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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.

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