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THE COMPOSITION OF THE POSITIVE COLUMN OF A HELIUM GLOW DISCHARGE AT
INTERMEDIATE PRESSURES
F. Dothan, Yu. Kagan
To cite this version:
F. Dothan, Yu. Kagan. THE COMPOSITION OF THE POSITIVE COLUMN OF A HELIUM
GLOW DISCHARGE AT INTERMEDIATE PRESSURES. Journal de Physique Colloques, 1979, 40
(C7), pp.C7-127-C7-128. �10.1051/jphyscol:1979762�. �jpa-00219468�
JOURNAL DE PHYSIQUE
Colloque C7, suppl6ment au n07, Tome
40,JuiZlet
1979,page
C7-127
THE
COMPOSITION
OF THE POSITlVE COLUMN OF A W L N M GLOW DISCHARGE AT lNTERMEDIATE PRESSURESF. Dothan and Yu. M. Kagan
Racah I n s t i t u t e of Physics, The Hebrew University of Jerusalem, Jerusalem Israel.
The concentration of atomic and mclecular ions and metastables is investigated for the positive co-
lumn of a helium glow discharge. Recently (1,2)
thesystem of differential equations for the helium af- terglow describing the time change of these plasma parameters was written and solved. In the statio- nary positive column we can neglect some processes which are importent in the afterglow. On the other
side we must take into account processes of exci- tation and ionization by electron collisions which can be neglected in the afterglow.
4 equations for the concentration of the atomic and molecular ions nl and n2 and metastables M1 and M2 on the axis of the cylindrical positive column can 6e written. For conditionsof pressure p between 5 and 60 Torr, electron concentration n between 1 0 ' ~ - 1 0 ~ ~ c m - ~ and electron temperatur: Te between lo4-4. lo4 0~(3), the equations can be s imp1 if ied and written in the following form:
~ , , M , ~ , + ~ X . ~ . N ~ = ( ~ + I ~ ~ ) ~ I (1
L - ~
=(&+ 6 ~ ' + dIi.fic') M.+ pllN? ( 3 )
W , ~ X ~ = ( ~ ~ + ~ ~ ~ U , + Y , ~ ~ + ~ C ~ ~ ~ ) M L (4) These equations are balance equations for creation
and disappearance of the four species per unit time and unit volume on the tube axis. In these equa- tions$;, anddL;are the coefficients of stepioni- zation by collisions of atomic and molecular metas- tables with electrons .d-(S gives the number of excitation of the atomic metastable level 2
35 from the ground state. 2 and s are the coefficients of conversion of atomic ions into molecular ions and atomic metastables into molecular metastables by collisions with two atoms in the ground state.
*,, &,h ,&are the times of diffusion of the various particles to the wall.
rl is the coefficient of the col l ision of the
I-%I# are proportions of atomic and molecular ions which appear by such col 1 isions. Eptr is the coeff i -cient of ionization by collisions between atomic and molecular metastables. The coefficients XI, ,
,TI
6 and X, are known from after- glow conditions (ls2). We must however take into account the dependence of these coefficients from Te and gas temperature
T .To calculate the coefficients of step ionization and the number of excitations of the atomic metas- table level2
35 we need the electron energy distri- bution function lm(&) in the positive column of helium at intermediate pressures. For this purpose we solve the Bol tzmann equat ;.on in two regions
;. . - -
region zwfiere EcE,
(&, excitation energy of the first levela'~) and regionzwhere &,E, . The
results show (3141 that the distribution in region
- I is near Maxwellian with a temperature Te while
-
in region it decreasesmuch faster than a Maxwell ian distribution (Figure 1).
1.0
44
0.1
I
O t o %I 22 23 a M
Fig.1
Electron energy distribution function for energies above 19.8
eVsecond kind between molecular metastables and elec- Therefore for the calculation of the coefficients trons. ~ P I I is the coefficient of ionization by of stepionizat ion
d l ~and dab we used a maxwell ian col laisions between two atomic metastables; and distribution with the temperature Te. For the
10
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1979762
creases w i t h c u r r e n t and decreases w i t h pressure. 5. H.W. Drawin, Z e i t . f. Phys.
164,
513, (1961) At t h e p r e s s u r e p=5 T o r r and c u r r e n t si
%loorA a1 1i o n s a r e p r a c t i c a l l y atomic ions. Even a t t h e lowest c u r r e n t ( i o l O * r A ) , a t t h e presshre p=5 T o r r , 67% o f i o n s a r e atomlc ions. The p r o p o r t i o n o f m o l e c u l a r ions decreases with c u r r e n t and i n c r e a s e s w i t h pressure. A t t h e p r e s s u r e p=40 T o r r
,
c r o s s - s e c t i o n o f s t e p i o n i z a t i o n we used t h e formula and c u r r e n t s i440,,,& p r a c t i c a l l y a l l ions a r e o f Drawin (5). For t h e c a l c u l a t i o n o f t h e number molecular. T h e i r c a l c u l a t e d c o n c e n t r a t i o n ati=Ib.,,A o f e x c i t a t i o n s o f t h e m e t a s t a b l e l e v e 1 t 3 5 from t h e and p = 4 0 T o r r istl+=?.1dog'. As shown i n f i g u r e 3 ground s t a t e we took i n t o account t h e f a s t decrease t h e c o n c e n t r a t i o n o f t h e atomic m e t a s t a b l e decreases o f t h e d i s t r i b u t i o n f u n c t i o n a t energies
c > E l ,
and w i t h pressure. The dependence o f t h e c o n c e n t r a t i o n proved t h a t i t i s p o s s i b l e t o r e p l a c e t h e number o f o f t h e atomic metastable on t h e c u r r e n t i s weak. The d i r e c t e x c i t a t i o n s o f t h e m e t a s t a b l e l e v e la35
by c o n c e n t r a t i o n o f m o l e c u l a r metastables increases t h e,
i.e. t h e d i f f e r e n c e between t h e w i t h pressure and decreases w i t h c u r r e n t . ~ t i = l o - ~ t o t a l number o f i n e l a s t i c c o l l i s i o n s of t h e f i r s t and p=40 T o r r t h e c o n c e n t r a t i o n o f m o l e c u l a r metas- and second k i n d . T h i s q u a n t i t y i s connected w i t h t a b l e s i s M2=8.10 10t h e t o t a l c r o s s - s e c t i o n o f i n e l a s t i c c o l l i s i o n s and was c a l c u l a t e d d i r e c t l y from t h e k i n e t i c e q u a t i o n
.
For h e l i u m t h e c a l c u l a t i o n g i v e s
+-@
= & ~,v,(\+ruIS4 iU' autc k
HIV s e u t . ~
(7)
where
u,= k ; 8 ,
,.* QZ=KTe
MVOc ' Zvor
( I+V%>%V
and 'Jac a r e t h e f r e q u e n c i e s o f e l e c t r o n e l a - s t i c c o l l i s i o n s w i t h atoms and o f e l e c t r o n - e l e c t r o n c o i l i s i o n s , r e s p e c t i v e l y ; q,a%,a.IOa
c**.
r e s u l t s o f t h e s o l u t i o n o f t h e equations ()>-(*>
f o r a tube o f r a d i u s
'R=\,a-.
a r e given i n t h e f i g u r e s 2 and 3.O A
-
- 0 / -
/ 0
- 0 -
0
L
-
0 /
/ I
.
I4 100 - 5
1020 30 p Xrr 40
5
200-
Fig.3 Normalized c o n c e n t r a t i o n s o f atomicmetastables (MI) and m o l e c u l a r metastables(M2) as a f u n c t i o n of pressure.
-
References- 0 0
nr
n,+n, -
1. R. Deloche, P. Monchicourt, M. Cheret and F. LambertPhys. Rev A,
2,
1140, (1976) 2. Yu.M. Kagan, J. Phys.D ( i n p r i n t )3. Yu.M. Kagan, R.J. Lyagushchenko, N. K h r i s t o v
5
1020 30 p
Torr40
Sov. Phys.-Techn.Phys 2 , 1 6 2 7 , (1972) Fig.2 P r o p o r t i o n o f atomic (nl) and m o l e c u l a r
i o n s (n 2 ) vs. pressure. 4. Yu.B. G o l u b o v s k i j , Yu.M. Kagan,R.J. Lyagushchenko
From F i g 2 we see t h a t t h e r e l a t i v e number o f atomic Sov. Phys.-Techn. Phys 2 , 1 5 5 3 , (1969) ions i s maximal a t t h e gas p r e s s u r e p=5 T o r r , i n -
