ELECTRON SWARM HAVING AN ANISOTROPIC VELOCITY DISTRIBUTION FUNCTION

HAL Id: jpa-00219190

https://hal.archives-ouvertes.fr/jpa-00219190

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 SWARM HAVING AN ANISOTROPIC VELOCITY DISTRIBUTION FUNCTION

T. Makabe, T. Mori

To cite this version:

T. Makabe, T. Mori. ELECTRON SWARM HAVING AN ANISOTROPIC VELOCITY DIS- TRIBUTION FUNCTION. Journal de Physique Colloques, 1979, 40 (C7), pp.C7-43-C7-44.

�10.1051/jphyscol:1979721�. �jpa-00219190�

JOURNAL DE PHYSIQUE Colloque C7, suppZ6ment au n07, Tome 40, J u i Z l e t 1979, page C7- 43

ELECTRON SWARM HAVING A N ANISOTROPIC VELOCITY DISTRIBUTION FUNCTION

T. Makabe, T. Mori.

Department of EZectricaZ Engineering, Faculty o f Engineering, Keio University, Yokohama, Japan.

INTXODUCTION gradient along the field direction ( z axis ),

In recent years there has been a renewed we find the integrodifferential equation interest in the velocity distribution for go , S , ^and g2 .

function of electrons in weakly ionized

v4NQm -

BF

3m I

gases. In this report we present the theoretical analysis of the electron swarm in a relatively high E/N, considering an anisotropy of the distribution function.

The present developed theory is applied to ₊ ^L _,Iv a

'+'

7

the electron swarms in neon.

BASIC THEORY

m v 1 2

+ / g Q T / N U . (v',v,w)dQdv'

v+vi a I

v-vr

The Boltzmann equation for the velocity - / gov / 2 ~ a ~ ( v , d , w ) d v ' d Q (3)

51 0

distribution function g(~,v,t) of electrons

In equation ( 3 ) , the first square bracket moving through a slightly ionized gas under

represents a divergence in velocity space, the influence of a uniform electric field _E

and the second square bracket shows a divergence 'in position space. The rest of where v is the electron velocity, e the theright side show the terms ofthe inelastic electronic charge, m the electron mass, collisions including ionization.

and J (g) the collision integral. Here, we may estimate g2 as We express the distribution function in the

form of the first three-terms of the

In these circumstances, the electron swarm spherical harmonic expansion in order to

is subject to a continuity equation oE the make clear the anisotropy of the funceim2

form 3 ~ 0 . 3 ~ - 1

g ( ~ , ~ , t ) = g o ( P , v , t ) + g l ( ~ , v , t ) o ~ ~ ~ e + g 2 ( P, v, a. a a

- _an -

-

vc

where go is the isotropic part of the

a ³

- =( D 3 ( z , t ) n ( z , t ) ) + v i ( z , t ) n ( z , t 1 ( 5 1 distribution function, gl andg2 the first

and second anisotropic parts, and e ^{the where c3}

D =

D o - ~ J e s n ~ LAB),,-(_

o m

I a v 4 2 1

1 4*

(2) is inserted into the equation (1) under

= (D ) = - ^--;

0 T 3 O N %

the condition of one dimensional spatial

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1979721

RESULTS and DISCUSSION

Theelectronenergydistribution functions in neon are computed from thepresent theory in a range of E/N from 141.3 to 1130 Td for a steady state condition. Figure 1 and 2 show each term of the energy distribution

4 *

functions

fR

The swarm coefficients derived from the present distribution functions, especially,

longitudinal and transverse diffusion coefficients are exhibited in figure 3.

It is found that the gradual increaseofthe

ELECTRON ENERGY (eV)

Figure 1. Theoretical isotropic and anisotropic parts of the distribution function for E/N of 282.5 Td in neon

--

---

ELECTRON ENERGY (eV)

Figure 2. Theoretical isotropic and anisotropic parts of the distribuqion function for E/N of 706.3 Td in neOn

--

E / N ( T d )

Figure 3. Longitudinal and Transverse diffusion coefficients ifi neon derived from the present distribution functions.