THE ROLE OF SINGLE-STEP IONIZATION BY THERMAL ELECTRON-ATOM COLLISIONS

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THE ROLE OF SINGLE-STEP IONIZATION BY THERMAL ELECTRON-ATOM COLLISIONS

G. Golubkov, N. Kuznetsov, V.V. Yegorov

To cite this version:

G. Golubkov, N. Kuznetsov, V.V. Yegorov. THE ROLE OF SINGLE-STEP IONIZATION BY THER- MAL ELECTRON-ATOM COLLISIONS. Journal de Physique Colloques, 1979, 40 (C7), pp.C7-89- C7-90. �10.1051/jphyscol:1979744�. �jpa-00219443�

JOURNAL DE PHYSIQUE CoZZoque C7, suppl6ment au n07, Tome 40, JuiZZet 1979, page C7- 09

THE ROLE QF SINGLE-STE P IONIZATION BY THERMAL UECTRON-ATOM COLLISIONS

G.V. Golubkov, N.M. Kuznetsov, V.V. Yegorov.

I n s t i t u t e of Chemical Physics, Academy of Sciences, Moscow, U.S.S.R.

The rekombination coefficient of the reaktion A

+

e- -+ A'

+

e-

+

e-had been calkulated in the diffusion approxi- mation in ref. [I]. Energy change by an elastic collision of electrons is not cha racterised by a small parameter (mass ra-

tio), The value of the ionisation rate constant (IRC) is mainly conditioned by bound elektron motion in energy region

lL I -T (T is temperature).fn this energy region the average square of energy

change per one elektron-elektron collisi- on <(&L)*> has the same order of magnitu- de as T 2

.

The diffusion approximation is correct if 4 (

&&I2>

/ T ~ C ~ 1. Nevertheless the diffusion approximation is qualita- tively true in the case

< ( 6 & 1 2 > / ~ 2 r

¹

too, However the diffusion theory fails within one diffusion step [c ( &€j2>

] ^%

near the boundary € = 0. In this energy region a single-step ionisation (SSI) plakes an important role. The SSI rate constant has a singularity at E = 0. Due to this singularity the distribution function

f (€1

is considerably smaller as

compared to the diffusion approximation result

f , (€1

in the region 1615 T. !Che IRC is obliged to change too.

The function +(El for bound electrons is described by modified Pocker-Plank

B,,(E)- density of

states,<[^^]^> -

^avera-

ge square of energy change per one se

-

cond,

K(€I -

single-step IRC. In eq. ( 2 ) the term K(t)f$,~)describes SSI. In a low temperature plasma (T-1; I

-

^{the gro-}

und state ionisation ~otential) hydrogen- -like states of highly excited atom

( IElfT) plsy the predominant role. The density of these states is

3M(6j

= Z+

I & I - ~ / *

,

( 3 )

I w -

bydrogen ionisation potential, Z+

-

-

ion statistical sum. According to ref.

[ I ] the expression of 4 faa2> is

<14t)2>.# ,sjfieqm-%n~-hIej

,

A.

h

( ~ ~ + f ) " , (4)

e and m are the charge and the mass of electron, ~ e - - ion charge. For KILJ we have K(E(

= S sL

(€I

I

JIEI dE

IEl

(5)

G(E) -

SSI cross section from energy le- vel €

, v v= , RE) -

free elec- tron equilibrium distribution function.

So far there are notneitherreliable theoretical nor experimental data on SSI cross section of highly excited states, which play the important role in thermal ionisation. So it is only possible to evaluate the character of the dependense and the order of magnitude of

K&.

As it is seen from eq.(5) I ( ( € ) mainly depends on magnitude oQ

5

&)but not on the pe- culiarity of $ ( E ) as a function of i5

.

equation 123 r The simpliest estimation of

%

^{(E) can be}

- ~ ( d f ~ , , $ ) ,

(2)

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1979744

made by using the Thomson classical the- ory

[

31 :

5

(E)B

+

_'Ra,

^-z4

_E

^{(,$ - :) ,}

^{( 6 )}

Gm

-

the maximum SSI cross-section at

I E l

=In ,

^Qo -the Bohrradius.

The right part of eq.(2) can be exp- ressed as the divergence of the total current =

ii ⁺ ,

^where

i,

^and

j2

are the diffusion current and the SSI

current : E

- <(AE)~>ME~[Z ^+i), j2= JK

^{( f 7} ~ ( E Y g,,l&~l. (7)

dl- 2 a € T .r

- A

j

is equal to the rate constant if

Y

g =

^0. So we have to solve

-

dd' ⁼ 0 (8)

a t de

with the boundary conditions

f(o1 =

o,

f(-I)

= f/z ,

^{( 9 )}

-

atomic statistical sum.

The eq. (7)-'(9) together with (3)-(6) have been solved numerically. The functi- on f

(€1

has been investigated near 6 =O analytically also. The results for f/f, and for IRC are shown on fig.1 and fig.2 for several values of the parameter

6 1 Gm

d z - - - -

15 A T a t

-

On the figures

the following notation is used: X r l € l / ~

;

% W - & ( d ) / d 0

^;

jo

-rate constant for the d.iffusion approximation (see ref.[4J).

As it is seen (fig.1)

f

tc

f,

in the reg- ion

!&

!

2

T. mevertheless the increasing of

k

as compared to

j,

is rather small

(fig.2). So the diffusion approximation for

k

(but not for f ( € j at llld T ) is quite satisfactory in spite of the rela- tively grate diffusion step for the electron-electron collisions.

References

[I) A.V. Gurevich and 3.1. P.Pitaevskii, Zh.

Sksp. Teor. Biz. 46, 1282 (1964) [23 Yu.P.Denisov and N.M.Kuznetsov, Zh.

Eksp. Teor. Ez. 61, 2298 (1971) [3] D.R.Bates, Atomic and Nolecular Processes (Academic Press, 1 962) f4] N.M.KuB~~~sov, Combustion and Bxplo-

sion Phys. 5, 683 (1 973)

,

^USSR