because, for instance, it gives a wider choice of isotopes (i.e.
ions with shorter half-life become accessible).
On the other
hand, a higher buer gas pressure also means higher pressure in the decay trap and in the spectrometer (i.e.
larger uncertainty on the recoil energy) and a
higher probability for charge exchange (i.e. larger losses of the initial ions). A good optimum thus has to be found. First a scan of the MCP signal as a function of the cooling time was performed for a buer gas pressure of 5 mbar.
39
K
ions are trapped in the
6.3 Trap tests
109
Figure 6.12: Oscilloscope pictures of the MCP signal (in [a.u.]). Graphs correspond
to dierent cooling times (100 ms, 150 ms, 200 ms, 250 ms, 300 ms, 500 ms) in the cooler trap. The buer gas pressure was 5 mbar. The t function used is Eq.(6.2)
Figure 6.13:
Oscilloscope signal for a buer gas pressure of 9 mbar and 25 ms ν+ (39 K)-excitation.
cooling time. None of the peaks moves under
CHAPTER 6 Very rst tests of WITCH
110
cooler trap, cooled there for some time and then transfered (without capturing) through the decay trap onto the MCP detector behind the WITCH trap structure. It was found that after
∼200
ms of cooling the MCP signal splits in
two dierent peaks (Fig. 6.12). This means that other ions then
39
K
appear
too, for instance, because the buer gas is not clean enough. Qualitatively the eect of the cooling can be seen in Fig. 6.12. To describe it quantitatively one can use the weighted mean value of the signal, the position of the minimum (the MCP signal is negative) and try to t the shape of the MCP signal with some function. The latter is a most complicated task since the MCP response is in uenced by the energy spread of the ions, the size of the cloud and saturation eects of the MCP detector itself, so that it is hard to derive an analytical expression.
However, it can be clearly seen that the
signal has a non-symmetric shape.
Dierent combinations of Gaussian and
exponential functions were tried but the most simple t was obtained with the ROOT Landau distribution (the ROOT Landau function is adopted from CERNLIB routine G110 denlan [CERN, 1996]) and as it can be seen from Fig. 6.12 this t gives a reasonable result. Finally, to evaluate quantitatively the MCP signal behavior the following estimators were used: 1. Weighted mean of the histogram (Mean ). When there are two peaks, the histogram is split in two parts and the mean number is calculated for the left and right part, corresponding to the rst and second peak, separately. 2. Minimum of the histogram after smoothing (ROOT smooth function is used) (Min ). Again, when there are two peaks, the minimum is calculated for the two parts of the histogram independently . 3. The ROOT Landau distribution was used to t the shape of the MCP signal. The most probable value (MPV ) is used in this case as an estimator of the peak position. To estimate the width of the signal the following approaches are used: 1. Standard deviation (dev ) over the histogram (or the part corresponding to the rst/second peak). 2. Sigma of the Landau distribution (Sigma ). For background evaluation the following method was used: 1. The background is tted with a linear function (fback (x)
= a + bx) at the
left and right side of the peak and subtracted from the original histogram. The new histogram is then tted with the Landau distribution function, yielding the MPV and Sigma values.
6.3 Trap tests
111
2. The values obtained in item 1) are used as input parameters to t the original histogram with the function
f (x) = a + bx + Landau(Const, M P V, Sigma)
(6.2)
in the full TOF range of the histogram. This provides MPV and Sigma. Next, background is subtracted as
fback (x) = a + bx
and the other para-
meters, i.e Mean, Min and dev are found. Results are presented in Figs.6.14 and 6.15. As can be seen, the measurements and analysis were also done for 3 mbar buer gas pressure. An attempt at 9 mbar (Fig. 6.13) showed a structure with several peaks already after 25 ms of cooling. However, none of the peaks could be moved/changed with a
ν+ (39 K)
excitation which most probably means that these peaks originate from impurities in the trap. The fact that at higher buer gas pressure the impurity peaks became more pronounced indicates that these impurities come mostly from the buer gas line and not from the rest gas inside the set-up. From Fig. 6.14 one can see that for a buer gas pressure of 5 mbar and cooling for 100 ms the ions are not yet cold and the time of ight from the trap to the MCP detector still increases with a larger cooling time (i.e. energy decreases).
After cooling for 200 ms the TOF stays more or less constant
(this is also the moment when the double peak structure appears; the step in the spectrum at TOF∼
200
ms is mainly due to the analysis procedure: at
this moment two peaks are t separately). If one takes this constant TOF∼
103 µs,
it can be estimated (for the con guration used and the position of
the MCP detector) that this TOF corresponds to an energy of O (eV) (see Sec. 6.3.4, p.120).
This energy is still much higher than room temperature
(i.e. 0.025 eV). However, it can be explained as the energy which the ions gain because of the ejection from the cooler trap while the energy of the ions in the trap is smaller than that. Analysing Fig. 6.15 one can see that the dierent estimators show a similar behavior of the width of the MCP signal, for both buer gas pressures used: rst it increases and later it drops down and stays approximately constant, which indicates that the cooling limit is reached. The initial broadening of the signal can be explained by the appearance of the rst peak, corresponding to an impurity, at nearly the same position as the peak.
39
K
The fact that the energy of the ions is decreasing and the width of
the signal after a certain moment stays constant proves that the buer gas cooling technique works. Similar behavior was observed also for longer TOF (i.e. using the spectrometer MCP): after a cooling time of 200 ms the maximum of the MCP signal stays more or less constant; the width of the signal is at rst decreasing with increasing cooling time and seems to become constant for longer cooling times (Fig. 6.16). Similar tests with 3 mbar buer gas pressure show the ion energy is still decreasing until a cooling time of is already too long for e cient WITCH operation.
∼ 500
ms, which
112
Figure 6.14:
CHAPTER 6 Very rst tests of WITCH
Time-of- ight values for
39
K
ions as a function of the cooling time
for dierent estimators and buer gas pressures of 5 mbar and 3 mbar.
Figure 6.15:
Width of the TOF signal for
39
K
as a function of the cooling time
for dierent estimators at buer gas pressures of 5 mbar and 3 mbar.
6.3 Trap tests
113
Figure 6.16: MCP signal (SPMCPD01) for dierent cooling times (100..900 ms).
On the x -axis is the time of ight (sec) and the y -axis shows the MCP signal in [a.u.]. The buer gas pressure was 5 mbar. Note the dierent range and scale on these axis!
CHAPTER 6 Very rst tests of WITCH
114
6.3.3 Excitations As was described in Sec. 3.2.2 the Penning traps allow to manipulate ions using the combination of the buer gas and an RF - eld in order to achieve better parameters for the ion cloud (remove impurities, cool down and center the cloud, etc.). As not all excitation schemes are required at the present level of WITCH operation, only the basic excitations were tested till now.
Dipole
ν+ excitation
In Fig. 6.17 the oscilloscope pictures corresponding to the dipole
ν+
excitation
are shown. With no applied excitation there are three peaks, the last one is identi ed as
39
K
while the others appear due to the ionization of the buer-
gas impurities (supposedly
H2 OH + and CO+ ,
i.e. the rest gas of the set-up or
gas coming together with the buer-gas). Next, the following scheme is used: rst the ions get cooled by collisions with the buer gas atoms in the cooler trap during 80 ms, secondly they are excited at B- eld) for 100 ms with an amplitude of
Aν+
ν+ (39 K) = 2363170 Hz (6 T = 10 V and nally they are
extracted. No systematic scan of the number of ions ejected from the trap as a function of the excitation frequency was done but only a qualitative study of the TOF oscilloscope spectrum.
It can be seen that the second peak in
Fig. 6.17b becomes larger and broader to higher TOF. This can mean that the applied amplitude is not enough to fully remove the of the trap so that the
39
K
39
larger, i.e.
K
K
ions from the center
peak gets broader and shifts towards the smaller
TOF (partially under the second peak). since the
39
Another explanation could be that
ions are not centered anymore, their radius of motion becomes
they occupy a larger volume and can thus ionize more atoms of
the buer gas or impurity. If now after
ν+
excitation the ions are cooled for
100 ms with the buer gas, the spectrum looks again the same as without excitation applied, which proves that the with
ν+ (39 K)
excitation the
39
K
ν+
excitation mechanism works, i.e.
were brought to a radius larger than the
radius of the pumping diaphragm but smaller than the internal radius of the trap electrodes, and after the
ν+
excitation they are again centered by buer
gas cooling.
RF
mass selective cooling
It was already mentioned in Sec. 3.2.3 that a mass selective removal of unwanted species can be achieved via a combination of dipole
νc
excitations.
ν−
and quadrupole
The idea is that due to the properties of the dipole
ν−
exci-
tation all ions of all masses are rst brought to larger radii and then using the quadrupole
νc
excitation with the frequency of the mass of interest, only
wanted ions are centered, meaning they can be brought through the dierential
6.3 Trap tests
115
ν+ of 39 K : a ) νrf = ν+ (39 K) = 39 to the excited K
Figure 6.17: Dipole excitation at the reduced cyclotron frequency
the ions are rst cooled for 80 ms and then b ) dipole excited at
2363170
Hz (Aν+
= 10
V) during 100 ms; the peak corresponding
goes away and c ) the ions are cooled again by the buer gas after the dipole excitation 39 of the K ; the 39 K peak appears again. The He buer-gas pressure was 8 mbar (at the gas dosing valve position). The magnetic eld was 6 T.
116
Figure 6.18:
CHAPTER 6 Very rst tests of WITCH
Mass selective cooling of
39
K : a ) no excitation is applied b ) ν− νc (39 K) excitation; 39 K ions come
excitation; all peaks disappear c ) quadrupole
back but the signal amplitude is, for some as yet unknown reason, much lower.
6.3 Trap tests
117
pumping barrier for further measurements. This technique was tried qualitatively for
39
K
ions. A dipole
ν+ ,
similar way as
i.e.
ν−
excitation (ν−
from an oscilloscope spectrum) with amplitude 50 ms, and followed by a quadrupole with amplitude
= 130
Hz, determined in the
checking at which frequency all ion peaks disappear
Aνc (39 K) = 1.6
νc
Aν− = 150 39
excitation (νc (
mV was applied for
K) = 3553729
Hz)
V for 3 ms (B- eld is 9 T). As in the previous
test no systematic scan of the excitation frequencies was performed but only a visual analysis of the TOF oscilloscope picture. The corresponding steps of the process are shown in Fig. 6.18. Fig. 6.18a displays the situation before any excitation, the second peak cor-
39
responds to
K.
When a dipole
ν−
excitation is applied, all ions are driven
out as can be seen in Fig. 6.18b (both peaks disappear). If now a quadrupole
RF - eld at
νc (39 K)
frequency is used, one can expect the
back while other impurities should disappear.
39
K
ions to recenter
However, Fig. 6.18c does not
fully correspond to this. As it is supposed to happen, there is indeed no other species than
39
K
present, but the signal corresponding to the
39
K
ions is sig-
ni cantly smaller and broader than the one without any excitation. A possible reason for this can be either wrongly chosen parameters (so that the ions hit the electrode and are lost), some electronics problem (electronic noise in some channels, dierent capacitance of the track: connection wires + electrodes) or space charge related eects (i.e. a shift of the cyclotron frequency, increase of the size of the cloud [Beck et al., 2001]). The dipole
ν−
20
N e ions ν− ' 140 Hz (to successfully remove all ions). 39 one in the K test leads to ν− = 135(5) Hz.
excitation was also applied while working with the
and the frequency used there was Combining this value with the Using this value of
ν−
and an estimation of the magnetic eld in the cooler
trap center (see next Subsection 6.3.5), one can deduce from Eq.(3.15) the trap parameter
U0 /d2 = 1.53(6) · 104
2
V/m . For the ISOLTRAP preparation
trap, which is very similar to WITCH cooler trap, one has
4
10
V/m
2
U0 /d2 = 1.8 ·
[Beck, 1997].
6.3.4 Estimate of the buer gas pressure As mentioned in [Savard et al., 1991], [Konig et al., 1995] and [Schmidt, 2001], in the presence of buer gas the parameters of the dipole and quadrupole excitations (which are used to manipulate the ions in order to clean the ion cloud from impurities and to cool the ions) depend on the properties of the buer gas, as well as on the pressure in the trap. Knowledge of the buer gas pressure is also necessary to estimate a possible systematic eect on the recoil energy spectrum, as the buer gas pressure in uences the pressure in the decay trap and in the spectrometer. Dierent methods used to estimate the buer gas pressure are therefore discussed below.
CHAPTER 6 Very rst tests of WITCH
118
Vacuum ow calculation This concept is based on a gas ow calculation in the molecular ow approach. Formulas can be found, for instance, in [Suurmeijer et al., 2000]. For this calculation only the spectrometer vacuum part was considered (i.e. between the SPTURB01 and SPTURB02 turbo pumps). The presence of the spectrometer and beamline electrodes was skipped. Since the rest gas pressure is dominated by the buer gas, other contributions, such e.g. out-gassing of materials were neglected. The pressure reduction of the pumping barrier between decay and cooler trap was taken as
10−3
(i.e.
pdecay trap = 10−3 · pcooler trap ).
The di-
aphragm in the pumping barrier has a diameter of 2 mm and is 20 mm long. Later, in order to reduce the eect of the magnetic eld on the turbo pump SPTURB01, a prolongation tube of
∼ 1
m was implemented in the set-up,
but this tube was not included in the vacuum calculation. The result of the calculation is that for a buer gas pressure in the cooler trap of
10−3
mbar, the
pressure on top of the spectrometer (i.e. at the top of the cryostat system) is
10−7
mbar. Based on this calculation the buer gas ow (5 mbar at the read-
out point) was adjusted such that the pressure measured on top of the cryostat system is several
−8
∼ 1 · 10
10−8
mbar (without the buer gas the pressure measured is
mbar).
Estimation from the dipole excitation The dipole excitation of ions brings them on a larger radius.
This radius is
also buer gas pressure dependent (Eq.(A.1) and Eq.(A.2)), meaning one can estimate the pressure range of the buer gas by varying the radius of the ion
Rdiaphragm and the (inner) inner radius of the trap electrode Relectrode . If rion < Rdiaphragm = 0.15 cm ions still go through the diaphragm and are counted on the detector, i.e. the (inner) eect of the dipole excitation is not visible; if rion > Relectrode = 2 cm ions hit the wall of the electrode and disappear, i.e. they can not be cooled again
motion
rion
between the size of the pumping diaphragm
and be detected. The radius of motion of the ions after they are dipole excited during a time
texc ,
supposing that the ions start from the radius
the applied frequency
ωrf = ω± ,
R± (texc ) = where
q Ud k0 = a m · ρ0
and
R(0) = 0
and
is given by Eq.(A.5):
α t e ± exc − 1 k0 · 2 (ω+ − ω− ) α±
δ ± α± = ∓ ω+ω−ω ·m −
(6.3)
(see Eq.(A.2), Eqs.(3.22÷3.24) and
Eqs.(3.16, 3.17)).
•
magnetron excitation (νrf
= ν− )
One can estimate from Eqs.3.21 and 3.17 that (q
= +1),
(α− · texc )
for the
at 6 T or 9 T magnetic eld, using the buer gas (He :
39
K ions Kmob =
6.3 Trap tests
119
pcooler (He) = O(10−4 ÷ 10−3 mbar) and the temperature T (He) = TN = 273.15 K) and at texc = 50 ms (also taking into account that ω+ ω− and ω = 2πν ) is: 21 cm2 /Vs),
assuming the pressure
α− texc ≈
ν− q p/pN · · ν+ m Kmob T /TN
· texc = O(10−3 ÷ 10−2 ) 1
(6.4)
Therefore, Eq.(6.3) can be rewritten as:
R− (texc ) = i.e. to rst order
R−
1 + α− texc − 1 k0 ≈ k0 · texc · 2 (ω+ − ω− ) α− 2ω+
(6.5)
does not depend on the buer gas pressure, so that one
can estimate the parameter
k0 .
Since the eect of the magnetron excitation is
clearly visible and at least some ions can be re-centered back with the quadru-
0.15 cm < R < 9 · 105 m/s2 < k0 < 1.2 · 107 m/s2 for an applied dipole excitation amplitude Aν− = 150 mV. If one takes directly the 39 expression for k0 (Eq.(3.24)) and takes a = 1, q = 1, m = m( K), Ud = (inner) Aν− = 150mV, ρ0 = Relec = 2 cm then k0 = 1.86 · 107 m/s2 . The discrep-
pole
2
νc
excitation (see Sec. 6.3.3) one can assume the radius
cm, which gives for
k0
the range
ancy is probably due to the fact that the applied dipole eld depends on the geometry of the trap (i.e. how many electrodes were used, the size of these electrodes and the number of electrode segments) but also on the capacitive and inductive coupling of all the cables and, most importantly, the trap structure itself [Beck, 2005a].
•
reduced cyclotron excitation (νrf
= ν+ )
Using the same values as above (for the combination of
39
K
texc = 100 ms, one obtains: q p/pN |α+ texc | ≈ − · · texc = O(10 ÷ 102 ), m Kmob T /TN
ions and He buer
gas) and
i.e.
e−|α+ texc | 1
meaning
k0 R (texc ) = 2 (ω+ − ω− ) +
−|α t| e + − 1 ≈ k0 · m · 2ω+ δ α+
(6.6)
Using now the expression for the damping coe cient (Eq.(3.17)) one can get a relation between the radius of the ion motion and the buer gas pressure:
pbuf f er gas = pN
mV), i.e.
(6.7)
k0 the value estimated above is scaled as (ν ) k0 = (Aν+ /Aν− ) · k0 − . The buer gas pressure
In order to calculate the parameter
Aν+ /(Aν− = 150
m Kmob T /TN k0 · qR+ 2ω+
CHAPTER 6 Very rst tests of WITCH
120
Measurement : R =
(ν ) k0 − (ν ) k0 −
5
= 9 · 10
m/s
7
= 1.2 · 10
2
m/s
2
5mbar (Aν+ 0.15
= 2V)
8mbar (Aν+
2
2 · 10
−4
3 · 10
−3
= 10V)
0.15
2 · 10
−5
2 · 10
−4
2
1.2 · 10
−3
1.6 · 10
−2
9 · 10
[cm]
−5
1.2 · 10
−3
[mbar] [mbar]
Table 6.3: Estimation of the buer gas pressure (in mbar) in the cooler trap. 39 The calculation is based on the dipole excitation of the K ions. Values are given (inner) for two radii (Rdiaphragm = 0.15 cm and Relectrode = 2 cm) and two estimates of the parameter k0 . Two series of measurements were done: at 5 mbar and at 8 mbar
pressure at the read-out point.
calculations for two independent measurements done at 5 mbar and at 8 mbar buer gas pressure at the read-out point (Fig. 6.21 and Fig. 6.17) are shown in Table 6.3.
As one can see there is quite a big range of possible pressures
obtained. This is due to the spread on the parameter
k0
and the range in values
for the radius of the ion motion. Also, one notes that the similar estimates of the buer gas pressure for the measurements at 5 mbar and 8 mbar at the read-out point do not correspond to the ratio 5:8 which one would in principle expect, but rather to about 1:5. This fact and the results obtained from the dierent methods are discussed at the end of this subsection.
Estimation from the TOF spectrum As was described in Sec. 3.2.2 in the presence of buer gas the damping of the ion motion can be described by the viscous damping force (Eq.(3.16)). Taking into account only this force, Eq.(3.16) yields the time dependence of the ion velocity:
v(t) = v(0) · e−δ t/m where
δ
is given by Eq.(3.17).
(6.8)
In a simple approach one can then write the
time dependence of the kinetic energy of the ion as follows:
Ekin (tcool ) = The parameter
m v 2 (tcool ) = Ekin (0) · e−2δ·tcool /m + Ekin (tcool → ∞) 2
Ekin (tcool → ∞)
(6.9)
takes into account a nite limit of the buer
gas cooling (in the ideal case the ions can be cooled to the temperature of the buer gas (viz.
0.025 eV, if the buer gas is at room temperature)) as well
as the energy which the ions can gain during transfer (viz. about 1 eV). The kinetic energy can be converted into the time-of- ight and compared to the measured TOF spectrum (Fig. 6.14) or vice versa, the measured TOF spectrum can be recalculated into kinetic energy. In order to nd the buer gas
6.3 Trap tests
121
pressure the latter possibility was used (Fig. 6.19).
To calculate the kinetic
energy a simple approach was applied, i.e. supposing that the ions after ejection from the cooler trap move with equal speed in the 2
nd
part of the cooler
trap and in the decay trap and thereafter move with the speed corresponding to the electrostatic potential of -700 V determined by the electrodes behind the trap (the eect of the magnetic eld is not considered). The in uence of the buer gas on the ions after ejection (i.e.
the fact, that the ions moving
in the direction of the detector still experience the presence of the buer gas) can be neglected, since the travel time through the second half of the cooler trap, O (100 µs), is much less than the cooling time, O (100 ms).
Two inde-
pendent ts of the data for 5 mbar and 3 mbar buer gas pressures at the read-out position (taking the MPV estimator) were performed using Eq.(6.9)
Ekin (0), Ekin (tcool → ∞) and the pressure-dependent ) were obtained (Table 6.4). Varying the conversion of TOF into ( 2·δ m Ekin (for reasonable parameters, e.g. Ekin (0) < 100 eV, which is the value of 2·δ the end-cap potential) it was found that the pressure-dependent part, ( m ), changes by no more than a factor of 3, while the parameter Ekin (tcool → ∞)
(Fig. 6.19). From these parameter
is O (eV). Using Eq.(3.17) one can write the following expression for the buer gas pressure in the cooler trap:
p = pN ·
2δ m
·
m Kmob T /TN 2·q
(6.10)
( 2·δ m ) was used, together with pN = = 21.5 cm2 /Vs, T = TN = 273.15 K. As
To calculate the pressure the tted value of
1013
mbar,
39
m = m( K), q = 1, Kmob
can be seen from Table 6.4 the estimated buer gas pressure in the cooler trap for 5 mbar and 3 mbar at the read-out position do not show the same ratio (5:3 ) as at the read-out point but rather a ratio 3.5:1. One can also convert the deduced
Ekin (t)
function into a TOF spectrum and compare this with the
measured one (Fig. 6.20). It can be seen that the t function obtained from the 5 mbar data and scaled to 3 mbar (TOF 3/5 5 mbar in Fig. (6.20)) does not work for the 3 mbar data.
The same holds for the t function obtained
from the 3 mbar data and scaled to 5 mbar (TOF 5/3 3 mbar). However, if the 5 mbar t function is scaled by a factor 5:2 (TOF 2/5 5mbar) and the 3 mbar t function is scaled by a factor 2:5 (TOF 5/2 3 mbar), reasonable agreement with the data is obtained. This fact can be partially explained if
∼ 30% of the buer gas gauge (Balzers PKR251 ) is taken into p5mbar = 5 mbar ± 30% and p3mbar = 3 mbar ± 30% which leads to = 1.7 ± 0.7.
the accuracy of account:
p5mbar p3mbar
Discussion and comparison of the dierent methods As one can see all three methods seem to give dierent values for the buer gas pressure. Because of the similar construction and use, the WITCH
CHAPTER 6 Very rst tests of WITCH
122
Figure 6.19: Fitting the Ekin (tcool ) spectra converted from the TOF spectra of 39 K (Fig. 6.14) with the t function given by Eq.(6.9). Data are taken for two buer
gas pressures, i.e. 5 mbar and 3 mbar, at the measurement point.
Figure 6.20:
Time of ight values for
39
K
ions as a function of the cooling time for
the MPV estimator, at pressures of 5 mbar and 3 mbar at the measurement point. The corresponding ts are shown as well.
6.3 Trap tests
123
buer gas pressure at read-out position :
5 mbar
3 mbar
Ekin (0), [eV] Ekin (tcool → ∞), 2δ/m [sec−1 ]
∼ 15 ∼ 1.5 ∼ 15.9 7 · 10−6
∼ 13 ∼ 1.3 ∼ 5.4 2 · 10−6
[eV]
p [ mbar]
Ekin (0), Ekin (tcool → ∞) and (2δ/m) as obtained for buer gas pressure
Table 6.4:
at the read-out point of 5 mbar and 3 mbar, and evaluation of the buer gas pressure in the cooler trap. The formula that was used to estimate the buer gas pressure is given in text.
cooler trap can be compared to the ISOLTRAP preparation trap. It can be [Kellerbauer, 2002, Blaum et al., 2003] that for He buer gas at
found in
−4
pressures O (10
÷ 10−3
mbar) the typical cooling time is several 10 ms for
the ISOLTRAP set-up. Comparing with the WITCH cooler trap, where cooling times of
100 ÷ 300
ms are necessary (5 mbar at the read-out point), one
can conclude that the buer gas pressure in the WITCH cooler trap is lower,
−5
i.e. O (10
÷ 10−4
mbar). It will be now brie y discussed why the dierent
approaches used above could fail. 1. For the vacuum ow calculation the pumping diaphragm was taken as a central cylindrical hole (diameter 2 mm, length 20 mm) while in the real set-up there is also space outside of the trap, i.e. between the pumping barrier and the wall of the magnet bore tube (with internal diameter
∼130
mm).
This space is partially covered with a kapton foil but this
is de nitely not a vacuum tight connection. This leads to a bigger ow of He gas into the spectrometer part, which means that the calculated pressure on top of the spectrometer will be reached already at a lower buer gas pressure. 2. As can be seen from Eq.(6.7) and Eq.(3.24) the amplitude of the
ν+
excitation scales with the buer gas pressure. However, one notes from Table 6.3 that the applied amplitudes of the dipole excitation are not in the same ratio as the buer gas pressure at the measurement point. We were also not able to excite
39
K
ions with the dipole excitation for 9 mbar
buer gas pressure at the read-out point (Fig. 6.13), which means that
Aν+ = 10
V (limit of the electronics) was not su cient to drive ions out,
while at 5 mbar the applied amplitude was
Aν+ = 2
V. It is interesting
to note from Fig. 6.13 and Fig. 6.17 that other species get ionized as well in the cooler trap (and this eect is larger at higher pressures). This can cause the applied dipole eld to be partially screened by the Coulomb eld of these ions. This means that the real eld necessary to drive ions out is smaller than the applied one, so that the values of the amplitude used
CHAPTER 6 Very rst tests of WITCH
124
give a too high estimate for the buer gas pressure. Also, a more precise determination of the parameter
k0 is needed. Further, the calculations νrf = ν+ . However, the method of the
above are based on the assumption
frequency determination is not precise (see Sec. 6.3.6), as can already be seen from the fact that in one case in another
39
ν+ ( K) = 2367100
ν+ (39 K) = 2363170 Hz (Fig. 6.17) and
Hz (Fig. 6.21) for the same 6 T magnetic
eld. This can signi cantly change the radius estimation (Fig. 6.22), i.e. the buer gas pressure (e.g.
for a shifted frequency the radius can be
smaller than the one corresponding to the resonance frequency and this leads to a too high pressure estimate, Eq.(6.7)). A last comment is that all the equations used for this estimate assume that only one ion is present in the trap, while during the tests the trap was lled with
103 ÷ 104
ions.
It is, however, not possible to estimate the eect of this in an easy way. 3. The estimation based on the analysis of the TOF spectra gives the lowest limit but it is by one order of magnitude lower then the one from the comparison with the ISOLTRAP set-up. This could be due to the fact that the cooling aects all types of motions while in TOF spectra mainly the axial motion plays a role. One can thus conclude that a more precise method for the determination of the buer gas pressure is needed. This is especially important since it in uences the e ciency of the cooling, e.g. it changes the optimal settings for the sideband cooling (for a given ion species, gas type, temperature and magnetic eld the required strength of the RF eld is completely determined by the pressure p [Konig et al., 1995]). This also means that a wrong assumption of the buer gas pressure could explain the failure of the mass selective cooling test (Sec. 6.3.3). Another result of this analysis is that the buer gas line should be better cleaned to avoid or limit the presence of impurities.
6.3.5 Magnetic eld in the center of the cooler trap The necessity to know precisely the magnetic eld at the trap center is based on the following two factors: 1) the cyclotron frequency, and therefore the centering and cooling of the ion cloud as well as the mass-selectivity, are directly de ned by the value of the eld, while 2) the response function of the WITCH spectrometer also depends on it. Originally the magnetic eld map was provided by Oxford Instruments for both magnets separately. However, this eld map resulted from a calculation/approximation based on measurements that were made at the factory, prior to the delivery and installation of the system at CERN. Also, inserting the traps structure with all the wiring may change the eld strength in the trap centers due to the magnetic susceptibility of the used materials. Direct measurement of the eld with an NMR probe is hardly possible because of the very di cult access to the area.
6.3 Trap tests
125
Isotope
26
Alm Ar 38 K 39 K 122 In 35
(Btheor )
νc [Hz] (Bestim. )
5318210
5329000(2000)
3951510
3959200(1600)
3639937
3647000(1500)
3547020
3553900(1400)
1133662
1135900(500)
Table 6.5: Cyclotron frequencies calculated for various isotopes for
Bestim. = (9.018 ± 0.004)
and
Btheor = 9
T
T in the center of the cooler trap.
An elegant way to estimate the magnetic eld is using a known isotope (i.e.
m) and experimentally nd the proper cyclotron frequency νc . B (see Eq.(3.4)). 39 From the excitation tests performed with a K beam, νc (39 K) was found via 39 quadrupole excitation of K (direct determination, νc = 3553729(2000) Hz) 39 but also via dipole excitation of K (which gives only ν+ = 3554019(2000) Hz but in another test also ν− = 135(5) Hz was determined, see p.117). The 39 estimated uncertainty for νc and ν+ is based on two ν+ ( K) measurements (2) 39 (1) 39 at 6 T eld: ν+ ( K) = 2363170 Hz (Fig. 6.17) and ν+ ( K) = 2367100 Hz 39 39 (Fig. 6.21), which leads to ∆ν+ ( K) = 2000 Hz. The nal result for νc ( K) is ν ¯c = 3554000(1000) Hz, which corresponds to a magnetic eld in the center of the cooler trap BCooler = 9.018(4) T (according to the eldmap from Oxford Instruments the magnetic eld in the center of the cooler trap is 9.001061 < B < 9.001072 T ). The set eld was 9 T for the lower magnet and 0.1 T for with known mass
This gives enough information to determine the magnetic eld
the top magnet of the system. Based on this value the cyclotron frequencies for the isotopes of interest for WITCH were estimated (see Table 6.5). The masses used were taken from [Audi et al., 1997].
Identi cation of the impurity peak The experimentally determined value of the B - eld in the center of the cooler trap can be used to identify the rst peak in Fig. 6.12. With was found to correspond to mass 19, and
ν+ (exp) = 7279948
1.
19
F
ν+ = 4845000
ν+
excitation it
Hz (6 T magnetic eld)
Hz (9 T eld). Two possibilities exist for mass 19 :
as part of the te on material, which is widely used in the WITCH
set-up (wire insulation, buer gas tube, sealing for buer gas line, etc.) 2.
H2 OH +
formed from water vapor.
CHAPTER 6 Very rst tests of WITCH
126
Figure 6.21: Identi cation of dierent peaks. Ions are a ) rst cooled for 200 ms νrf = ν+ (39 K) = 2367100 Hz (Aν+ = 2 V) during
and then b ) dipole excited at
100 ms and c ) at the reduced cyclotron frequency (Aν+
= 0.5
νrf = 4845000
The peak corresponding to the excited mass disappears. 6 T. The
Hz
∼ ν+ (mass 19)
V) during 100 ms (in this case the ions were rst cooled during 400 ms).
He
The magnetic eld was
buer-gas pressure was 5 mbar (at the gas dosing valve position). The
increase of the MCP signal after removing the rst peak could be related to MCP eects (see Sec. 6.4.3)
6.3 Trap tests
127
19
ν+ [Hz]
7289000(3000)
Table 6.6:
H2 OH +
ν+ (exp)
7281000(3000)
7280000(2000)
F
ν+
frequencies calculated for
T.
39
K data it is νc frequency for both elements and, using the measured ν− = 135(5) Hz, to extract the ν+ frequency for 19 F and H2 OH + . Results are + shown in the Table 6.6. As can be seen the ν+ (H2 OH ) frequency is closer to ν+ (exp), leading to the identi cation of the impurity as H2 OH + . Taking the B- eld value
B = 9.018(4)
B = 9.018(4)
T calculated from the
possible to calculate the
39
K , the ν+ excitation was also N e ions and the experimental frequency was found to be ν+ (20 N e) = 6910000(2000) Hz. In the same way as above the B - eld can now be calculated. This yields B = 8.997(3) T which diers by more than three 39 standard deviations from the estimation based on the K measurements. The 19 + frequencies ν+ ( F ) and ν+ (H2 OH ) are now also dierent (Table 6.7) and seem to be quite far from ν+ (exp) = 7280000(2000) Hz. However, similarly to what was done for
20
performed for
19
ν+ (Hz)
7272000(2000)
Table 6.7:
ν+
H2 OH +
ν+ (exp)
7264000(2000)
7280000(2000)
F
frequencies calculated for
The reason of this large dierence with the wrongly determined
ν+ (20 N e)
39
K
B = 8.997(3)
T.
measurement could be either a
frequency or a wrong magnetic eld value. For
instance, a too broad resonance peak for used could lead to an incorrect value of
20 N e in combination with the method ν+ (20 N e) (see subsection 6.3.6). Also,
the magnetic eld in the cooler trap will be slightly smaller if the top 0.2 T magnet is switched o. One additional comment about the identi cation of mass 19 is related to chemistry: i.e.
19
F
is the most electronegative and most reactive of all elements,
it immediately interacts with its environment.
19
−1
Further, the ionization
39 K is −1 19 only 418.0 kJ mol [WebElements, 2005]. This means that if a F ion is 39 ionized by collisions with K , the free electron most probably will be adopted 19 almost immediately again by F rather than by 39 K , so that there will be no 19 charge exchange between F and 39 K . It can be concluded that the mass 19 19 is most probably not F but H2 OH + (this was recently con rmed by the new tests [Coeck, 2005a]). potential of
F
is
1681.0
kJ mol
while the ionization potential of
CHAPTER 6 Very rst tests of WITCH
128
6.3.6 Discussion on the frequency measurement All estimates made above were done supposing that the frequency
νrf = ν+ .
However, the frequency was not determined with high precision. Only a rough estimate was made in order to get qualitative understanding of the trap basics. The radius of the ion motion under dipole
ν+
excitation can be calculated
using Eqs.(A.1 andA.3). As can be seen from Fig. 6.22 if one tries to nd the proper
ν+
frequency from a qualitative study of the oscilloscope picture (i.e.
the peak corresponding to the excited ion mass disappears because the ions get on the radius larger than the opening of the pumping diaphragm) one can get only a rough estimate of the frequency, or even fail in some cases (especially at higher buer gas pressure). One can also note that if the applied frequency
νrf
is shifted by 3 kHz, the radius of the motion of the ions started from the
center of the trap may already be larger than the opening of the diaphragm (R
= 1.5
mm). This also means that the estimate of the radius can be o by
10−4 mbar). Concluding: 1) a precise measurement of the ν± and νc frequencies is nec2 essary in order to determine the characteristic trap parameter U0 /d and the an order of magnitude (for a buer gas pressure below
magnetic eld in the trap center, needed to identify the dierent species in the trap; 2) a better procedure to estimate the buer gas pressure in the cooler trap has to be developed.
6.4 More tests During the commissioning of WITCH more tests were done in order to have a better understanding of the set-up. This section gives an overview of these tests.
6.4.1 First radioactive ions in WITCH In November 2004 WITCH got its rst radioactive beam time (with
35
Ar).
A
CaO ISOLDE target and a plasma ion source with cold transfer line were used. However, due to a sintering of the target material and non-optimal ISOLDE tuning the yield for yield is
7
2.1·10
35
Ar
was about 400 times less than expected (the usual
atoms/s for this ion source/target combination [ISOLDE, 2005]).
Retuning and optimizing the ISOLDE settings reduced this loss to a factor 40. Mainly this fact (the e ciency of WITCH is not high enough yet to deal with this reduced intensity) prevented us from going for the rst recoil spectrum measurement. Still, the decay of
35
Ar
two short measurements is: 1.775(4) s).
35
was observed on the VBDIAG01 MCP
Ar obtained as the weighted average of T1/2 (35 Ar) = 1.70(5) s (the value in literature is
detector (Fig. 6.23). The half life of
6.4 More tests
Figure 6.22: Calculated radius of the ion motion (in [meters]) under
129
ν+
excitation
as a function of the frequency shift, i.e. ν+ − νrf (in [Hz]). The plots are for dierent −3 buer gas pressures: 10 ÷ 10−6 mbar and for two values of the parameter k0 (see 39 p.119). Calculations are done for K ions in He buer gas using Eqs.(A.1 andA.3) (ν− ) with R(0) = 0, texc = 100 ms, Aν+ = 2 V and k0 is scaled as k0 = (Aν+ /Aν− ) · k0 . The calculation is done in the single ion approach. Radius of the pumping diaphragm is also indicated. Note the logarithmic scale on the y -axis!
CHAPTER 6 Very rst tests of WITCH
130
χ2 / ndf
35Ar halflife measurement
160
179.1 / 185 4.962 ± 0.014
Constant
-0.3867 ± 0.0150
Slope
140 120 100 80 60 40 20 0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
time, sec Figure 6.23:
35
Ar
half-life measurement on the VBDIAG01 MCP detector.
6.4.2 Preliminary spectrometer tests In order to study the WITCH spectrometer and its response function in the best possible way a radioactive beam is necessary. Trying to do this with a stable beam meets some serious restrictions on what can be tested:
the response
function is mainly aected by the processes in the trap, so one has to capture rst ions in the decay trap and in order to reproduce the decay situation the stable ions then have to leave the trap at a few hundreds eV energy. The latter can be realized by accelerating ions in the trap electro-statically but with the present trap electronics this is not possible (ions can get only
∼20 eV). Another
possibility is to inject ions directly into the spectrometer without capturing them in the traps. However, this excludes the eect of the trap processes, i.e. it does not reproduce a recoil spectrum measurement situation. Also adiabatic conversion of radial into axial energy can not be properly tested in such tests. Nevertheless, this kind of tests has to show if the spectrometer works as a electrostatic barrier. Since the rst attempt with radioactive beam did not allow to study the WITCH spectrometer because of an insu cient amount of radioactive ions, a simple electrostatic test was performed.
During this test the WITCH ion
source was used and no magnetic eld was set. The results are presented in Figs. 6.24.
It can be seen that the spectrometer electrodes work ne as an
electrostatic barrier.
The fact that the integral spectra have a peak shape
might be explained by the electrostatic focusing which can play a role in the absence of the magnetic eld. The WITCH spectrometer was also successfully tested for sparking up to
6.4 More tests
131
Figure 6.24: Integral spectrum measured with the SPMCPD01 detector for dierent
ion source acceleration voltages de ning ion energies of 100 V, 130 V and 145 V. The WITCH ion source was used. Note the logarithmic scale of the y -axis.
600 V, which is above the recoil ion end-point energy for the isotopes of interest.
6.4.3 MCP regime The working principle of an MCP detector was shortly reviewed on page 53. Special care has to be taken about the operation regime of an MCP since it directly in uences the interpretation of the measurement.
Under certain
conditions an MCP is not sensitive anymore to the number of incident particles (Fig. 6.25), meaning that the detector misses some events. This state is known as the saturation of the MCP. The reason for it is that after a channel of the MCP res, the charge in the channel walls must be replenished and as long as this is not done, this channel is not sensitive anymore. The typical dead-time of one MCP channel is in the order of several tens of milliseconds [Wiza, 1979]. For the WITCH diagnostic MCPs it is
∼30
ms.
The saturation of an MCP
depends on:
•
the ion current density, i.e.
the number of incident particles per MCP
channel and per second (the more particles in the bunch are incident the higher the probability that some of them arrive in the same channel); Fig. 6.25 and Fig. 6.28 ;
•
the MCP acceleration voltage applied between the front of the rst and the back of the second plate of the MCP (the MCP e ciency increases
CHAPTER 6 Very rst tests of WITCH
132
Figure 6.25: Summed MCP signal as a function of the number of incident particles
(per bunch). MCP HV = 1.4 kV (VBDIAG03 detector). The plot shows a combination of two independent measurements. As can be seen, the MCP saturates if the 5 number of incident particles is ≥ 4 · 10 per bunch.
with the voltage, i.e. the MCP eectively sees more ions (until it reaches a plateau at typically
∼2
kV for the diagnostic MCPs)), Fig. 6.27;
The eect of the ion current density is shown in Fig. 6.25:
after a certain
amount of ions in the bunch the MCP signal stays constant. However, already much earlier the dependence of the MCP signal on the number of incident ions ceases to be linear. This behavior can be explained by partial saturation: Fig. 6.27 shows that at MCP HV=1.25 kV the
23
N a+
signal has a block shape
while at higher MCP voltage the signal still increases but shows a signi cant drop in intensity for later arriving ions. This means that the early arriving ions saturate a certain fraction of the MCP channels, leading to a decrease of the MCP registration e ciency for later ions. This can be also seen from Fig. 6.28: when the early arriving ions are removed with a time window before they reach the detector (the WITCH beam gate is used for this) the signal corresponding to the late ions increases. More careful studies were performed in [Coeck et al., 2005b] where it was also found that for a given beam spot the shape of the MCP detector is mainly aected by the incoming beam intensity and the voltage over the MCP plates. In addition, these measurements were extended to the case of two separate pulses arriving on the detector in a very short time interval (compared to the recovery time of the detector). This showed that the second pulse can be seen as a continuation of the rst one (Fig.6.26). Finally, in this work it was also shown that Monte-Carlo simulations using a reservoir model reproduce the qualitative behavior of the measurements [Coeck et al., 2005b].
6.4 More tests
133
Figure 6.26: Signal shapes in the case of a double ion bunch (an initial bunch has
a rectangular shape distribution). Two consecutive pulses are drawn directly behind each other, thus omitting the real time interval between them. 1: pulse shape for one long pulse of 580
µs;
3: second of two 300
2: rst of two 300
µs
pulses separated by 100
µs
µs
long pulses that are separated by 50
µs; 4: µs long
µs
µs;
long pulses separated by 50
rst of two 300
µs.
pulses separated by 100
5: second of two 300
(from [Coeck et al., 2005b]).
long
CHAPTER 6 Very rst tests of WITCH
134
The eect described above in uences the measurements and has to be taken into account for the e ciency estimates.
This was not noticed in the very
beginning and was therefore investigated only after the trap tests were done. Thus the real trapping e ciency can dier from the numbers in Table
6.1.
The eect was partially taken into account for the measurement of the PDT e ciency but at that time the beam gate to set the proper time window was not used. This means that the early and late ions (in the sense of the PDT HV switching), which arrive onto the MCP before the well bunched ions, can saturate the MCP so that the e ciency to register the correctly pulsed ions is lower.
This could explain the dierence between the measured e ciency
and the estimated one and would mean that the measured e ciencies are most probably lower limits for the actual values. The saturation of the MCP also plays a role in the beam tuning.
If the
MCP detector works in the saturation regime, it is not sensitive anymore to the absolute number of ions. Even more, a better centered ion beam can cause saturation of the central channels, while a wide beam will lead to a larger MCP signal, since the detector is not saturated and more channels are covered by the beam spot. voltage.
One of the solutions for this is to work at lower MCP high
This decreases the saturation threshold but a drawback is that the
MCP registration e ciency is also reduced. Another possibility is discussed in Sec. 7.1. The dead-time and saturation of the MCP can also in uence the recoil spectrum measurement, since in real measurement conditions the recoil ions are supposed to reach the recoil MCP detector at a rate
> 105
Hz.
This
requires a careful study. Combining MCP detectors with one or two Ni meshes at the entrance (to avoid saturation) should improve the situation. This is currently being tested.
6.4 More tests
Figure 6.27:
135
Change of MCP signal shape with the applied MCP HV and the
saturation eect (VBDIAG03 detector).
Figure 6.28:
Eect of the WITCH beam gate on the MCP signal (VBDIAG01,
MCP HV=1.6 kV): removing early arriving ions with the beam gate increases the MCP signal of later arriving ions.
Chapter 7 Perspectives The WITCH set-up was completed only recently and it is clear that the set-up is not yet optimized. Thus there is still room for many improvements. This chapter gives an overview of possible solutions to problems encountered during the commissioning.
Also more tests are necessary to better understand the
behaviour of the set-up and to learn how to tune it better. A short overview of future physics goals is also presented.
7.1 Possible improvements From the technical point of view the WITCH set-up is not yet fully optimized. Also, new ideas still appear during every new test that is performed.
7.1.1 Beamline The e ciency of injection into the high magnetic eld (i.e. cooler trap) was originally considered to be about 40% (Table 5.1). However, during commissioning it turned out that this e ciency is only about
0.1 ÷ 1% (see Sec. 6.2.2).
This discrepancy could be explained via MCP related eects either directly (i.e. the real injection e ciency is higher than the measured one, because the measurement is damped by the MCP saturation eects, see Sec. 6.4.3) or indirectly via non-optimal tunning (the di culty of tunning is also related to the proper working regime of the MCP detector). Moreover, the diagnostic system with the collimator strip, which performed well in the HBL, was not reliable enough and did not provide the necessary information for tuning. 137
138
CHAPTER 7 Perspectives
Figure 7.1: Time-of- ight spectrum on the detection MCP (oscilloscope picture).
Signals corresponding to the non-pulsed 30 keV part of the beam and the well bunched ions are indicated. No trapping was performed, only injection into the high magnetic eld.
7.1 Possible improvements
139
Figure 7.2: Split anode of the new diagnostic MCP.
Beam gate One of the problems during tuning and e ciency measurements is that only a fraction of the incoming ion beam can be correctly pulsed down (Sec. 6.2.1). The non-pulsed high energy 30 keV ions then arrive rst on the diagnostic MCP and can cause saturation of the detector, reducing the MCP sensitivity to the later arriving well-bunched ions. Part of these energetic ions also reaches the detection MCP at the end of the spectrometer, in spite of the magnetic eld (Fig. 7.1). This can again cause saturation of MCP, which will in uence the measurement of the recoil ion spectrum. Another drawback is that during a radioactive run, the decays of non-pulsed 30 keV radioactive ions implanted directly on the detection MCP will lead to additional background. All these problems can be avoided if one uses a beam gate installed in the HBL (or
VBL) in order to select the part of the original beam which corresponds to the correctly pulsed down ions. The necessary electronics to switch the voltages in the range of 1000 V within several 100 ns is currently being developed.
Diagnostics A new system of VBL diagnostics is currently under development. It is based on an MCP detector with split anode (Fig. 7.2) and a Ni -mesh in front of the MCP. The latter reduces the intensity of the incoming beam in order to avoid saturation of the detector. The transparency of this mesh can be measured to good precision with laser light. The split anode system provides the possibility to check the beam size and its position on-line.
The combination of the
Ni -mesh and the split anode will allow to avoid the problems caused by the saturation of the MCP during the beam tuning. The corresponding electronics in a minimal version can be almost the same as for a standard MCP detector with a single anode but adding one more device to read all the anode sections
CHAPTER 7 Perspectives
140
in series. A 2D picture can be reconstructed by software. This type of MCP with a position sensitive anode can also be useful for some of the trap tests (see Sec. 7.2). However, this will require a position sensitivity of better than 1 mm. Another modi cation which appeared to be necessary is the installation in the beamline of a few Si p-i-n diodes in order to measure the radioactivity. During a radioactive run it is good to check the intensity of the radioactive beam component at dierent places in the set-up to determine the transport e ciency but also to check whether the radioactive beam contains a stable component which can not be distinguished without such measurement. During the rst commissioning run the ions were rst implanted on the MCP detector and thereafter the
β -particles were detected with the same MCP. It was realized
that this method is not very suitable as it has two problems: the implanted beam can cause saturation of the detector, i.e. decrease the MCP sensitivity, and, in addition, the detection e ciency for
β -particles
is low. Both problems
can be avoided by implanting the beam in a foil that is observed with Si p-
i-n diodes, since this detector assembly will be sensitive only to radioactive ions. Implanting in a foil and not directly in the detector is necessary to avoid damage of the diode by the beam. This system is planned to be installed in the coming months.
7.1.2 HV switch The original scheme of the HV switch system was copied from the ISOLTRAP experiment and was slightly modi ed for the WITCH purposes. However, the experience of the ISOLTRAP set-up showed that during standard ISOLDE operation at 60 kV the BEHLKE HV switch develops a leakage current with time. This means that the required voltage of
∼ 60 kV is not delivered anymore
to the set-up. A new HV scheme was therefore developed for ISOLTRAP in
1
close cooperation with the company Elektronik-Beratung . Based on the same new HV switch system a similar scheme was also developed for WITCH by this company.
This new system has also the advantage that the switching
time is improved by a factor of
2 ÷ 3.
This is done with an approach of a
clamping diode, which ties the decreasing voltage to a pre-de ned value for a limited period of time. Fig. 7.3 shows the expected behaviour in time and Fig. 7.4 shows a possible circuit implementation. The switching process in this case starts as usual, the voltage of PDT of the 60 kV goes down towards the negative biasing voltage V2.
0.2 µs
In the graph in Fig. 7.3 a time constant
is assumed. After roughly 600 ns, corresponding to
3 × τ,
τ
of
the voltage
has dropped below the value of an auxiliary voltage supply, to which the diode is connected. The diode therefore becomes conducting and prevents the PDT -
1 Dr. Stefan Stahl - Elektronik-Beratung, Sonderanfertigungen · Kellerweg 23, D - 67582 Mettenheim · Germany.
7.1 Possible improvements
141
Figure 7.3: HV of the PDT as a function of time in case of a standard exponential
decrease with
τ = 0.2 µs
(1) and using the clamping diode (2) (from [Stahl, 2004]).
Figure 7.4: Improved HV circuit scheme, modi ed by adding the clamping diode
(D1) to improve the switching speed (from [Stahl, 2004]).
CHAPTER 7 Perspectives
142
voltage from a further decrease [Stahl, 2004]. Another possible modi cation of the HV switch system is related to the repetition rate. The current system, as well as the newly developed one, can operate at 1 Hz. This should be enough if the half life of the isotope of interest is of the same order.
On the other hand, a higher repetition rate opens a
wider range of possible candidates (as e.g.
46
V,
might also be necessary to measure noble gases.
35
Ar
Table 4.1).
In addition, it
For instance, if
106
ions of
are released within one second from the ISOLDE target, in order to get
them all in the REXTRAP set-up the accumulation time should be of the same duration. But due to the high charge exchange probability the amount of ions will be reduced signi cantly after
∼ 100
35
Ar
ms [Delahaye, 2004]. However, if
one could operate WITCH at 10 Hz this would permit to trap the majority of
35
the
Ar
ions produced by the ISOLDE target. The repetition rate of the HV
system is de ned by the capacitance of the PDT (90 ÷ 100 pF) and the resistor
R1 = 600 MΩ
(Figs. 4.20, 7.4).
The resistor R 1 serves to limit the current
owing through the FUG power supply (which provides +60 kV) because this can hold only 0.1 mA (FUG HCN 6,5M 65000). If a power supply with a higher current limit is used, for example, 1 mA, the corresponding resistors can be 10 times lower and the system should be able to operate at 10 Hz.
7.1.3 Traps During the commissioning period it was realized that varying the negative part of the HV switch system in order to give more energy to the ions improves the injection in the cooler trap. However, the present electronics (GAF switchable ampli ers, see Sec. 4.15.1) limits the end-cap potential to ions with energy
< 90
∼ 90
V, i.e. only
eV can be successfully trapped. As an upgrade of the
end-cap power supplies the same type of device as was developed for the beam gate can be used, allowing to apply higher voltages on the end-caps. It was shown in Sec. 6.3 that the buer gas of the cooler trap contains impurities.
100
Taking into account that the obtained cooling time is O (few
·
ms) and that it was not possible to increase the buer gas pressure in
order to decrease this cooling time because of impurities, it is clear that the buer gas system has to be improved. First of all, the external line has to be as short as possible (the internal part can not be changed), then this line has to be cleaned, baked out and pumped to remove contaminations. To further clean the buer gas, one can in addition cool this line with liquid nitrogen. The latter should be helpful especially if the buer gas line is not completely vacuum tight and some air can get inside. Two more issues which, nally, might be useful are the following: a ) a procedure to align the trap structure and b ) a better vacuum separation between
7.1 Possible improvements
143
the cooler and the decay trap (from the external side of the traps). As to the rst, it is important to better know the exact position of the center of the decay trap in order to study the response function. The second issue in uences the vacuum in the decay trap.
7.1.4 60 kV ion source As was already mentioned the current e ciency of ion injection into the cooler trap (including the VBL e ciency) is far from the expected one.
To carry
out e ciency tests and improve the beam tuning in WITCH, transport of ion beams through the complete WITCH beamline is necessary.
At present this
can be done either with an ISOLDE beam or with the REXTRAP ion source. Naturally, the ISOLDE beam is primarily meant for physics measurements and not for technical studies. The REXTRAP ions source is often needed by the REXTRAP team for tests and developments and, in addition, can not be used during experiments involving the REXTRAP set-up (since it blocks the ISOLDE beam at the entrance of REXTRAP). This limits the time available for testing with WITCH signi cantly.
A design study was therefore started
to develop an ion source for WITCH similar to the one of REXTRAP and to implement this in the horizontal beamline.
7.1.5 Spectrometer The idea here would be to improve the power supply and electrical insulation (i.e. also the electrical connector from vacuum to outside) in order to be able to reach +1500 V. This will extend the range of isotopes for which a recoil ion spectrum can be measured. At the same time it will also allow to study electron capture peaks from more isotopes so as to investigate the response function of the spectrometer and to provide its energy calibration. With respect to the detection part, the 8 cm diameter MCP detector with position sensitive anode might be used to study the size of the recoil ion beam, a possible dependence of the beam on the ion energy and the
β -background.
This MCP with necessary electronics will be provided by the LPC-Caen group [Roentdek, 2005, Liénard et al., 2005]. However, such installation would mean a re-design of the detection vacuum chamber, since the whole MCP assembly (also taking into account the high voltage requirements) does not t in the present chamber (with CF150 ange size). The corresponding design has already been started.
7.1.6 Vacuum The vacuum of the WITCH system is not bad for normal WITCH operation but it can still be improved to avoid pressure related systematic eects and
CHAPTER 7 Perspectives
144
to reduce the charge exchange probability. The WITCH spectrometer was designed with the possibility to use non-evaporable getters (NEG). This material is widely spread in the eld of high vacuum.
The getters are used as high
and ultra-high vacuum pumps to remove active gas molecules from the vacuum environment through a chemical reaction on their active surface [Mazza, 2002]. The advantage of this vacuum material is that it can be distributed in the system, i.e. one can reach almost any place in the set-up to provide the necessary pumping in-situ. Also, once activated this material does not require any additional eort.
350 ÷ 450◦ C
The activation temperature of this material is about
(St707 NEG). It can also be activated by sending a high current.
One more bene t of this material is nally that it can be cut and suitably bent by the user to adapt to the speci c application. The pumping capacitance of a NEG strip of
100 cm2
can be several 100 l /s, depending on the activation
temperature and time.
7.2 Additional tests This section is dedicated to the suggestions for o-line tests in order to study the set-up and clarify some of the parameters.
7.2.1 REXTRAP tuning The REXTRAP set-up provides a bunched beam for the WITCH experiment. The main properties of the beam are therefore de ned by REXTRAP. As was pointed out in Sec. 6.2 the pulse length of the REXTRAP bunch is at present too long for e cient HV switching in the PDT cavity.
Up to now the trap
settings of REXTRAP (which determine the characteristics of the bunch) were not optimized for WITCH purposes. The necessary tests should therefore be done. In order to achieve a shorter time structure of the bunch one can e.g. increase the depth of the trapping potential. However, this will also force the ion cloud to expand into radial direction, i.e. the transversal emittance of the bunch would increase. This could reduce the transfer e ciency [Delauré, 2004]. Tests have to show the optimal balance for WITCH. One can, nally, maybe also work on the extraction electrical eld of REXTRAP. This eld in uences the energy spread of the ion bunch, i.e. to a certain extent it plays a role also in the time structure of the bunch [Delauré, 2004].
7.2.2 The excitation frequencies It was already pointed out in Sec. 6.3 that good knowledge of the dipole and quadrupole frequencies can give important information about the set-up, i.e.
7.2 Additional tests
Figure 7.5:
145
The number of ions ejected from REXTRAP as a function of the
excitation frequency
νdipole
(from [Schmidt, 2001]).
magnetic eld value, depth of the potential of the trap
U0 /d2 ,
buer gas pres-
sure etc. Some methods to increase the precision of the frequency measurements are presented in this subsection. One also has to remember that the results of experiments performed at REXTRAP [Forstner, 2001] have shown deviations from the single particle theory already for
104
stored ions: shifts in the reso-
nance frequencies of the ion motions were observed. This means that to avoid such eects during frequency measurements one has to deal with
< 104
ions.
magnetron excitation The idea is similar to what was used before: to excite the ions at variable frequency close to
ν−
and determine the number of ejected ions. The amplitude
and the time of excitation has to be chosen in such a way, that at the frequency
νdipole = ν−
the radius of ion motion is larger than the pumping barrier open-
ing. This can be done either qualitatively, by simply looking on the oscilloscope picture or quantitatively, using Eq.(A.5). Once the amplitude and excitation time are estimated one should obtain the spectrum
Nions vs. (νdipole − ν− ) with νdipole = ν− .
good precision. A minimum in the count rate will correspond to
An example of such a scan performed at REXTRAP for magnetron excitation is shown in Fig. 7.5. When the magnetron frequency is known, one can study the behaviour of the amplitude/excitation time combination and also extract the trap potential depth
U0 /d2
via Eq.(3.15).
CHAPTER 7 Perspectives
146
The number of ions ejected from REXTRAP as a function of the
Figure 7.6:
shift of the excitation frequency νdipole (from [Schmidt, 2001]). Both spectra shown 133 are for Cs+ ions, excitation time texc = 10 ms, Adipole = 100 mV (• symbol) and
Adipole = 200 mV (◦ symbol).
reduced cyclotron In the same way, measuring the number of ejected ions after can determine
νdipole = ν+ .
The only dierence with the
ν−
ν+
excitation one
excitation is that
the reduced cyclotron frequency depends on the ion mass while the magnetron excitation frequency does not. Taking into account that
νC = ν+ +ν−
and that
the reference ion is known, it is possible to extract the magnetic eld value in the trap (Eq.(3.4)). An example of a frequency scan for the reduced cyclotron motion of
133
Cs+
in the case of REXTRAP is shown in Fig. 7.6.
quadrupole excitation In the case of quadrupole excitation one can use two methods to determine the frequency: one is based on the cooling e ciency (in the presence of the buer gas) and another one is based on the time-of- ight technique (in case of no buer gas damping). In the rst method the same procedure as required for mass selective cooling is applied: rst ions are brought to a larger radius via magnetron excitation and they are then centered back with a quadrupole excitation at applied frequency corresponds to
νc
νrf .
If the
the cooling is most e cient and one can
expect a maximum in the number of ejected ions, since the cloud will then pass through the hole of the pumping barrier. This case is demonstrated in Fig. 7.7 where the number of ions was measured as a function of excitation frequency
νrf
in the ISOLTRAP set-up for
87
Rb
and
85
Rb
ions.
The second method is based on the fact that the initial magnetron motion can be completely converted into cyclotron motion by a quadrupole excitation
7.2 Additional tests
Figure 7.7:
Cooling resonances for
147
85
Rb
and
87
Rb
ions.
Shown is the number
of ejected ions from the preparation trap of the ISOLTRAP set-up vs. the applied frequency (from [Konig et al., 1995]).
Figure 7.8: Cyclotron resonance for
trf = 3.6
85
Rb
ions obtained for an excitation time of
s in the precision trap of the ISOLTRAP set-up (from [Konig et al., 1995]).
CHAPTER 7 Perspectives
148
with the appropriate amplitude and duration if
νrf = νc .
This leads to an
increase of the radial kinetic energy of the ion motion [Konig et al., 1995]. The ejected ions then drift through the inhomogeneous eld which transforms radial energy into axial one. The ions in resonance with the RF eld will thus have the shortest time-of- ight to the detector. The corresponding TOF spectrum measured in the precision trap of the ISOLTRAP set-up is shown in Fig. 7.8. Both methods can be applied for WITCH in order to nd the correct cyclotron frequency.
The rst one should be used in the cooler trap and the
second one in the decay trap. The di culty to use the second method also in the cooler trap (switching o the buer gas) is caused by the small opening of the pumping diaphragm. It is to be noted also that the resonance structure of Fig. 7.8 is in uenced by the rest gas, i.e. one can use this fact in order to estimate the rest gas pressure in the decay trap. We would nally like to mention again here, that from Eq.(3.4) and a known isotope one can calculate the true magnetic eld in the center of the trap. To increase the precision of the extracted value and to perform a validity check of the result it is interesting to repeat such a magnetic eld measurement for dierent isotopes. Varying the set eld with the magnet power supply, one can thus calibrate the power supply to the real eld values.
Estimates for all frequencies for a number of isotopes of interest for the WITCH experiment are given in Table 3.1.
7.2.3 The ion species in the rest gas and buer gas Once the magnetic eld is known and calibrated, a scan of either
ν+
or
νc
frequencies in the same way as described above will give information about the ion species in the buer gas or in the rest gas in the traps.
However, these
ions rst have to be ionized. This can be done either with an electron gun or by injecting ions of a noble gas. The noble gases have the highest ionization potential which means that with high probability they will attract the electrons from the rest gas atoms, ionizing them in this way. To produce noble gas ions the WITCH ion source can be used [Coeck, 2005a]. To check the composition of the rest gas in other parts of the system a small commercially available gas analyser can be used.
These analysers are
available to mount either on a CF63 or a CF40 ange.
However, since it is
based on a quadrupole system it is impossible to use such an analyser while the WITCH magnetic eld is switched on. The analysis of vacuum residuals and their intensities can also give information about out-gassing of the system and possible vacuum leaks.
7.2 Additional tests
149
7.2.4 Buer gas pressure It was already stated that good knowledge of the buer gas pressure in the cooler trap and of the rest gas pressure in the decay trap is important for proper excitations and for a good understanding of the response function of the spectrometer (Sec. 6.3.4 and Sec. 5.3). Till now it was not yet possible to draw precise enough conclusions about these pressures (Sec. 6.3.4). So, more tests are necessary to clarify the situation.
It is also important to mention
that the purity of the buer gas system has to be veri ed rst. Otherwise the method based on the ion motion in the trap can be aected by charge exchange or damping by other ion species.
pressure calculation It is possible to do more extensive vacuum ow calculations and introduce more free parameters (like the e ciency of the pumping barrier or out-gassing of the system) which can be checked experimentally. The example here would be to estimate the pressure not only at the top of the system but also at the bottom, vary the pumping capacitances and calculate the corresponding readout pressures.
All these circumstances can be checked in practice and more
precise conclusions should be drawn.
using properties of the magnetron motion Another possibility is to use the fact that the radius of the magnetron motion increases with time (Eqs.(3.20 and 3.21)). First ions have to be centered with sideband cooling (Sec. 3.2.3) and then, due to the exponential increase of the radius of magnetron motion with time, the number of ions extracted through the pumping diaphragm will exponentially decrease with time.
An example
of such measurement and extrapolation of data points in case of ISOLTRAP is shown in Fig. 7.9. However, one also has to consider the time scale of the radius increase. For instance, in the case of the WITCH cooler trap (U0 /d
2
= 1.53·10 V/m ) for K ions, 9T magnetic eld and a helium buer gas pressure −1 −4 of 3 · 10 mbar the decay parameter α− is ∼ 75 s. Considering that to get −1 enough data points the measurement has to be done for several α− , this time 4
2
is very long. time becomes
39
On the other hand, if the eld is reduced to 1 T the decay
∼1
s. So, to use this method one has to decrease the WITCH
magnetic eld to about one Tesla. To achieve better precision one can also vary the eld around 1 T and make the measurement with dierent ion species. It is di cult to use this method in the decay trap for two reasons: since the pressure there has to be much lower the ingly (α−
∝ p);
−1 α− -parameter
there is no diaphragm to select the ions.
increases accord-
The latter can be
solved by introducing a position sensitive detector: instead of selecting with
CHAPTER 7 Perspectives
150
Figure 7.9: The number of ions ejected from the ISOLTRAP preparation trap as
a function of the delay between the end of cooling by means of an RF - eld and the 133 extraction (from [Savard et al., 1991]). The measurement is done for Cs and a −4 helium buer gas pressure of 3 · 10 mbar; the magnetic eld is 0.7 T. The line is a t to an exponential decay with a decay constant
1/α− = 22
ms (Eq.(3.21)).
the diaphragm, the evolution of the position and intensity of the ions after ejection is then measured. To decrease the measurement time one can increase the pressure in the cooler trap. If this test will not permit to give the rest gas pressure in the decay trap one can still estimate an upper limit and verify the functionality of the pumping diaphragm.
7.2.5 Cooling time In principle if one knows the buer gas pressure the corresponding cooling time (i.e. the time the ions need to reach the temperature of the buer gas) can be calculated. Nevertheless it is also interesting to check this time experimentally. In Fig. 7.10 the method used in the ISOLTRAP experiment is demonstrated. It is based on the measurement of the width of the ion signal extracted from the RFQ ion trap as a function of the cooling time. The pulse width decreases because of the decreasing ion temperature and the smaller axial distribution of the ions in the trap. At ISOLTRAP one generally considers that the ions are cooled enough if the width is less then
1 µs.
However, one should keep in
mind that normally ISOLTRAP operates with
