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Submitted on 1 Jan 1979
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NUMERICAL SIMULATION OF NITROGEN
DISCHARGE : FORMATION OF ELECTRON SHOCK WAVE
I. Abbas, P. Bayle
To cite this version:
I. Abbas, P. Bayle. NUMERICAL SIMULATION OF NITROGEN DISCHARGE : FORMATION OF ELECTRON SHOCK WAVE. Journal de Physique Colloques, 1979, 40 (C7), pp.C7-265-C7-266.
�10.1051/jphyscol:19797130�. �jpa-00219103�
JOURNAL DE PHYSIQUE CoZZoque C7, suppllment au n07, Tome 40, JuiZZet 1979, page C7- 265
NUMERICAL SlMULATION OF NITROGEN DISCHARGE : FORMATION CF ELECTRON SHOCK WAVE
1. Abbas, P. Bayle.
Centre de Physique Atomique, .Laboratoire associd au C.N.R.S. n0277, Universitl Paul Sabatier, 31 077 TaZouse Cedex, Frame
The formation and propagation of ionizing wa- ves in a gas discharge under pulsed electric field
-0
i s essentially governed by the space charge field $( x ) i s a function that takes into consideration the that super imposes the applied field E geometrical factor and the secondary effects.
0'
We a i m to investigate the effect of certain pa-
Davies (2) has shown that the numerical solu- . . r a m e t e r s , namely the reduced field E /P and plas-
o tion of this system was improved by making use of m a initial conditions, on the structure of the r e s u l -
the continuity equations for the net charge. The sys- ting ionizing wave, and particularly on the forma-
tem was solved by the method of double characte- tion of intensive local gradient f o r both the electrcn
ristics for both average and high overvol- densities and field. This turns to be evident a t the
tages()lOO %). T o investigate the disch:rge a t high discharge tip and i s a characteristic of the shock
overvoltage, the system was solved for the only - effect. It i s found that the shock formation i s not
part of the gas including the discharge perior to only related to the conditions of gas p r e s s u r e and the
shock formation. This procedure permitted the use applied electric field but it depends also upon the
of smaLler space increments leading to increased spatio-temporal distribution of the initiating prima-
precision and stability without any increased com- r y electrons.
putin'g time. The boundary conditions for the catho- The one dimensional continuity equations des- de were left inchanged while those for the virtual cribinp the ionization growth a r e
The calculation of the resulting space charge
anode, assumed a t distance x = d/4 o r d/8 were ne(x , t)=n+(x , t)=0. The field outside the dischar- ge region i s assumed equal to the applied field E
0'
and hence we a r e led to the condition
- -
field in a filamentary discharge i s calculated by the . We investigate the influence of the initial conditions method of discs (1). The boundary conditions on the on the evolution of the discharge and paiticularly electrodes a r e the following : on the formation of the electron shock wave. The
= - e , o a t the cathode x=O time function of the primary electrons liberated by
- a% -z- at the anode x=d the ultraviolet hight flash from the cathode I (t)
A 2 0
On the other hand, n (d, t)=O on the anode s u r - was simulated a s I (t)= - exp(-t / T ~ ) and the com-
t 0 T
face i s implied by the condition I + (d, t)=O for a con- putation was c a r r i e d out for different values of t$e tinuous analysis of the discharge, but for a numeri- parameter T , representing width of the UV flash.
cal analysis time and space discretisation introdu- We have studied the discharge in nitrogen un- ced a better conditionn(d,t+bk)=~?d,k]+~~dt~~-yb,t] d e r homogeneous applied-field created by plane pa-
+ a
which improves both the stability and precision of r a l l e l electrodes distance 3 cm apart. The elec- the numeric solution. The boundary conditions f o r tron cloud i s evolved in three successive phases the electronic c u r r e n t on the cathode surface i s (fig. 1). In the f i r s t phase the space charge effect i s negligible and the electron cloud conserves i t s
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19797130
gaussian profile, In the second phase, the space c h a r g e effects a r e m o r e important and the field bet- ween the e l e c t r o d e s i s non uniform. One o b s e r v e s a n enlargement of the e l e c t r o n cloud towards the e l e c t r o d e s . T h e cloud l o s e s i t s gaussian profile.
~ a k i n ~ into consideration the r o l e of the e l e c t r i c field,both velocity and amplification a r e not the
s a m e for a l l points of the profile with the r e s u l t of deforming p r o g r e s s i v e l y the profile. The e l e c t r o - nic density gradient i n c r e a s e s to end towards the shock conditions. T h e following i s a r a t h e r rough explanation for this evolution. If one c o n s i d e r s a profile of e l e c t r o n density and a r e p a r t i t i o n of the field a s defined on fig. 2 , f r o m equation (1) and.(2), the e l e c t r o n density a r e a nl i s moving towards both cathode and anode with following speeds
L
v , z % ( % / ~ + q I v,C= Y . ( o [ ~ I L - I )
V i s the d r i f t velocity, f i r s t Townsend coefficient in a field n e a r to applied field E T h e peak of e -
0'
l e c t r o n density n2 is moving with following veloci- ties
cL u,v, -9.v.
5: c- N,V& -a,v,
k + V r J, - k - "2
T h e r e s u l t i s that v2\ Vt and v~>v: which
yields an important modification of the wave profi- l e ending by a s t r o n g shock wave ( s e e fig. 3). It i s found that the shock effect i s much m o r e s t r o n g on the e l e c t r o n i c density level than that of the e l e c t r i c field where the variation i s l e s s s e v e r e . T h u s one can v e r i f y only partially the Albright hypothesis(3) which i s r e a l i s t i c a s much a s concerning the e l e c - t r o n density but l e s s r e a l i s t i c a s concerning the r e s u l t a n t e l e c t r i c field. T h e appearance of a shock wave i s highly conditionned by the profile of the e - l e c t r o n cloud and that is why i t i s v e r y sensitive for the function I (t). T h i s function implies d i r e c t l y the s a m e number of the cathode emitted e l e c t r o n s for different e l e c t r o n avalanche profiles. Fig. 1 shows the propagation of the m a x i m u m of e l e c t r o n densi- ty a s function of the UV flash width m e a s u r e d by T until1 the formation of the shock. It is c l e a r that the shock development is m o r e f a s t foP n a r r o w e r f l a s h e s and for higher E P values. We observed
0
the s a m e shock conditions f o r high overvoltages only few nanosecondes a f t e r the application of the high voltage pulse.
I
80 loo 1 2 ~ tins) J
Fig. 1. Propagation of the maximum electron
~ ~..
density with r e s p e c t to width of the UV flash.
Fig. 2. Schematic d i a g r a m of electron cloud and field profile.
L o g t n , )
F i g 3 Characterisation of electron shockwaves E /P = 53 V:cm. t o r r ; P = 200 t o r r .
0
(1) Davies (A. J . ) , Evans (C. J . ) : P r o c . I E E , vol. 114, n o 10, 1547-1550, (1967).
(2) Davies (A. J. ), Evans (C. J. ), Woodison (P. M.) P r o c . IEE, vol. 122, n o 7, 765-768, (1975).
(3) Allbright (N. W. ), Tidman (D. A. ) : Phys.Fluids, vol. 15, n o 1 , 86-90, (1972).
