THEORETICAL INVESTIGATION OF RADIO-FREQUENCY DISCHARGE IN γ- REGIME

HAL Id: jpa-00219478

https://hal.archives-ouvertes.fr/jpa-00219478

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.

THEORETICAL INVESTIGATION OF

RADIO-FREQUENCY DISCHARGE IN γ - REGIME

V. Godyak, A.S. Khanneh

To cite this version:

V. Godyak, A.S. Khanneh. THEORETICAL INVESTIGATION OF RADIO-FREQUENCY DIS- CHARGE IN γ- REGIME. Journal de Physique Colloques, 1979, 40 (C7), pp.C7-147-C7-148.

�10.1051/jphyscol:1979772�. �jpa-00219478�

JOURNAL DE PHYSIQUE CoZZoque C7, supptgment au n 0 7 , Tome 40, J u i Z Z e t 1979, page C7- 147

TI-IEORETICAL INVESTIGATION OF RADIO-FREQUENCY DISCHARGE IN Y

-

^REGIME

V.A. Godyak, A.S. Khanneh.

Moscov ' s t a t e U n i v e r s i t y , Department o f P h y s i c s Moscow, U.S.S.R.

The existence of two different regimes of RF discharge ( d and

f

-regimes) was first mentioned i n paper /?/.As the lumi- nosity of the high voltage regime was ob- served t o be similar t o t h a t of the glow discharge, the author / I / put forward a bp-

p o t b s i s that secondary emission from the electrodes (

f

-process) plays an impor- t a n t role i n this regime ( )/ -discharge).

It is presumed t h a t -processes are neg- l i g i b l e i n the low voltwe regime (

4 -

discharge)

I n t h i s paper the ionization balance and the characteristics of a symmetric RF

beam;

E

-mean beam energy; f, -energy losses f o r one ionization; A -the beam damping lenght; -ion velocity a t the boundary.

The solution of (1) f o r a cylinder with radius ^I? and lenght 2 d if << Ph

,

h2

<( R: d2 is: ^{'7; 17}

discharge taking into account -proces-

s e s are studied.

m i m=--

If the ioniz;ation by the f a s t electron

2 r i a

beam injected from the sheath i s taken in- w b r e f70 -plasma density a t the centre t o account the ambipolar d i f f ~ s i o n e q ~ a t i - ₍

x ,o,

^{y so) ;}

5:

^t

yk

^d' -its relative pa- on becomes: lue a t the boundary; & -the electron tem-

~ ( p f i )

+ ~⁺ n

G

= 0 perature.The values of ffl and 2' as ^fun- ctions of

r

are show i n Fig.1 f o r d =

where

n

-the plasma density; Z -the io- niaation frequency of the plasma e l e c t

-

ko.ng; -the ambipolar diffusion ooeff i- cient; -the ion current deneity a t the plasma-sheath boundary ( X ^P i d ⁾ and

G

-the r a t e of beam ionization i s given by expression:

where Je -current density of the electron

R

^:.

IOA .

It can be seen (Fig.?) that when

f7

5 1 _beam ionization brings ab- out a drop i n the pla-

r

sma ionization fregu-

I

-

^{ency ( Z + 0} ) . T h i s

rm ,should lead t o a de- I crease i n the elect- - - - ron temperature and 1 the effective R F f i -

Big .I e l d in plasma E

.

When f<<. ^{j (} d. -discharge) the influence of the beam ionization on the plasma i s negligible.

f

i s limited by the maximum value :

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1979772

A d r 3 =

[I-

~ ~ 4 ~ f h 2 . 4

which follows from (2) i f Z' =O.When

r =

r m beam ionization becomes the main pro- cess ( )( -discharge) .In this case ² is negligible and the axial plasma distribu- tion ist

Calculations show that when theufact that 2

' is a function of E and thura of X co- ordinate /2/ is taken into account f o r the

-discharge (

f

=

r,

^{) Y(x) is deter-}

mined by (3) only when d c L ( L i s ^gi- ven below).~or d22R ( d - R Y L ) in

r -

discharge th6 axial plasma distribution i s homogeneous ( y(dlr d ) a d z =

(yyl.

^the

range ( X I <

d-

^t!. .Thus

-&

and

E

are the same a s i n the pla~ma of' the positive colwnn(~.) of the doc. dischargeiIn the range

[ X I > d-L

the plasma distribution is

can be seen that in -discharge the ma- ximum plasma densii;y is a t a distance of about

h

iron the boundary.When gas ioni- zation in the sheath i s taken into account

r

is given by,

f = Q.,

Y ( ~ X P

jd(x.tl

d x )

= r ^(uC,

^ps,+5)

Y

⁺

1 -

(ex p

fsd(x,f)dr

)

a

where )f -%he electron-ion emission coef f i- cient; d -!Jornmsend*s f i r s t ionization co- efficient;

S , ^S,

-sheath thickness and i t s - maximum value respectively; P -the gas pressure and

uc

-the aniplitude of RF voltage fn the sheath+According .to /3/ ur

and

S,,,

are given bg

where

V,

-the amplitude of the discharge voltage; J -electron-atom collision fre- quency.The equation f a

rm

⁴ leads t o a

PS, -dependence a t & e which is B i d . 1 ~ t o the P& -dependence a t ^{Q K} ( U K

,

^{t K}

--

the cathode f a l l and the cathode f a l l re-

gion i n the glow discharge).

Big.2 shows a qualitative

Ps,

(&]cuTv~,

,

corresponding t o

r

^{=I ,When} increasing

U,

t o a c r i t i c a l value UJy (point A in Pig.2)

f' sharply increases f r o m a negligible va- lue ( f c < I) t o f =I, indicating t h a t a tra- nsition from t o

I

^d

->

^Uc discharge takes place.

Further increase of

~ i g . 2 ^{k c} leads t o a drop- ping o f S m thus t o an increase in the ste- epness of the of the volt-ampere curve of the diacharge (

3- 2

^{) .If PSm in the low}

voltage disoharge is large enough

3-

^(gjcur-

ve of the discharge my happen t o be nega- t i v e (a transition a t point B in Fig.2).

T h i s may be the cause of the discharge current instability .Since i n

b/

-discharge

$, i s determined byPS,

=

P.$

=f(uC)

^the

current density i s (sheath conduction cur- rent is neglected) t

The plasma

density

^and

Ik

f i e l d a t the bo- Plasma density

no

i s obtained from (3), (7)

FOE

d < +no

= & p 2 u , / i ~ e ( ~ ~ t ) 2 ~ h z . 4

%]-I .

aord-f?>f; ~ Y U & ( ~ & ~ ~ Z S ~ E , , ) - ' t

where L is defined by T h e expression f o r

scharge are qualitatively different /3/:

~ w ~ 2 u c ( ~ ~ ) - ' ;

^fld

-

^{W ' U .}

^(%)-'

Conduction c m e n t in b/-discharge she- 61th is negligible and plasma density i s time independent (

d $ ' < ~ )

^when

w

P ^"

(PSJ ($# pu,)'

^Y2

where

A;

-ion mean free path; M -the ion mass.Th3.a definers the range of slpplicabi- l i t y of the theoretical inode1 presented i n this paper.

References:

/I

/.

C.M.~ledu~c~ui;, N T P ~ 2 ~ ~ 3 7 0 , 195 3;

/2/.W*P*Allis & all,J?hys *Rev., 84.51 9,1951.

/3/.

a.

^{A, r0W7.K,} % ~ U K & h / l ~ 3 M b l ,

-

2 , I 4 1 , 1976.