HAL Id: jpa-00219237
https://hal.archives-ouvertes.fr/jpa-00219237
Submitted on 1 Jan 1979
HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.
L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
ELECTRON ENERGY DISTRIBUTION FUNCTION IN Xe PLASMA IN THE PRESENCE OF COULOMB
COLLISIONS
A. Ershov, A. Kuzovnikov
To cite this version:
A. Ershov, A. Kuzovnikov. ELECTRON ENERGY DISTRIBUTION FUNCTION IN Xe PLASMA
IN THE PRESENCE OF COULOMB COLLISIONS. Journal de Physique Colloques, 1979, 40 (C7),
pp.C7-521-C7-522. �10.1051/jphyscol:19797252�. �jpa-00219237�
JOURNAL DE PHYSIQUE CoZZoque C7, suppzdment au n07, Tome 40, JuiZZet 1979, page C7- 521
ELECTRON ENERGY DISTIUBUTION FUNCTION IN Xe PLASMA IN THE PRESENCE CF COULOMB COLLISIONS
A.P. Ershov and A.A. Kuzovnikov.
Physics Department, Moscow State University, Moscow, U. S . S. R.
Ionization degree o< positive column t i c cross section from /2/ and of ioniz- plasma i n n o b l e g a s e s i s u s u a l l y e q u a l t o i n g c r o s s s e c t i o n f r o m / 6 / ; energydepen- 70'~ - and depending on value of E/p, dence of exitation cross section is given
( e l e c t r i c f i e l d t o pressure r a t i o ) the i n by
fluence of coulomb collisions on plasma $(v) = i. 8. .i6 (7~- 8.3)
characteristics can be considerable /I/.
However the role of t h i s factor f o r Xe has been investigated neither experimental l y nor theoretically.
E a r l i e r calculations /2,3/ performed without coulomb collisions made it possib- l e t o correct the energy dependence of e l a s t i c collision cross section f o r e l e c t rons i n Xe and t o discribe the ,dependence of the d r i f t velocity and of the r a t i o of the diffusion coefficient t o the mobility
In collision integral elaseic elect- ron-atom , electron-ion , electron-elect- ron collisions and exited and ionizing collisions were taken into account. Ener- gy losses a t i n e l a s t i c collisions was assumed t o be equal t o the threshbld of i n e l a s t i c process.
The kinetic equation i s solved by i t e r a t i o n method allowing nonlinear integ ro-differencial equation traasform t o linearized recurrent dif f erencial equati-
/& on value E/p f o r an coefficient L3e
= -{fi,
~ / p , s 7 0 V/cm torr. However calculated values of the f i r s t Tomsend ionisation coefficient d are 4-6 times larger than experimental ones /4/. This means t h a t electron distribution function i n inelas- t i c region i s determined with conciderable error connected with e r r o r i n i n e l a s t i c cross section. Since the error i n e x i t a t i - on cross section is more greater than er- r o r i n ionizing cross section the e x i t a t i - on cross section was corrected t o provide the agreement be tween calculated and erne- rimental data f o r an E/p, i n the range
with boundary conditions
y . ( o ) = i y,(4)=0
and with norm l i z a t i o n requirement
c ffi g ( y ) d w = l
Here n - is i t e r a t i o n number. Energy sca- l e is chosen i n accordance with cnndjtion
y,(d) = 0. This extremely task i s solved
by economic method /7/. The coefficients
KxO, %XI. Z ( x ) a n d $ x ) Were formed w i t h method requirements. I t e r a t i o n s had been performed u n t i l the difference between value of E/p, determined from balance from 20 t o 30 V/cm t o r r . A t these values equation ee- ex
LeeE/p, electron distribution has c~nsiderab- I/UF L C = & < v . /CI v s + < v bx;+<v>~ye
l e value up t o V .r< 20 eV when ext;rapolati- and requirement value became smaller 1%.
on mistace i s not a c h but ionizing cross Calculation r e s u l t s are given i n section is measured with good precision. Pig.1 - 4. Pig.1 schows examples of calcu-
Electron distribution was calculated l a t e d electron energy distribution using energy dependence of electron elas- f o r various values E/p and 3 .
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19797252
r I
I I l I0 5 10 15 20 25 v,e~
Fig.1 Electron energy distribution functions in Xe at various E/p and ioniza- tion degrees.
10-"L
70 20 30 40 50 E/p,V/cm torr
~ i g .2 ~ i r s t Townsend ionization
coefficient at various ionization degrees.
One can see that coulomb collisions increase the number both a slow and fast electrons. Significant increase of' the number of fast electrons with increasiag ionization degree
J )results in rapid increase of Townsend coefficient for E/p 3 10 V/C~ t0rr /Fig.2/. Electron dist ribut ion deformation at low energy results in strong depending of electron mobility on ionization degree /Fig.3/. This effect would be more strong without. electron-ion collisions exerting influence on mobility for JI L 1 04. Whereas man electron energy depends relatively weakly o n ~3 .over a wide range of E/p and of ~3 /Fig.&/.
However 4. Ju, ratio increasing E
4 '
signif ican l y at smallf depends on 3
much strongly keeping nevertheless differ
- 1 0 ~ 10-5 lo4 10-3 g
Big.3 Electron mobility coefficient as a funotion of ionization degree at various E/p .
ence from < even at 9 -10-3.
Results of calculation show that coulomb collisions in Xe plasma should be taken into account.
References
7, .R.Winkler Beitr, P1. Phys. 12,317,1972.
2. L,~rost,A.Phelps Ph, Rev.l36,A1538,1g64.
3 . S.FYau,AoRutscher An.Ph~?s. 22,166,1969.
4. S.Pfsu,H.Scheibner %it ,P1. 9,425,1%9, 5. Y.Schaper,X.Scheibner B.I?l. 9, 45,1969.
6. D.Bapp, P.Englander-Golden J . Ch.Pbys.
43,1464,1965.
7.A.A.Cabiapc~Etl T e o p ~ s pa3~ocarrm cxeB lil. 19'77.
1 - --' 4
I I I t
