MONTE CARLO SIMULATIONS OF ELECTRON DRIFT VELOCITIES IN THE NOBLE GASES AND THEIR MIXTURES

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MONTE CARLO SIMULATIONS OF ELECTRON DRIFT VELOCITIES IN THE NOBLE GASES AND

THEIR MIXTURES

A. Davies, J. Dutton, C. Evans, A. Goodings, P.K. Stewart

To cite this version:

A. Davies, J. Dutton, C. Evans, A. Goodings, P.K. Stewart. MONTE CARLO SIMULATIONS OF ELECTRON DRIFT VELOCITIES IN THE NOBLE GASES AND THEIR MIXTURES. Journal de Physique Colloques, 1979, 40 (C7), pp.C7-63-C7-64. �10.1051/jphyscol:1979731�. �jpa-00219300�

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JOURNAL DE PHYSIQUE Colloque C7, suppl&menl; au n07, Tome 40, JuiZZet 1979, pa@ C7- 6 3

MONTE CARL0 SIMULATIONS OF ELECTRON DRIFT VELOCITIES IN THE NOBLE GASES AND THEIR MIXTURES

A.J. Davies, J. Dutton, C.J. Evans, A. ~ o o d i n ~ s * , P.K. Stewart.

*Department o f Physics, U n i v e r s i t y ColZege o f Swansea, S i n g l e t o n Park, Swansea, SA2 8PP, U . K . U.K.A.E.A., W i n f r i t h , Dorset, U.K.

INTRODUCTION. where ^G-1 and u 2 a r e the respective cross-sections of

Mixtures of noble and molecular g a s e s a r e widely used the gaseous components. Then f o r each collision a in neutron counters under reactor conditions. However, random number R, uniform in lo, 1 , was generated, there a r e problems in their operation, concerned with and if R was l e s s than P the collision was taken to be

1

radiation, electron attachment and the electrodes,which with the f i r s t constituent, and if R was g r e a t e r than P1 could largely be overcome by the use of noble g a s e s

alone, provided a mixture with a sufficiently high drift velocity, t o give a n adequate counting rate, can be found 1

.

This problem has stimulated the investigation of drift velocities in noble g a s mixtures, the initial results of which a r e reported in this paper.

METHOD.

A Monte-Carlo method, originally developed in this Department by Thomas and Thomas2, was modified for use a t the low E/IV(-3Td) commonly found In neutron counters. The applied field was assumed to be uniform and the cross-sections f o r the various elastic, inelastic and ionization processes were taken from a number of source:-'.' In a l l simulations isotropic scattering was assumed and the step length was chosen to correspond to 0. 1 of the mean f r e e path. The initial electron energy was s e t a t 0. OleV and this was the minimum allowed energy of the electron during the simulation. In a l l calculations the gas molecules were assumed to be stationary and the p r e s s u r e was taken a s 1 torr. The mean energy

(c)

of the test electron was taken to be given by its time average and was assumed to be identical with the ensemble mean energy of the electron swarm. The electron drift velocity (W) was obtained from the gradient of the distance - time (z, t) graph.

In the c a s e of mixtures the probability of a collision with a given constituent was determined a s follows. If fl and f a r e the respective fractions of the two gaseous con- 2 stituents in a binary mixture (i. e. fl

+

f = I), then the

2

probability that any given collision involved the f i r s t constituent was taken to be:

p = fl "1 1 f l ~ + f

2 w2

then with the second.

RESULTS. -

Figure 1 shows a typical plot of z - ( y ) v s . t f o r Ar, using the NAG (Numerical Algorithms Group) random number package: G05AAF(Y) f o r E/N = 3.0341 Td (i. e.

-1 -1

E/p = 1 volt cm t o r r and T = 293K).

z-ki -

eE t

x ~ o - ~ S E C

Fig. 1. Monte-Car10 ^{( a )}simulation of electrons drifting in Argon a t E/N = 3 03Td. Experimental Drift

~ e l o c i t ~ ~ ~ 4.0 x 10 cm/sgc. 5

F o r clarity of presentation z

{ 's)

^,r a t h e r than z, i s plotted because this gives a curve from which the high frequency fluctuations a r e eliminated and f o r which the gradient is the same. A remarkably s i m i l a r curve was recently given in the literature1', where the 'breakaway"

in the upper part of the curve was attributed to runaway electrons occurring in the neighbourhood of the minimum in the momentum transfer cross-section. However, in the present study, it was found that, using the random number routine G05AAF(Y), breakaway occurred in a l l the noble g a s e s (including even the c a s e of a constant

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Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1979731

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cross-section, in He). This suggests that runaway electrons a r e not responsible. Other random number generators give different results s o that it i s possible that this effect is related to the random number routine.

However, one cannot come to any final conclusions about this because even in the most e x t r e m e cases the results lie within the possible spread of the z, t curves resulting f r o m diffusion. As in ref. 11 , good agreement was obtained, with the experimental drift velocity, using the relatively linear portion of the graph before breakaway.

Since drift velocities w e r e the prime interest in the present investigation, a random number generator was chosen which gave a long initial linear portion, of the z -(*)versus t curve, and such that the drift velocity computed from the gradient was in good agreement with the experimental value f o r He a t E/N= 3. 03Td.

The s a m e random number sequence, when used in He f o r the E/N range: 0.03

-

30.34Td, gave the results in Table 1. The e x p e ~ i m e n t a l values f o r the drift velocities4' l 2 a r e given f o r comparison and the calcul- ated mean energies a l s o tabulated. Good agreement with the experimental values of drift velocity 3,4,12, was also obtained in the c a s e of the other noble g a s e s : Ne, Ar, Kr and Xe, f o r the same E/N range, given in Table 1.

In a l l cases, approximately 8 x 10 elastic collisions 5 were recorded.

TABLE 1 HELIUM

E/N W(cm/sec) W jcm/sec)

-

E

Monte-Carlo Experimental eV

Results f o r the binary noble g a s mixture: He/Ar a r e shown in Figure 2 (again f o r E/N = 3.0341Td).

Fig. 2. Computed electron drift velocities f o r He/Ar mixtures a t E/N = 3.03Td.

It is seen that a maximum in the value of the drift velocity occurs f o r a mixture of 70% He with 30% Ar, the drift velocity in this mixture being 12% g r e a t e r than in helium alone. Further investigations of other mixtures a r e now in progress and r e s u l t s will be reported a t the Conference.

ACKNOWLEDGEMENTS.

The work presented in this paper was c a r r i e d out under a research contract financed by the United Kingdon:

Atomic Energy Authority. The authors would like to acknowledge the encouragement provided by the s t d f of C. & I. Division, AEE, Winfrith.

REFERENCES.

1. A. GOODINGS: "Experience with high temperature radiation detectors and cables f o r r e a c t o r

instrumentation systems"1AEA-SM-226/7, 1978. . 2. R. W. L. THOMAS and W. R. L. THOMAS: J. Phys. B.

(Atom. Molec. Phys):2, 562-570 (1969).

3. A. GILARDINI: ' ' L o w ~ n e r ~ ~ Electron Collisions in Gases: Swarm and Plasma Methods Applied to their Study". John Wiley and Sons (1 972).

4. L. G. H. HUXLEY and R. W. CROMPTON: "The Diffusion and Drift of Electrons in Gases". John Wile y & Sons (1 974).

5. T. ITOH and T. MUSHA : J. Phys. Soc. Japan: 15, -

1675-1680 (1960).

6. P. LABORIE, J-M ROCARD and J. A. REES:"Electronic Cross-sections and Macroscopic Coefficients.

1 -Hydrogen and Rare Gases" Dunod:Paris (1968).

7. H. S. W. MASSEY and E. H. S. BURHOP: "Electronic and Ionic Impact Phenomena", 2nd Ed. Vol. 1, Oxford University Press (1969).

8. Y. SAKAI, H. TAGASHIRA and S. SAKOMOTO: J. Phys.

B. (Atom. Molec. Phys. ):5, 1010-1016 (1972).

9. Y. SAKAI, H.

T A G A S H I R A ~ ~ ~

S. SAKAMOT0:J. Phys.

D. (Applied Physics):lO, 1035-1049 (1977).

10. R. W. L. THOMAS: Ph. Thesis, Physics Department, University of Wales (1 968).

11. H. B. MILLOY and R. 0. WATTS: Aust. J. Phys: 30,

73-82 (1977).

12. J. DUTTON: J. Phys. Chem. Ref. Data:

+,

^577-856

(1 975).