Jun 26, 1991 - Naval Research Laboratory. Washington, DC 20375-5000. AD-A237 ..... Harry Diamond Laboratories. Department of the Army. 2800 Povder ...
Naval Research Laboratory Washington, DC 20375-5000
791 AD-A237 iiI 1i 11 11111
NRL Memorandum Report 6783
il IN!i 111ll1 111
Further Investigations Using the NEUTRAL Code JOHN M. LES AND ROBERT E. TERRY
Radiation Hydrodynamics Branch Plasma Physics Division
June 26, 1991
80This research was sponsored by the Defense Nuclear Agency, under Subtask Code and Title: RL RB/Advanced Technology Development, Work Unit Code 00079, MIPR No. 89-565.
91-04315 Approved for public release; distribution unlimited
REPORT DOCUMENTATION PAGE
I
Form Approved OMB No 0704-0188
Publ, repoting burden for this colleClion of infornation iqestimatel to average 1 nour oer resoorse. -cu in - 'e time fOr reviewing instirmotns earcnhng e-uting data sources gathering and rnantaining the data needed, and comofeling an reewi,, g the collection Of information Send comments regarding this burden esimate or any other a Of this oec colle> wo/qE, where q is the ion charge, E is the magnitude of the electric field, and wo is the "cut off energy" of the charge-exchange cross section (see equation (1)), spatial effects are unimportant. It is only when xo - wo/qE or less that spatial effects become appreciable. For w o = 10 Key, q = 4.8 x 10-10
cm.
Thus one
can
see
from
esu
and
this
E = 1 MV/cm, we find that xo
example
that
-
0.01
if one knew the charge-
exchange cross section with reasonable inside the charge-exchange region, then
accuracy, and the electric field by measuring the average neutral
energy one could estimate the
of
thickness
the background neutral gas or
anode plasma (see memol).
Time Rising Electric Field The NEUTRAL code
has
also been modified to simulate a linearly rising
electric field in time, in the
charge-exchange region.
The time dependent
electric field E(t) is assumed to have the form
E(t)
-
(dEt dt
(6)
and t is the time in seconds. The quantity dE/dt is a constant and is just the slope of the time varying electric field. This modification to the NEUTRAL code is important since the electric field inside the anode plasma of the reflex switch is not
static,
as
assumed
in memol.
Thus we can
estimate the average energy of a neutral as it enters the vacuum gap (see memol again for more details) as a function of time. At this point we would like to mention that a time rising electric field is only one part of the entire physical picture and this report. The NEUTRAL code was run equation (6), with
4
will with
be
discussed later on in this the electric field, given by
d-
=
statvolt7
7.335681 x lol
and one half this value, namely
()
= dt 3.667841
x 10l
statvolt cm sec
The first value of dE/dt was chosen the electric field had the
final
(8)
such that at the end of the simulation value of 3333.3333 statvolt/cm, which is
just the electric field used in the reference run of memol. Also the background neutral gas and the charge-exchange cross section were assumed to be constants in these simulations,
with
the same values as used in the
formerly mentioned reference run. This makes comparison with a simple analytical model possible. We note that this time varying field version of NEUTRAL also uses an improved particle
pusher
simulation using the
given
results are given
value
by
the
of
dE/dt
circles
and
algorithm. by
the
dashed
approximate best line fit, extrapolated to zero this data.
The solid line, with
equation
Figure 5 is the (7).
straight
The code line is an
energy, at time t = 0., to
the dagger point markings, is the plot of
the equation
(t)
=
(qE(t)X)[
(
L max
)(e- (Xmax (x
/X) /X1
+ (9)
where (t) is the average neutral vacuum gas interface, or x = electric field given by (equation (15) of memol,
xmax.
equation but
energy
with
as
a function of time at the
E(t) is of course the time dependent (6). the
Note
that
equation (9) is just
static electric field replaced by
E(t). This substitution, though somewhat questionable, should be valid if the electric field rises so slowly over time that the system goes through a succession of equilibrium states,
i.e.,
5
the problem is quasirtatic.
As
one can see from figures 5 and 6, this does not seem to be a too bad of an assumptic,.
Figure 6 is the same
by equation (8).
This case was
the simulation results to
situation except that dE/dt is now given run
to see if a smaller dE/dt would cause
approach
the
expression given by equation (9).
As one can see the code predicts nearly
the
equation (9),
accuracy
but for later
figure 5, roughly ±3 Kev. in figures 5 and 6 is
times
the
same energy at t = 2.27 ns as is
about the same as in
To determine if the difference in slopes as seen
caused
by code inaccuracies, we plotted the average
neutral energy as a function of electric
field, as given in figure 7.
The
code generated results are given by the circles, and as in figures 5 and 6, the dashed line is an eyeballed
best
line fit, extrapolated to zero.
The
solid curve is the analytical result,
at
in memol, see also equation (9).
also would like to point out, before
we continue, that the neutral running the static electric was done in memol. the
time step,
energies field
which
statvolt/cm, or the
problem
figure 4
about
7 we see that, for a fixed Kev at E = 3.333 x l03
These
differences in energy may be due to certainly the case when E = 6.666 x 103
is
the time step used,
the simulation were found by
for different field strengths, as
to by
differ
encrgies
from
case
Referring again
statvolt/cm, which is 1 MV/cm.
NEUTRAL code.
We
x = xmax, given by equation (15)
may
be
due
to
the
particle pusher in the
Anyway we can be reasonably confident that the difference in
slopes that are found in both figures 5 and 6 can be attributed to the code numerics and not some physical process.
Time Rising Current Density
As
was
mentioned
earlier,
the
inclusi n of a time varying electric
field, though very informative,
is
problem.
field
Usually
an
electric
current, this can be seen from
the
only in
simple
half a
of the full time dependent plasma
is
accompanied by a
Ohm's Law, given by (in c.g.s.
units)
I
(10)
=
6
where J is the current density, E (scaler) conductivity, and the from this simple argument would result
in
a
is
arrows
that
a
argument, again using (10) would
=
reflex
current, see references 1
imply
-
a
current.
field,
4.
Now
assuming
problem must include a time
varying
we
From a computational
conductivity
helpful in
to
by
I =
, where n is
t
by
for the moment a uniform J
by J = I/A, where A is
that the full time dependent density
viewpoint,
if
in order to be more
we input a known linearly
field, this automatically determines equation
theoretically
(10).
determine
empirical formula for anomalous gap closure by Creedon et al. ,
to
current
electric
the resistivity or
6
given
one certainly observes a time rising
conclude
3
similar reverse
switch
So
trying
A
From the various measurements that
some cross sectional area.
and
We see
1/a.
related
rising current density
quantities.
time varying current density is
current density J, the current I is
realistic.
vector
rising electric field in time
rising
electric
called the resistivity and n have been done on the
denote
linearly
proportionally
related to a time evolving
the applied electric field, a is the
the
This could be very value
of
K
in the
in the reflex switch, as given
This formula has the form
1
3 t
=
(11)
K DAK
with =
dJ dt
-
a constant
where 3 is the time rate of
change
of
primary gap shorting time, with
DAK
memol for a
reflex
diagram
of
the
the current density
being
the
switch.
and ts is the
primary gap spacing. At
this
See
point in time
preliminary work has been done to model the effect of a time rising current density and will be the subject of future reports.
7
Sumawry and Conclusions We have used
NEUTRAL code to simulate the charge-exchange neutral
the
al.1 .
problem as discussed in Prono et.
width of the
gas
background
also
was
study
A parameter
the two results.
There was good agreement between
found Lhe corresponding average
and
region
run in which we varied the
We concluded that such parameter study would be beneficial
neutral energy.
We have also modified
in determining the width of the anode plasma region. linearly
time
an
analytic
expression
compared these results
to
replacing
the
electric
comparison
of
agreement.
It does seem
static the
code
rising electric field
and
the
causes
with
the
analytical
which time
was derived by
varying
expression
We
one.
A
showed limited
from the code results, a linearly
that,
howev,
noticed
energy. It was also
field
electric field.
rising
a
handle
the NEUTRAL code to
a
similar
that
by
increase
varying
the
in the average neutral electric field in the
static case, NEUTRAL predicted lower than predicted average neutral energies. This may be caused by not choosing the correct time step or may even be the
fault
of
particle
the
pusher,
this should be investigated
further.
Future Vork
We
are
beginning
density, since such a
to
work
problem
operation of a reflex switch.
on is
Such
the a
more
problem of a time rising current accurate representation of the
a simulation will provide useful input
to future models describing the shorting of the vacuum gap.
Acknowledgements
One of us, J.M.L.,
would
like to thank Jim Geary for his encouragement
and suggestions during this project.
This work was sponsored by the Defense Nuclear Agency.
REFERENCES
1.
D.S. Prono, H. Ishizuka, E.P. Lee, B.W. Stallard, o"id W.C. Turner, J. Appl. Phys. 52, 3004 (19P1).
2.
J.M. Cree in, L.J. Demeter, B. Ecker, C. Eichenberger, S. Glidden, H. Helava, and G.A. Proulx, J. Appi. Phys. 57, 1582 (1985).
3.
3.S. Levine, J.M. Creedon, M. Krishnan, K.D. Pearce, and P.S. Sincerny, 7th Conference on High Power Particle Beams, Karlsruhe, July 4-8 (1988). TInternational
4.
L.J. ?meter, in Opening Switches, ed. by, A. Kristiansen, and T. Martin, (Plenum Press, N.Y., 1987).
5.
N.R.L. Memorandum Report (to be published).
6.
J.M. Creeaon, Private Communication.
7.
R.A. Mapleton,
Theor-y
of
Guenther,
M.
Charge Exchange, (Wiley, N.Y., 1972), pgs.
210, 214.
9
C
q6
>
Tq i
N
/
u-14
'-ix
-
__ ; *c
I
3.
4
,____-
____
_1
-
( )
Ox IC ' -
-ol
X
6 ,, 1 D "q x ~)jli
E
22C' C i
6'
4
/
-/
Iq
?~i 1 16
-
12X 1oll
0
c0
.02
.03
oq
.05
.06
.07
.08
x (cm)
Ion Flux as a Function of x Figure1
10
.09
.10
NE UT.
TM:CE-G
Y
I
I C
I
FLU-X V
E/
L 4-A
zI
0
0
.01
.02
.03
.04
.05
.06
.07
.08
.09
x (cm)
Neutral Flux as a Function of x Figure 2
.10
,,
.
