Accelerator Physics Lectures Part 2 - Lancaster Experimental Particle ...

Accelerator Physics Lectures Part 2

Frank Zimmermann CERN, BE‐ABP Ambleside Linear Collider School 2009

Table of Contents – Part 1  (E. Wilson, yesterday)  1. 2. 3. 4. 5. 6. 7. 8.

Synchrotrons, storage rings and linacs Hills Equation and transverse focusing  Phase stability – buckets and bunches Beam Emittance and Conservation Luminosity Non‐linear effects (Beam‐beam limit) Collision region

Table of Contents – Part 2 (today)  9. SC and room‐temperature linacs 10. Particle Sources (e‐ and e+) 11. Synchrotron Radiation and Damping 12. Intensity limits and Beam Stability 13. Beam Delivery (final focus & collimation & beam‐beam effects) 14. ILC overview 15. CLIC two‐beam scheme 16. Contrasting Parameters ILC and CLIC

9. SC & room‐temperature linacs

RF acceleration Ez

bunches time

fixed location  s

Ez fixed time

distance s

RF acceleration

A. Mosnier

RF accelerating structure  =  converter of RF power into E‐field and hence  into electron energy Efficient acceleration if:

• concentration of E‐field and • synchronism of e.m. wave with particles

in a uniform waveguide: vph approaches light velocity asymptotically for high ω the simplest and straigthforward method: use of disc‐loaded structures with individual cells coupled through the beam holes  wave‐ guide disk‐loaded waveguide multicell cavity individual cavities

disk‐loaded wave guide ~ chain of coupled cavities

“Brillouin” dispersion diagram

uniform guide

finite passband fundamental TM010 mode L phase shift / cell generally chosen for TW (transit factor & Q, group velocity)

SW structure (ILC)

electromagnetic waves in a periodic structure Floquet theory Achille Marie Gaston Floquet (1847 ‐1920) (3D) equivalent in solid‐state physics: Bloch theorem

Ez =

n =∞

∑a

n = −∞

n

J 0 (k rn r ) e

i ( ω t − kn z )

2

where k n = k0 + 2 π n / L and “space harmonics”

⎛ω ⎞ k = ⎜ ⎟ − k n2 ⎝c⎠ 2 rn

in the limit v→c: (1) synchronous wave number krn=0, and accelerating force is  independent of radial position of synchronous particle (2) radial force is proportional to radial position and defocusing, but  vanishes as the particle velocity approaches the velocity of light => these properties greatly facilitate the operation of electron linacs!

ILC π

ω L/c 2π

CLIC

speed of light line, ω = β /c

2π/3

π synchronous

π/2

π/2

0

π/2

βL

π 0

Erk Jensen

cavity resonators using RF fields in cavity resonators accelerating voltage

W : stored RF energy P : RF power very high Q  Î small RF power to obtain accelerating voltage; only power taken by beam needs to be replaced superconducting cavities: Q about 1010  Cu cavity:  about 104 G.Geschonke

Erk Jensen

RF microwave linacs • RF acceleration is THE technology which could  provide TeV range e+/e‐ collisions in the near  future • RF microwave acceleration – 2 examples – L‐band (1.3 GHz). superconducting cavity, standing  wave (ILC) – X‐band (11‐12 GHz), normal conducting cavity,  traveling wave  (CLIC) T. Higo

wave length / frequency / band Wave length

Frequency

60cm 20cm 10cm

1.3GHz

2.6cm 1cm

3mm

11GHz

Band

From Microwave Tubes by A. S. Gilmour, Jr.

T. Higo

CLIC RF structure – Normal Conducting (NC) ‐ Copper ~20 cm,

CLIC contains  ~140,000  20‐ cell NC cavities,  each one ~20  cm long

copper 18 cell CLIC X‐band structure, cell length ~1 cm, ~20 MV accelerating voltage over 20 cm

iris radius ~2.35‐3.3 mm

ILC RF structure – Superconducting (SC) – Niobium  – all dimensions about ten times bigger!  9‐cell ILC SC L‐band structure,  cell length ~10 cm, ~30 MV accelerating voltage  over 1 m

Nb‐Ti

iris radius ~35 mm ILC has 16,000 9‐cell SC cavities,  each one ~1 m long

a few figures of merit

geometric optimisation of accelerating structures

Shunt Impedance as high as possible (to minimize dissipated power for a given Eacc)

2 a

E R= dP / dz

Surface fields as low as possible

effective accel. field seen by the particle power dissipated per unit lengh

(which limit the maximum achievable Eacc) max magnetic field SC SW 1.3 GHz

NC TW 12 GHz

~ 1 kΩ/m

~ 16 kΩ/m

Q

1010

~6200

R

107 MΩ/m

100 MΩ/m

Es/Eacc

~2

idem

Hs/Eacc

~ 4 mT/(MV/m)

idem

R/Q

max electric field

A. Mosnier

Linac traveling wave (TW) structures „ „

NC standing wave structures would have high Ohmic losses => traveling wave structures

pulsed RF Power source

d

RF load

RF ‘flows’ with group velocity vG along the structure into a load at the structure exit

„

E. Adli

CLIC – NC Traveling Wave

Linac standing wave cavities „

Superconducting standing-wave cavities: small Ohmic losses

(from P. Tenenbaum, ILC@SLAC)

E. Adli

ILC – SC Standing Wave

Erk Jensen

25 ‐35 MV/m

SC linac (at 2 K) needs cryo power for 1.3‐GHz SC linac:

E Pcr = A + BDEg static g dynamic heat load

XFEL1 ILC2

heat load

Accelerating gradient g [MV/m] 23.6 31.5

Duty factor D 0.65% 0.75%

D ≈ 0.0075 A ≈ 350 W/m 2 −10 B ≈ 10 Wm/ (eV ) extracted from XFEL and ILC designs by Anders Eide

Static Dynamic heat load heat load [W/m] [W/m] 410 781 337 728

ILC total electrical cryo power ~40 MW  (half of which for dynamic heating at 2 K)

Standing Wave vs Traveling Wave • R/QTW = R/QSW X 2 – the space harmonics of SW propagating against beam  cannot contribute to the net acceleration, while the reverse‐ direction power is needed to establish the SW field. 

• Many NC Linacs at high gradient use TW – high field needs high impedance  – power not used for beam acceleration or wall loss needs to  be absorbed by outside RF load – microwave power flow in one direction; beam coupled to  the field associated with this power flow

T. Higo

LINAC example parameters ILC and CLIC

SW

TW

units

ILC(RDR)

CLIC(3 TeV)

ELinac

GeV

25 / 250

9/ 1500

Acceleration gradient

Ea

MV/m

31.5

100

Average beam current

Ib

μA

42

9

Peak RF power 

Pin peak

MW/m

0.37

275

Average RF power

kW/m

2.9

3.7

Initial / final horizontal emittance

εx

μm

8.4 / 9.4

0.38/0.66

Initial / final vertical emittance

εy

nm

24 / 34

4/20

RF pulse width

Tp

μs

1565

0.24

Repetition rate

Frep

Hz

5

50

Number of particles in a bunch

N

109

20

3.7

Number of bunches / train

Nb

2625

312

Bunch spacing

Tb

360

0.5

468

6

Parameters Injection / final linac energy

Bunch spacing per RF cycle T. Higo, G. Geschonke

Tb/ TRF

ns

accelerating voltage

ILC “beam loading” fill time

beam

time 0.62 ms accelerating  voltage

0.94 ms

CLIC factor 6300! (not to scale)

fill  time

84 ns

beam

time

filling time scales as 1 / (beam current)  156 ns

two challenges: gradient & efficiency „

e+e- pass through accelerating cavities only once

„

the length of the linac is given by 1. 2.

„

ECM RF accelerating gradient [V/m] & filling factor

⇒ 1st main challenge of future linacs: maximize acceleration gradient G to keep collider short and construction cost acceptable !

„

gradient limited by field break down etc.

„

⇒ 2nd main challenge: rf-to-beam-power conversion efficiency

1st challenge: acceleration gradient filling factor F ~0.70 (ILC), 0.80 (CLIC) = fraction of the linac length occupied  by accelerating RF structures; “active length”/total length two‐linac length 2L ~ ECM/(F x G)  ex. G=100 MV/m, ECM=1 TeV: → 2L~ 1012/(0.7x108) m ~ 14 km

linear collider luminosity #bunches/pulse linac repetition rate

L=

#particles/bunch

f rep nb N b2 4πσ σ * x

* y

horizontal & vertical rms spot sizes at collision point

HD correction factor for  “hourglass effect” & disruption  enhancement

linear collider luminosity rewritten electrical  “wall‐plug” power

#beamstrahlung photons per electron (positron), ~1 wall‐plug‐to‐beam power conversion efficiency

⎛ 5 ⎞ Pwall η L ≈ ⎜⎜ ⎟⎟ Nγ * σy ⎝ re ⎠ Eb beam energy

Pbeam = f rep Eb nb N b Pbeam = ηPwall

vertical rms spot size at collision * N Point  ε β y y σ *y = γ recipe for high luminosity: small εy, small βy*, large efficiency η

limits on collider spot size low‐beta  quadru‐ pole beam envelope

to decrease the beam size at the collision point we can reduce either β* or ε

≈ l ε β*

s~β*

β *ε

other limits from beam‐beam effects and from SR in final  quadrupoles (“Oide effect”)

l σz bunch

β*: ‐ must remain larger than σz - quadrupole aperture must be respected reducing ε decreases σ at IP and at quadrupole!

2nd challenge: power conversion efficiency ILC: SC cavities, low loss,… η~9.4% (RF + cryo power) CLIC: drive beam accelerated with full beam  loading, loss‐free transport,… η~7.1‐7.3%

SC cavity preparation long and complex procedure … ¾ High purity niobium sheets of Residual Resistivity Ratio RRR=300 are scanned by eddy‐ currents to exclude foreign material inclusions like tantalum and iron ¾ Industrial production of full nine‐cell cavities: – Deep‐drawing of subunits (half‐cells, etc. ) from niobium sheets – Chemical preparation for welding, cleanroom preparation – Electron‐beam welding according to detailed specification ¾ 800 °C stress annealing of the full cavity removes hydrogen from the Nb • Option: 1400 °C high temperature heat treatment with titanium getter layer to increase the thermal conductivity (RRR=500) further ¾ Cleanroom handling: – Chemical etching or electropolishing to remove damage layer and titanium getter layer – High pressure water rinsing as final treatment to avoid particle contamination • Option: Final bake out (120°C) to change oxygen distribution near Nb2O5/Nb interface A. Mosnier, 2005

y different from DC, at RF the resistance 

is not exactly zero, but just very small: 

1.3 GHz

y non‐superconducting electrons oscillate

in the time‐varying magnetic field and  dissipate  power in the material;  significant heat load (1 W of head at 2 K  ~ 1 kW of primary ac power) y maximum accelerating gradient is limited by the maximum possible

surface magnetic field (“superheating field”, 180 mT for Nb, 400 mT  for Nb3Sn) y however, max. acc. gradients obtained for Nb (ILC, ≈ 40 MV/m) Erk Jensen

Progress in SC RF accelerating field

H. Padamsee

A. Mosnier, 2005

America SC cavity R&D: Nine‐cells new series

Preliminary

- Five 9-cell cavities: built by ACCEL, and processed/tested at Jlab. - All of them processed with one bulk EP followed by one light EP and by ultrasonic pure-water cleaning with detergent (2%).

R. Geng - JLab

L. Lilje, TILC09 AAP April 2009

Preliminary

19.4.2009 TILC09 AAP Review

R. Geng Lutz Lilje - JLab

Global Design Effort

33

L. Lilje, TILC09 AAP April 2009

CLIC – NC linac ‐optimization procedure , f, ∆φ, , da, d1, d2 BD

Bunch population N

Cell parameters

Q, R/Q, vg, Es/Ea, Hs/Ea

Structure parameters

Ls, Nb

Ns

Q1, A1, f1

Bunch separation

η, Pin, Esmax, ∆Tmax rf constraints NO A. Grudiev, ~2006

YES

Cost function minimization

BD

CLIC optimization constraints Beam dynamics (BD) constraints based on the simulation of the main linac, BDS and beam-beam collision at the IP: • •

N – bunch population depends on /λ, ∆a/, f and because of short-range wakes (reduced since last ACE) Ns – bunch separation depends on the long-range dipole wake and is determined by the condition: Wt,2 · N / Ea= 10 V/pC/mm/m · 4x109 / 150 MV/m

RF breakdown and pulsed surface heating (rf) constraints:

• ΔTmax(Hsurfmax, tp) < 56 K

• Esurfmax < 250 MV/m (it was 380 MV/m before) • Pin/Cin·(tpP)1/3 = 18 MW·ns1/3/mm A. Grudiev, ~2006

optimum CLIC: 100 MV/m at 12 GHz Optimisation:  (A.Grudiev)  Structure limits:  • RF breakdown – scaling • RF pulse heating  Beam dynamics: • emittance preservation – wake fields • Luminosity, bunch population, bunch spacing • efficiency – total power Figure of merit: • Luminosity per linac input power take into account cost model

after > 60 * 106 structures: 100 MV/m 12 GHz chosen, previously 150 MV/m, 30 GHz EPS 2009 G.Geschonke, CERN

A .Grudiev, PAC 2009?

CLIC Gradient Main limitation = RF breakdown Very fast dissipation of stored RF energy High electric surface field leads to explosive electron emission High magnetic surface field leads to RF pulse heating ¾ RF breakdown = fast and local dissipation of stored energy ¾ Several Joules of rf energy can be absorbed in a single cell, and in the process, surface melting and evaporation occurs in an area of a few 100 μm2 ¾ Strong electron emission, acoustic waves, gas desorption, X‐rays and visible light is  observed during a breakdown event ¾ The majority of breakdowns are concentrated in areas of high surface electric fields ¾ In areas with high surface currents but not necessarily high electric fields, surface  defects like particles, voids and contaminants have been found to be sources of  breakdown ¾ The stress imposed on the copper surface by pulsed heating resulting from high  surface currents alone is also believed to lead to breakdown. Structure designs with a  pulsed temperature rises 80%

>80%

>80%

Electrons/microbunch Number of microbunches Width of Microbunch Time between microbunches

Charge per macropulse

Polarization

L. Rinolfi

example polarized electron guns

JLAB   100 kV electron gun  (courtesy  from M. Poelker) 

L. Rinolfi

SLAC   120 kV electron gun  (courtesy  from J. Sheppard) 

positron source • pair production, γ → e+e-, by photons (or e‐) hitting target • polarized photons → polarized e+ • most popular schemes/proposals: • bremsstrahlung of polarized e‐ beam hitting  amorphous target (JLAB,  SuperB) • channeling radiation in crystals (KEK,LAL,CLIC)  – not polarized • laser Compton‐backscattering source (KEK,LAL,CLIC) • high‐energy e‐ beam passing through undulator (UK,ILC) – polarized or  unpolarized [Balakin & Mihailichenko 1979]

• Compton back scattering or helical undulator ‐ equivalence

‐ coupling of main beam and e+ source ‐ limited intensity & possible need of “stacking”

CLIC unpolarized hybrid‐target e+ source optimized configuration e‐ beam on crystal: ‐ energy = 5 GeV ‐ beam spot size = 2.5 mm

e‐ e‐

e‐

First target: crystal ‐ 1.4 mm thick  W oriented along  axis  where channeling process occurs Second target is amorphous:  10 mm thick W

γ

thin  crystal

Charged particles are swept off after the crystal:  only γ (> 2MeV) impinge on amorphous target Distance between the two targets = 2 meters L. Rinolfi

e+

e+ amorphous

only photons hit the amorphous target!

energy deposition in amorphous target MeV/e‐

simulated peak energy density of 0.66 GeV/mm3 much reduced compared to case w/o crystal! target destruction ~4 GeV/mm3 (SLAC experiment) L. Rinolfi

laser Compton backscattering

T. Omori

CLIC ERL Compton scheme Presented by T. Omori at  the 4th "ILC/CLIC e+ studies" meeting

4.4x109 e+/bunch

L. Rinolfi

50 Hz Linac (if necessary)

Two Storage Rings concept 

T. Omori L. Rinolfi

Put 2 Storage Rings (SR) between ERL and PDR to separate stacking and damping functions.

ERL 3 312

3 2 1

2

1 321

SR1

C = 48m

3

1 321

2

SR2

C = 48m

47 m

PDR C = 400 m Kill 321 - 312 = 9 bunches

Timing chart: CLIC Compton ERL source Time [ ms ] ERL (CW)

0

20

40

60

80

100 120 140

to SR1 to SR1 to SR1 to SR1 to SR2 to SR2 to SR2

SR1 (25Hz)

stack damp stackdamp stackdamp stack to PDR

SR2 (25Hz)

to PDR

to PDR

stack damp stack damp stack damp to preDR

to preDR

to preDR

from SR1 from SR1 from SR1 from SR2 from SR2 from SR2

PDR (50Hz) DR (50Hz) L. Rinolfi

undulator planar undulator

helical undulator S.H. Kim

German wikipedia

Periodic dipole magnet structure (1: magnets). The static magnetic field is alternating along  the length of the undulator with a wavelength  λu. Electron beam (2) traversing the periodic  magnet structure are forced to undergo  oscillations and radiate (3: radiation).

A model of a double‐helix coil for the  low‐carbon steel poles and beam  chamber. A double‐helix SC coil with  equal currents in opposite directions in  each helix is to be inserted between the  steel coils. 

The ILC Baseline Undulator Source

Positrons per Bunch Bunches per Macropulse Macropulse Rep Rate (Hz) Positrons per second J. Clarke

SLC

ILC

3.5 x 1010

2 x 1010

1

2625

120

5

4.2 x 1012

2.6 x 1014

ILC baseline critical Issues

• Target

J. Clarke

– Rotating titanium wheel • • • • •

Eddy current heating (~ 5kW for 1T) Photon beam heating Pressure shock waves Cooling/vacuum/radiation resistance Prototype exists and Eddy current effects will be  carefully measured and quantified/benchmarked • Analysis of pressure shock waves ongoing

20 April 2009 Review

AAP

Global Design Effort

62

undulator radiation = Compton scattering  of virtual photons

B02 λu number density  nu = 2 μ 0 hc of virtual photons B. Lengeler, RWTH Aachen, lecture on coherence

⎛ K2 ⎞ v = v⎜⎜1 − 2 ⎟⎟ ⎝ 4γ ⎠ *

=0.934 B [T] λ[cm]) 

References for Section  10 L. Rinolfi, private communications  L. Rinolfi,  Present Roadmap for the  CLIC Positron Sources, POSIPOL2009 Lyon M. Kuriki, Electron Source for Linear Colliders, 2nd ILC School Erice, 2007 M. Kuriki, Positron Source for Linear Colliders, 2nd ILC School Erice, 2007 T. Omori, ERL Compton scheme for CLIC, 4th "ILC/CLIC e+ studies" webex meeting  R. Chehab, POSIPOL2009 Summary, 5th "ILC/CLIC e+ studies" webex meeting  J. Clarke, The Positron Source, TILC’09 AAP Review, Tsukuba, April 2009 POSIPOL2009 workshop, Lyon June 2009,  http://indico.cern.ch/internalPage.py?pageId=1&confId=53079 V.E. Balakin , A.A. Mikhailichenko, Conversion system for obtaining highly polarized  electrons and positrons, INP 79‐85

11. synchrotron radiation & damping

L. Rivkin

L. Rivkin

L. Rivkin

Julian Schwinger mastered the trade of classical  electrodynamics in his wartime efforts on  microwave propagation at the MIT Radiation  Laboratory, work which had a direct bearing  on highly effective new radar techniques (later) he continued ..., and showed that  synchrotron radiation contains many higher  harmonics, extending into the visible range.  In 1949, shortly after his monumental papers  on relativistic electrodynamics for which he  went on to receive the 1965 Nobel Prize, he  published another elegant masterpiece ‐ 'On  The Classical Radiation of Accelerated  Electrons'

heuristic description narrow angular spread

G. Margaritondo, EPFL Lausanne

peak wavelength in e‐ frame related to cyclotron motion

G. Margaritondo, EPFL Lausanne

eB v' = 2πγm0

γeB v' = 2πm0 2πcm0 λ'= 2 2γ eB

cyclotron frequency in lab frame

cyclotron frequency in e‐ frame

peak emission in lab frame after Doppler shifting

G. Margaritondo, EPFL Lausanne

Synchrotron radiation effects cCγ E 4 Pγ = 2π ρ 2

synchrotron radiation power

re 4π Cγ = 3 me c 2

(

energy loss per turn

)

3

= 8.8460 × 10 −5

m GeV 3

ds U 0 = ∫ Pγ dt = ∫ Pγ c E[GeV] 4 U 0 [keV] = 88.46 ρ [m]

photon energy & flux

M. Sands, H. Wiedemann

8 uc , 15 3 15 3 Pγ

u = N& =

8

uc

u2 =

11 2 uc 27

3 γ u c = hc 2 ρ

3

critical photon energy

Damping – classical phenomenon reference point in phase space

ΔE ⎞ ⎛ , z ⎟ = (0,0,0,0,0,0 ) ⎜ x, x ' , y , , y ' , δ = E ⎠ ⎝

damping occurs for all six degrees of freedom Pγ = f (E ) dE and τ damped because transverse damping radiation carries transverse momentum away, but rf-system restores only longitudinal momentum Pγ damping decrements α x, y = x = A x β x cos [ω β , x t ]

Robinson criterion: M. Sands, H. Wiedemann

2Es

αx +αy +αz = 4

Ax = Ax , 0 e −α xt Pγ Es

Excitation – quantum effect quantized emission of photons gives rise to growth of energy spread

dAs2 dt

∞

s ,excitation

= ∫ u 2 n(u )du = N& u 2 0

transverse phase space: Sudden emission of photon with energy δE causes sudden change of reference orbit by Δ(s)δΕ/Ε

growth of beam emittances

M. Sands, H. Wiedemann

equilibrium in phase space yields final “emittance” dA 2 dt

with

+

dt

s ,excitation

Cq =

energy spread

bunch length

M. Sands, H. Wiedemann

dA 2

=0 s , damping

55

hc −13 = 3 . 831 × 10 m 2 32 3 mc

⎛ σ E2 ⎜⎜ 2 ⎝E

σs =

2 ⎞ Cqγ ⎟⎟ = 2ρ ⎠

2π c

ω0

− ηE 0 σE heVrf cos φ s E 0

Equilibrium transverse beam emittance u u ; δx β' = − D ' E E

δx β = − D

2 2 1 ⎛ u ⎞ 1 ⎧⎪ 2 ⎛ ⎞ ⎫⎪ δA = ⎜ ⎟ ⎨ D + ⎜ βD'− β ' D ⎟ ⎬ 2 ⎝ E ⎠ β ⎪⎩ ⎝ ⎠ ⎪⎭ 2 x

2 x

dA dt

= s ,excitation

εx =

N& u 2 Hx E

s

2 0

C qγ

2

H /ρ3

1/ ρ 2

s

s

2 ⎫⎪ 1 ⎧⎪ 2 ⎛ 1 ⎞ with H (s ) = ⎨ D + ⎜ βD'− β ' D ⎟ ⎬ β ⎪⎩ 2 ⎠ ⎪⎭ ⎝

ε y ≈ 0.01ε x M. Sands, H. Wiedemann

wiggler – permanent or SC magnets enhance damping w/o adding much excitation SC wiggler  (CESR)

permanent‐magnet  wiggler (PETRA‐III)

Parameters of SC CLIC wigglers

BINP

Karlsruhe/CERN

Bpeak [T]

2.5

2.8

λW [mm]

50

21 or 40

Beam aperture full gap [mm]

20

24

NbTi

Nb3Sn

4.2

4.2

Conductor type Operating temperature [K]

Damping wigglers add horizontally deflecting wiggler with Nperiod periods and  sinusoidal field variation in a dispersion‐free section of the storage ring

β x,w 2 ρ0 3 1+ ϑw γ N period 15π ε x,0 ρ w ρ w ε x,w = ρ0 1 ε x,0 ϑw 1 + N period ρw 2 λp with ϑw = 2πρ w 4Cq

M. Sands, H. Wiedemann

Effect of radiation damping CLIC damping ring 0.12 ms

1.8 ms

Levichev (2007) 0.6 ms

2.4 ms

1.2 ms

3 ms

„ 3.6 ms

4.2 ms

4.8 ms

Damping to the stable resonance islands?

„

Including radiation damping and excitation shows that 0.7% of the particles are lost during the damping Certain particles seem to damp away from the beam core, on resonance islands

P. Piminov, E. Levichev, ESRF workshop 2008, and PAC’09

Recipe for small emittance choose beam energy; not too low (intrabeam  scattering etc), and not too high because natural  normalized emittance increases as (energy)3 design an optics with small value of H in the arc  dipole magnets ‐ “theoretical minimum emittance” add damping wigglers in the straight sections to  increase damping and further reduce emittance →emittances in light sources and linear colliders

vertical damping‐ring emittance Y. Papaphilippou, 2008

„ Swiss Light Source achieved 2.8pm, the lowest geometrical vertical emittance, at 2.4 GeV, corresponding to ~10nm of normalised emittance „ Below 2pm necessitates challenging alignment tolerances and low emittance tuning (coupling + vertical dispersion correction) „ “Safe” target vertical emittances for ILC and CLIC damping rings

horizontal emittance vs. energy

™ NLC

CLIC„ NSLS II

™ ILC

™

Z. Zhao, PAC’07

0.6nm @ 3GeV, including damping wigglers and IBS

normalized emittances at damping rings Horizontal Emittance (μrad-m) 0.1

1

10

100

10.000

30

Vertical Emittance ( μrad-m)

SLC 1.000

NSLS II scaled

0.100

CLIC 3 TeV

0.010

CLIC 500 GeV

ILC

ATF achieved

CLIC DR design

ATF Design

0.001

G.Geschonke, EPS2009 Krakow

SLS

References for Section  11 H. Wiedemann, Synchrotron Radiation in Storage Rings, Section 3.1.4 in Handbook of  Accelerator Physics and Engineering, A. Chao and M. Tigner (eds.), World Scientfic 1998 H. Wiedemann,  Electron Storage Ring, Turkish National Accelerator and Detector  Summer School, Bodrum, Turkey, 2007 M. Sands, The Physics of Electron Storage Rings – An Introduction, SLAC‐121, 1970 L. Rivkin, Synchrotron Radiation, ICTP School on Synchrotron Radiation and Applications,  Trieste, 2006 G. Geschonke, The next energy‐frontier accelerator ‐ a linear e+e‐ collider?, EPS HEP2009  Conference, Krakow, 2009 Giorgio Margaritondo, Synchrotron Light in Nutshell, EPFL Lausanne

12. intensity limits & beam stability

beam particles are like elephants…

• they have good memory • they won’t forgive you • easily perturbed and mistakes add up

… and they are not alone!

particles do not move independently; many of the limits of accelerator performance arise from interactions between beam particles = collective effects

intensity limiting phenomena • wake fields – beam break up in linac – single- or multi-bunch instabilities in damping ring

• “electron-cloud” effects (for e+ beams) • ion effects for (e- beams)

wake fields • the real vacuum chamber (beam pipe) is not a perfectly conducting pipe of constant aperture • a beam passing an obstacle radiates electromagnetic fields and excites the normal modes of the object • consequences: Instabilities! – – – –

beam loses energy energy can be transferred from head to tail of a bunch the head of the bunch can deflect the tail energy and deflections can be transferred between bunches if the high Q (quality factor) normal modes

• the wake fields characterize (“are”?) the beam induced energy losses and deflections

calculation by T. Weiland

emittance growth in linacs & linear colliders • 1st example of impact of wake fields • advantage of 2-particle model for getting insight single particle injected on axis travels down linac

if injected off-axis, quadrupoles surrounding linac → oscillation about axis cartoon - scales are not correct!

2nd particle follows 1st, wake from 1st deflects 2nd

deflected outward, amplitude grows amplitude of second particle (bunch tail) grows, effective emittance growth

multi-particle simulation by Karl Bane, large growth in effective emittance

possible solutions: 1. “BNS damping” (Balakin, Novokhatsky, Smirnov) 2. reduce wake fields (damping, detuning) BNS damping – analogy classical driven oscillator response

natural frequency

ωdrive=ωhead, ωnat=ωtail

ωdrive

if ωhead ≠ ωtail two effects : 1) response is reduced 2) initial tail oscillation beats with driven response

multi-particle simulation by Karl Bane, SLC with BNS damping

ω head ≠ ω tail can be achieved by : 1) rf quadrupoles (previous version of CLIC) 2) E head ≠ Etail (SLC)

instabilities in circular accelerators • stick with 2-particle model • head produces wake that acts on the tail WAKE FIELD of charge q/2 each TAIL

HEAD

• head and tail interchange due to synchrotron oscillations 1/2 T

Δγ/γ

Δγ/γ

TAIL

τ HEAD

s

later

TAIL

τ HEAD

result: synchrotron motion in ring gives stability below “threshold”

observations of electron cloud at various accelerators INP Novosibirsk, 1965

Argonne ZGS,1965

ISR, ~1972

BNL AGS, 1965

PSR, 1988

Bevatron, 1971

AGS Booster, 1998/99

KEKB, 2000

CERN SPS, 2000

electron cloud and ions where do the e- (or ions) come from? ¾ ionization of residual gas - collisional ionization ~ gas density, typical ionization cross section ~ 1 Mbarn, typically ~10-6 e-/ions per meter per beam particle - tunneling ionization in collective beam field if beam sufficiently small (ILC, CLIC, FFTB [5 GV/m])

¾ photoemission from synchrotron radiation - typically 10-4 - 1 e- (ions) per meter per part.

¾ avalanche build up via acceleration in the beam field - electron-cloud build up - pressure bump instability

secondary eδmax yield

R. Cimino, I. Collins, 2003

probability of elastic electron reflection may approach 1 For zero incident energy, independently of δ*max

electron cloud in the LHC

schematic of e- cloud build up in the arc beam pipe, due to photoemission and secondary emission [F. Ruggiero]

effects of electron cloud • • • • •

heat load (LHC), poor vacuum coherent tune shift 2γQs single-bunch instability ρ e,thr ≈ πβ y r0 C multi-bunch instability large incoherent tune shift → poor lifetime, emittance growth

electron-cloud effect – example KEKB e+ ring beam size

“threshold” residual growth below threshold beam current

multitude of countermeasures: • multi-bunch & intrabunch feedback (INP PSR, Bevatron, SPS, KEKB) • clearing electrodes (ISR, BEPC, SNS) • antechamber (PEP-II) • TiN coating (PEP-II, PSR, SNS) • high Q’ (SPS) • octupoles (BEPC) • solenoids (KEKB, PEP-II, SNS) • grooved surfaces (NLC)

effects of ions (on electron beam): • tune shift • incoherent tune spread • emittance growth in presence of dispersion • trapped-ion multi-bunch instability • fast beam-ion multi-bunch instability

critical ion mass

minimum gap

Acrit =

N b Lsep rp

2σ y (σ x + σ y )

Lg ,lc ≥ 10 ×

ion oscillation frequency

incoherent tune shift

required to avoid trapped-ion instability

c πf i

c fi = 2π

ΔQion ≈

heavier ions are trapped between bunches

⎛ ⎞ 2QN b rp ⎜ ⎟ ⎜ AL σ (σ + σ ) ⎟ y ⎠ ⎝ sep y x

N b nb reC

π

(γε x )[γε y ]

1/ 2

⎛ σ ion p ⎞ ⎜⎜ ⎟⎟ ⎝ k BT ⎠

trapped‐ion instability seen in SLC Damping Ring time dependence of  amplitude of 13f0‐fβ vertical sideband  during a 16.6 ms  store at the SLC DR  with only two  bunches under poor  vacuum  conditions   in 1996; two tall  peaks are injections; irregular bursts  correspond  to the  ion‐driven  instability 

fast beam-ion instability single-pass: fast beam-ion instability (FBII)

τ FBII 2

γσ yσ x ⎛ k BT ⎞ 8 ⎛ σ f ⎞ ⎜⎜ ⎟⎟ ⎜⎜ ⎟⎟ ≈ N b nb cre β yσ ion ⎝ p ⎠ π ⎝ f i ⎠ i

simulations confirm analytical estimates CO ions are cleared in CLIC inter-train gap > 3 m

H ions are overfocused within the CLIC train

in CLIC with a gap of 7.5 m few ions are accumulated from train to train; the average gap is >70 m! central CO ion density

transverse H ion distribution during single CLIC train passage: some ions re-stabilize at large amplitudes and so could contribute to beam instabilities

W. Bruns

Ion Effects in ILC and CLIC Damping Rings 2006 parameters, average CO pressure 0.2 ntorr

Potentially serious issue for ILC damping rings. At realistic CO pressure values of 0.1-0.2 ntorr, ion-induced tune shift approaches integer values, and exponential fast beam-ion instability rise time is about 1 turn. For CLIC, ion effects appear more benign, with tune shift of a few 0.001 and rise time of a few hundred turns. Possible solution for ILC is to split the beam into about 100 trains separated by large gaps of 20-100 m in length each. Simulations also suggest that some ions which are overfocused during a bunchtrain passage may not be lost but instead form an ``ion cloud'‘.

References for Section  12 R. Siemann, Accelerator Physics – Wakefields, Impedance, Collective Effects and  Instabilities, SLAC SLUO Lectures,1998 K.‐H. Schindl, several CERN lectures on space charge and collective effects in  accelerators F. Zimmermann, Collective Effects in Particle Accelerators, Turkish National Accelerator  and Detector Summer School , Bodrum, Turkey, 2007 F. Zimmermann, W. Bruns, D. Schulte, Ion Effects in the Damping Rings of ILC and CLIC,  EPAC’06 Edinburgh C.L. O’Connell, Plasma Production Via Field Ionization, PhD Thesis, Stanford U, 2005

13. beam delivery

beam delivery functions • demagnification to small spot size and  collision with opposing beam • removal of beam halo and detector  background control • machine protection • ε diagnostics, correction & IP tuning • preservation of beam quality • beam disposal

final focus chromaticity δ0 δ=0 Δσ *y

σ *y 0

spot size increase due to  (uncorrected) chromaticity, with δrms~0.1‐0.3%

= ξδ rms

σ *y 0 ≡ β y*ε y

ξ FF = ∫ [KQ − DKS ] β sin (ϕ y, IP→s ) ds 2

IP

chromaticity in selected FF systems project

status

βy* [mm]

L* [m]

L*/βy* 

ξy

σy* [nm]

SLC

measured

2.0

2.2

1100

6000

500

FFTB

design

0.1

0.4

4000

17000

60

FFTB

measured

0.167

0.4

2400

10000

70

ATF2

design

0.1

1.0

10000

19000

37

ATF2 pushed

proposed

0.05

1.0

20000

38000

σy

classical and quantum SR regime • If “upsilon” parameter