KINETIC ASPECTS AND SOME APPLICATIONS OF DIFFUSE GAS DISCHARGES IN TURBULENT FLOWS

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KINETIC ASPECTS AND SOME APPLICATIONS OF

DIFFUSE GAS DISCHARGES IN TURBULENT

FLOWS

Y. Khait

To cite this version:

JOURNAL DE PHYSIQUE Colloque C 9 , suppZ6ment au n o l l , Tome 41, novembre 1980, page C9-317

KINETIC ASPECTS AND SOME APPLICATIONS OF DIFFUSE GAS DISCHARGES IN TURBULENT FLOWS

Y.L. Khait

Department of Physics, Ben Gurion University of the Negev, Beer Sheva, Israel.

RQsumC.- L'equation cinctique pour une seule gQn6ration Qlectronique (EG) B E / P bas dans l e s d6charges d i f f u s e s turbulentes (TDD), e t des Qvaluations sur l e s i n t e r v a l l e s de temps c a r a c t c r i s t i q u e s pour E/P divers, sontobtenues. Les propriSt6s de TDD qui sont e s s e n t i e l l e s pour application plasma-chimi- que e t l a s e r sont discutQes.

Abstract.- The k i n e t i c equation f o r a s i n g l e electron generation (EG) a t low E/P i n turbulent d i f f u s e discharges (TDD) and estimates of c h a r a c t e r i s t i c time i n t e r v a l s f o r various E/P a r e obtained. TDD' properties e s s e n t i a l f o r plasmachemical and l a s e r applications a r e discussed.

Introduction i t i o n s (GPT) under t h e influence of e l e c t r i c f i e l d Recent study of d i f f u s e discharges i n t h e E (xO, yo, zO, t ) during a s h o r t residence time hydrodynamically turbulized gas speedily passing A T W La/v of the gas moving through the d i s - thrcugh t h e region with a high e l e c t r i c f i e l d charge zone with t h e mean v e l o c i t y v , where strength E has shown t h a t the turbulence causes

ro

= IxO? yo, zO1 are coordinates i n t h e unmoved deep changes of properties and parameters of the coordinate system. The behaviour of t h e moving discharge and leads t o l a r g e obsenrable e f f e c t s gas affected by E during i s s i m i l a r t o t h a t such as: Ci)

A-

sharp increase of power consumption Of the ~nmoved gas affected by a short-term pulse W and e l e c t r i c current I a t prearcing mode up t o of the e l e c t r i c We s h a l l consider t h i s

2 3

10 t o 10 times of non-flow conditions without problem following the ideas suggested i n r e f . 3 . losing the discharge s t a b i l i t y . ( i i ) A great Some TDD properties e s s e n t i a l f o r TDD applications enhancement of transport c o e f f i c i e n t s , e.g., of are a l s o discussed. The TDD k i n e t i c s represents. an

turbulent ambipolar d i f f u s i v i t y extension and a combination of the following-

where Re and Re* << Re a r e t h e Reynolds and the c r i t i c a l Reynolds numbers;

E

and

Ei

<<

E

a r e t h e mean energies of electrons and ions, and e.g.,

5 2

DAt can reach values DAt m 10 cm /S a t RejRe* W

3

-

2

3.10

.

Le/ci 10' and Di 0 . 2

an

/S, and s o on.

Turbulent d i f f u s e discharges (TDD) a r e of substant- i a l i n t e r e s t due t o t h e i r possible applications t o plasma chemistry,to turbulent gas discharge l a s e r s

(TGDLs), e t c . l y 2 . Howqver, t h e TDD k i n e t i c s has been studied very l i t t l e . In t h i s paper we s h a l l consid& the k i n e t i c aspects and a non-stationary s t o c h a s t i c model of unionized gas-to-plasma t r a n s -

phenomena whose study is f a r from being accbm- plished: (5) The hydrodynamics and physical chemical hydrodynamics of turbulent but unionized gases (see e . g . , r e f . 4-8). ( i i ) The hydrodynamics and k i n e t i c s of turbulent plasma j e t s (see e.g., r e f s . 9-11)

.

( i i i ) The k i n e t i c s of discharge phenomena i n non-flowing or laminary flowing gases affected by short term pulses of the e l e c t r i c f i e l d (see e.g., r e f s . 11-14). (iv) PKenomena i n

t

unmoved gases affected by non-uniform e l e c t r i c f i e l d s (see e.g., r e f s . 15-19). This i s why one can hardly expect t o solve the considered problems exactly. We s h a l l r e s o r t , therefore, t o t h e use of approximation analysis, similitude theory and

JOURNAL DE PHYSIQUE

approximate s t o c h a s t i c modeling of t h e processes i n question, t o obtain q u a l i t a t i v e and semiquanti- t a t i v e r e s u l t s f o r the main f e a t u r e s of t h e problem and t o come t o some observable consequences. On

t h i s b a s i s , we combine some q u a l i t a t i v e and semi- q u a n t i t a t i v e r e s u l t s of theory of turbulence and gas discharges with a s t o c h a s t i c model of the charged p a r t i c l e behaviour t o obtain expressions f o r t h e considered values.

Some Kinetic and Stochastic C h a r a c t e r i s t i c s of Turbulent Gas Discharges

Consider a turbulent unionized gas c o n s i s t e n t of N = G N

=

P/kT d i f f e r e n t kinds of p a r t i c l e s

B

63

(per 1 cm

3

of mass

M@

and concentration N =

B pB/kP (B = 1,2, ...) entering t h e discharge zone with mean v e l o c i t y

v

a t pressure P = C P

B

B,

tempera- t u r e T. This gas has random turbulent pulsations characterized by t h e smallest space s c a l e A0 and i t s corresponding frequency Q0 given by

A, (Re*/Re)

'144

and

no

W (Avjl) (Re/Re*)

'I4

( l ) A s a t i s f i e s the conditions 1

0

h << L 2*/Q << AT W La/v

,

0 a ' 0 (2)

where

1

i s the l a r g e s t s c a l e of t h e turbulence, AV W V i s t h e corresponding v e l o c i t y

of

t h e

turbulent pulsations, La a r e t h e c h a r a c t e r i s t i c space s c a l e of t h e discharge, e.g., t h e s c a l e of

4 t h e corona zone. For instance, i f AV

s

v 10 cm/s,

2

L

w 4 cm, kinematic vfiscosity y 0.2 cm /S and

5

Re* m 50 one can obtain Re U 2.10

,

A. 1 0 - ~ cm,

6 -1.

A. M 10 S

.

The gas entering the discharge has very low i n i t i a l e l e c t r o n concentration n f O ) =

aCO)

* N

_{associated with very small i n i t i a l degree} of gas ionization a(') 10-12 t o 10-l3 caused by cosmik rays, by n a t u r a l r a d i o a c t i v i t y , e t c . This

. '

gas speedily passing through the discharge zone with space s c a l e La (e.g. corona zone) i s a f f e c t e d by t h e e l e c t r i c f i e l d only during s h o r t time AT,=

La/v. The GPT can occur i n the moving gas only i f the GPT time eCg) < A T

.

During O(g) time- dependent electron concentration n ( t ) = a ( t ) .N increases up t o = a(g).N which s a t i s f i e s the condition

(9) ; (i(g)/4ne2.n(g))' ; (;(g)/477e2 .a(g) P D

Therefore t h e time-dependent Debye radius (3) . 2

p,(t) = [E(t)/,ne n(t)]' = [ ; ( t ) / m e 2 a ( t ) .N]' (4) rapidly decreases from t h e i n i t i a l value Or0) UP t o pLg) where r ( t ) i s t h e mean e l e c t r o n energy a t t determined by

E(t) = l ~ . f ( ~ , t ) d ~ and j f ( e , t ) d c = l , (5) f (E , t ) i s the e l e c t r o n energy d i s t r i b u t i o n function, L i s t h e space s c a l e of t h e discharge zone where the GPT occurs, e.g. L i s t h e s c a l e of turbulent corona zone on ~ e / R e * . l I f

> A 7 t h e GTP has no time t o occur. Time

a

depends on E/P, on n(g)/n(0), e t c . and can vary from one discharge t o another, and even with- i n the same discharge volume. To estimate

and compare it with AT we introduce the follow- a

ing c r i t e r i a f o r the low, moderate and high E/P: e-E-lmin << W m W or

E/P

< <

-

.

-

=

0 kT Omax e

I (63

N

e-E*Xmin x<

WO

o r &P I ( E / P ) ~ (7)

e.E. h 7 WO W o r E/P > &/P)

min b ' (8)

where hmin = [Nu,,] -1

,

omax i s t h e maximum t o t a l e f f e c t i v e cross-section within t h e considered electron energy i n t e r v a l , e.g., within i n t e r v a l [O,WO] with WO being t h e threshold energy s u f f i c i e n t t o s t a r t ionizations of gas p a r t i c l e s with ionization p o t e n t i a l W. The e f f e c t i v e t o t a l e l e c t r o n cross-section and t h e mean f r e e path length a r e given by

h-' = C A-' = Z(uB(c) ON@]; U ( € ) = ~ ' l - 1 o (E)

.NB

'

B B B B

o ( E ) i s t h e t o t a l c r o s s - s e c t i o n of e l e c t r o n

B

c o l l i s i o n s with p a r t i c l e s of type B, t h a t includes t h a t of e l a s t i c ,

ageL,

i o n i z i n g , a

.

and e x c i t i n g

61'

(of l e v e l W ), o c o l l i s i o n s . Therefore, t h e

Bs Bs

a p p l i c a b i l i t y of low, moderate and high E/P approximations t o p a r t i c u l a r cases depends on c h a r a c t e r i s t i c r a t i o

'0 'max (E/PO)b = (P/PO) CE/P) =

-

_kTo

-

_e

_'

where To = 273 K , P = PT /T. For example, i f

0 0 2 0 = 2.10-" cm (e.g., i n Ar a t cm a 12 eV), max T S 300 K and WO = 1 t o 20 eV (e.g. i n A r , W FJ 0 16 eV)

.

One can o b t a i n from [ l l ) : (E/P)b FJ

3

( ~ / p ~ ) ~ FJ 65 t o 1.3.10 /cm t o r r and i f P FJ 760

3

t o r r s , one has E fir 50 t o 10 KV/cm. However, i f

b -16

o f FY 3.10 cm (e.g., Ne a t E ' m 25 eV) and

max

m

o t h e r c o n d i t i o n s equal, one has (E/Plb m 9.5 t o 190 V/cm t o r r . Consider now

a

s t o c h a s t i c model o f t h e GTP and r e l a t e d phenomena, following t h e approach suggested i n r e f . 3 .

1. The low

E/P

approximation

Condition (6) means t h a t every low energy e l e c t r o n (e.g., t h e i n i t i a l one o r t h e one t h a t has l o s t i t s energy during an i o n i z a t i o n c o l l i s i o n ) with energy E << WO a t to s u f f e r s a s amny as

0

unionizing c o l l i s i o n s with gas p a r t i c l e s during

N

time A t = t - to FJ a-t b e f o r e t h e e l e c t r o n g a i n s

energy AE = W

-

E FJ WO s u f f i c i e n t f o r i o n i z a t -

0 0

ions; a f t e r t h a t t h e e l e c t r o n with energy E 3 W ₀ s u f f e r s 6a FJ (o/oi) a d d i t i o n a l unionizing

N C

c o l l i s i o n s during time 6 t FJ 6a-.re, b e f o r e t h e

f i r s t i o n i z i n g c o l l i s i o n , where

%v

= v-I L v

e B (13)

i s t h e mean energy l o s s

.

p e r one unionizing e l e c t r o n - g a s p a r t i c l e c o l l i s i o n ,

AWB

i s t h e p a r t i a l l o s s given by -1 AW = U - ( Z AWBs'uBs 0 S + E - 6 1 3 e t ' " ~ e ~ ) (14) N - 1 v = T = C V e e 6 6 115)

i s t h e frequency of e l e c t r o n c o l l i s i o n s with gas

N

p a r t i c l e s , ue FJ (2~/m).', FJ 2m/MB, o = i o

.

.

i

B

B 1

The mean time between t h e two i o n i z i n g c o l l i s i o n s

A??

=

AT

+ 6 7 r~ ( a + 6a)y ₍₁₆₎ can be t r e a t e d a s t h e l i f e t i m e o f a s i n g l e e l e c t r o n generation (EG) with n M c o n s t . This EG i s formed by t h e e l e c t r o n s of t h e previous EG and by t h e secondary ones c r e a t e d by i o n i z i n g c o l l i s i o n s of t h e previous EG. Then t h e time Q ( ~ ) of formation of

g =

(h

K)-' Ln(n(g)/n(O1) ₍₁₇₎

E G s can be estimated hy

N

o ( ~ ) g*P0 M g(ct + 6 . ) ~

,

C 1 8) where ( K - l ) i s t h e average number of secondary e l e c t r o n s formed by one e l e c t r o n o f a s i n g l e EG

N

during A0, i n many cases K FJ 2. The energy

d i s t r i b u t i o n f ( ~ , t ) of a s i n g l e EG i s

where G ( E , ~

l

eO, to ) i s t h e conditional p r o b a b i l i t y of t h e e l e c t r o n t r a n s i t i o n from t h e s t a t e with energy E a t to i n t o t h e one with E a t t . G

0

i s determined by t h e Fokker-Plank equation i n t h e energy space

c l o s e l y connected with t h e s t o c h a s t i c equation of e l e c t r o n motion dE - = e E ud

-

Al + g t;(t)

,

d t (21) where A = e E u

-

A1, A = v

OAF

,

1 e 122) u FJ n - ' . e - ~

5

i s t h e e l e c t r o n d r i f t v e l o c i t y , ' d 2 2 g = B, B FJ (eE) Dl-l, Dl1 i s t h e e l e c t r o n , >

C9-320 JOURNAL DE PHYSIQUE

"

i s SO high t h a t A% > Q;', one h a s D + D 11 A t (see Eq. ( l ) ) . Equation (20) t a k e s t h e p a r t of t h e k i n e t i c equation of a s i n g l e EG a t low E/P. A s i s

well-known t h i s equation can be solved f o r some p a r t i c u l a r c a s e s . For instance, when B and A can be replaced by averaged constant values = c o n s t and A = const, one can o b t a i n 20

[ E - € - Z . ( t - t ) ] 2

G(€) = GO exp - 0 0

2 X ( t - t o )

Equations (12) - (22) allow v a r i o u s conclusions and e s t i m a t e s ; among them a r e t h e following: ( i ) Systematic d r i f t of E towards h i g h e r values i s determined by depending on t h e g a s n a t u r e , E, e t c . , and

#

0 i f E/P i s n o t t o o small.

( i i ) Values a

AT

and eCg) p r o p o r t i o n a l t o A-' a r e n o t t o o l a r g e iihen A and E/P a r e n o t t o o low; ( i i i ) n ( g ) and

@)

a r e exponential f u n c t i o n s of time :

,(g' = n ( 0 ) e x p ( e ( g ) . h K / A ~ ) (23)

where A; depends on parameters o f t h e p r o c e s s . ( i v ) Rate c o e f f i c i e n t s of i o n i z a t i o n s , e x c i t a t i o n s , r e a c t i o n s , r a d i a t i o n , e t c . , induced by e l e c t r o n impacts w i t h c r o s s - s e c t i o n s uR(€) a t moment t M @(g) a r e

(v) The GPT time @ ( g ) can be estimated from (3) and (24) i n t h e form

" ,..

I f (e~.u~-y;AE) eEu time can become d'

-1

g r e a t e r t h a n A. and can even approach Ara i f E/P i s r a t h e r low. For i n s t a n c e a t P 760

3

t o r r s , T M 300K,

E.%

10 V/cm, a (0) 10-13

3 - I O - ~ , am_ ~ 2 . 1 0 - ~ ~ c m , u = 1 0 2 N -15 c m , 2

K M 2 and W W 16 eV one can f i n d g W 32, 0

,.,

T m 3 . 1 0 - l ~ S,

2. A t moderate and high E/P a s s o c i a t e d with c o n d i t i o n s (7) and (8) e l e c t r o n s gain energy A€mWO d u r i n g A t T o r A t T e' and t h e s i n g l e EG l i f e t i m e

and W g.*; a r e much s h o r t e r than t h o s e a t e

low E/P and t h a n A;' and A T . In t h i s c a s e c a l c u l a t i o n s of f ( ~ , t ) d i f f e r from t h o s e a t low E/P and r e q u i r e a s p e c i a l c o n s i d e r a t i o n , : b u t

AZ

and @(g) can be e a s i l y estimated from Eq. C28). For i n s t a n c e , a t P m 760 t o r r s , T m 300K, K W 2,

E

w 2910' V/cm ( n e a r corona e l e c t r o d e p i n s ) -16 2 U M 10 cm

,

( a / a , ) = 30, WO = 22 eV, a = i n max 3 - 1 0 - l ~ cm2, a(') = 10-13 and .(g) = 3.10-4,

U fir 3 . 1 0 ~ cm/s one can o b t a i n E/P = 260 V/cm t o r r

2 W 210 V/cm t o n , r a 10-l2 S , A0

3 . 1 0 ~ ~ ~ S, g W 30, 0(30) m 3.10 -11 S. Therefore

even d u r i n g r e s i d e n c e time 6~ 6L/v << AT i n small regions with space s c a l e 6L << L (e.g.,

a

i n small p a r t s o f t h e corona region i n which f i e l d l

E i s approximately uniform ) many e l e c t r o n g e n e r a t i o n s and a l a r g e amount o f e x c i t a t i o n s of g a s p a r t i c l e s can be formed.

Discussion and Conclusion

-

Remarks

The approach considered i n t h e previous s e c t i o n can be a p p l i e d t o v a r i o u s TDDs. Consider f o r example, p o s i t i v e t u r b u l e n t corona (PTC) a t P FJ 1 a t , d e s c r i b e d i n r e f . 1. The PTC d i f f e r s

very much from i t s c o u n t e r p a r t i n non-flow c o n d i t i o n s , although t h e f i e l d E ( r ) i s a l s o

0

p i n s (e.g. E W 50

-

200 kV/cm and Ea/P w a

70-250 V/cm t o r r ) and much lower i n regions f a r removed from t h e p i n s (e.g.

,

Er W 1-5 kV/cm and

E W 1.3-6.6 V/cm t o r r ) . Only p a r t of t h e gas e n t e r i n g t h e discharge volume p a s s through t h e corona region and i s a f f e c t e d by f i e l d Ea. How- e v e r , i n t e n s i v e i o n i z a t i o n s and e x c i t a t i o n s i n t h i s p a r t o f gas produce e l e c t r o n s , i o n s and promote i n t e n s i v e r a d i a t i o n which can form p h o t o e l e c t r o n s and i o n s i n regions f a r removed from t h e p i n s ( e . g . , i n simple gases A r , H _2' He, e t c . ) . Turbulent p u s l a t i o n s d i r e c t l y i n v o l v i n g i o n s and a f f e c t i n g e l e c t r o n s through Coulomb coupling:

( i ) Affect much formation o f t h e space d i s - charge1". ( i i ) Spread charged p a r t i c l e s over t h e discharge zone and i n c r e a s e s h a r p l y c r o s s s e c t i o n Sc o f conducting channall and t h e volume V

a Sa.La o f t h e corona zone with r e l a t i v e l y h i g h e l e c t r o n c o n c e n t r a t i o n n and E, n o t t o o l a r g e ,

b u t s u f f i c i e n t f o r e x c i t a t i o n s of n o t very h i g h l e v e l s , f o r pumping, f o r i n i t i a t i o n s of plasma chemical r e a c t i o n s , e t c . ; t h i s volume can be enlarged by overlapping of such zones formed by neighbouring ( i i i ) Prevent from streamer

formation and from breakdowns o f t h e d i s c h a r g e a t r e l a t i v e l y high c u r r e n t s I and power i n p u t

w . ~ "

( i v ) Lead t o much h i g h e r smoothness of t h e d i s - charge i n time and space, and causes a s i g n i f i c a n t i n c r e a s e of e f f e c t i v e l y working e l e c t r o n a r e a

- -

Et = n ss a s s o c i a t e d with t h e corresponding P P

growing up of t h e number, ;i of. simultaneously

P

_-

working p i n s and of working a r e a s s p e r p i n . 1 P

(v) Promote b e t t e r cooling of e l e c t r o d e s ( i f t h e y a r e heated) and lower h e a t i n g o f t h e g a s passing through t h e discharge z o n e . l y 2 The aforementioned p r o p e r t i e s can be used f o r i n i t i a t i o n of plasma chemical r e a c t i o n s and f o r pumping of t u r b u l e n t g a s discharge l a s e r s (TGDLts) i n r e l a t i v e l y l a r g e

a c t i v e volumes

.'

A s i m i l a r approach with some modifications can be applied t o t r a n s v e r s e TCs. Note t h a t t h e k i n e t i c s of phenomena i n near- e l e c t r o d e plasma l a y e r s (PLs) i n hydrodynamically t u r b u l e n t gas, caused by t h e secondary electxode emission, can be considered through t h e c o r r e - spondingly modified approach used i n r e f . 21 f o r t h e treatment of processes i n PLs i n laminar flows.

Summarizing a l l t h e a f o r e s a i d one can make t h e following conclusions.

1. A g a s p o r t i o n e n t e r i n g t h e discharge volume i s a f f e c t e d by t h e non-uniform time-dependent f i e l d E c r , ~ ) d u r i n g a s h o r t time where r = {x,y,z) a r e t h e space c o o r d i n a t e s i n t h e moving coordinate system accompanying t h e gas flow. This f i e l d can be a random f u n c t i o n o f time T due t o random t u r u l e n t p u l s a t i o n s even i n t h e c a s e when E(ro) does n o t depend on time.

2. A p a r t of t h i s g a s i s a f f e c t e d by t h e s t r o n g e l e c t r i c f i e l d E n e a r t h e p i n e l e c t r o d e s , a s s o c i a t e d with h i g h E/N, e . g . , E/N fir 10-l4 t o

-10-15 v*cm2 a t N m 3 . 1 0 ~ ~ cm-3 and E

(3 t o 1)

* l o 5

V/cm. I n t h e s e short-term c o n d i t i o n s t h e h i g h l y non-equilibrium and non-stationary e l e c t r o n energy d i s t r i b u t i o n f ( ~ , t ) (which can be a l s o a n i s o t r o p i c ) tttunetf i n t o e l e c t r o n i c e g c i t - a t i o n s and i o n i z a t i o n s of gas p a r t i c l e s . For example, i n He/N2/C02 mixture with t h e molar r a t i o 3/2/1 t h e l a r g e r and l a r g e r amounts of power go i n t o t h e i o n i z i n g p r o c e s s , beyond E/N of about 2 * 1 0 - ~ ~ ~ - c m ~ . ~ ~ I n t e n s i v e avalanche form- a t i o n , t h e CPT, e l e c t r o n i c e x c i t a t i o n s and

C9-322 JOURNAL DE PHYSIQUE

coronas can work without any e x t e r n a l i o n i z e r waves and f l u c t u a t i o n i n t h e newly formed plasma. ( e l e c t r o n i c beam, e t c . ) Our knowledge on t h i s f i e l d i s very poor and t h i s

5. The discharge volme

vR

n o t t o o c l o s e to t h e ~"ble"' d e s e ~ e s t o b e s t u d i e d i n d e t a i l . e l e c t r o d e p i n s , enriched by e l e c t r o n s having n o t 6. We t h i n k t h a t a s p e c i a l a t t e n t i o n should be t o o high energy, can be used f o r pumping of l a s i n g p a i d t o t h e problem of t h e non-stationary non- l e v e l s and a s a plasma chemical r e a c t o r . For low e q u i l i b r i u m e l e c t r o n energy d i s t r i b u t i o n s a t high

E/P

t h e r a t e c o e f f i c i e n t s o f t h e s e processes can E/P, when c h a r a c t e r i s t i c GPT time i n t e r v a l s a r e be presented i n t h e form, using Eqs. C22) and (25).

where K can depend on space coordinate and t a l s o through n, A and B . Therefore, such a

discharge with volumetric temperature and discharge s t a b i l i t y c o n t r o l , w i t h n o t small power i n p u t W and c u r r e n t I and with t h e r e l a t i v e l y h i g h a c t i v e volume VR can be considered a s a s c a l a b l e d e v i c e r e l y i n g n e i t h e r on w a l l s n o r low p r e s s u r e s f o r o p e r a t i o n . I n p a r t i c u l a r , f o r t h e aforementioned mixture H

IN^

/ C O ~

a t

E/N of about 10-l6 V cm2 more energy e n t e r s t h e upper l a s e r s t a t e s than t h e lower, and i n v e r s i o n s a r e p o s s i b l e . 22

4. The problem of t h e q u a l i t y and o p t i c a l homo- g e n e i t y o f t h e l a s e r medium i n t h e TDDs a r i s e s i n connection with t u r b u l e n t p u l s a t i o n s . This problem should be c a r e f u l l y e l a b o r a t e d . However, one can expect t h a t f i n e - s c a l e t u r b u l e n c e w i t h small A0 and high Q0 and Re/Re* should be l e s s s e v e r e t h a n l a r g e - s c a l e . Therefore, it can be expected t h a t t h e i n c r e a s e o f Re/Re* can promote n o t only t h e h i g h e r t r a n s p o r t c o e f f i c i e n t s , power i n p u t s W and c u r r e n t s I b u t a l s o a h i g h e r degrpe of o p t i c a l homogenepty of t h e l a s e r medium. 5 . The r a p i d CPTs i n t h e hydrqdynemically t u r b u l i z e d g a s l e a d t o t h e problem o f i n t e r a c t i o n s of t h e hydrodynamic t u r b u l e n t p u l s a t i o n s with

small and formation of high-energy runaway e l e c t r o n s i s r a t h e r probable. These e l e c t r o n s can have an a n i s o t r o p i c n o n - s t a t i o n a r y d i s t r i b u t i o n f u n c t i o n and t h e conventional approaches t o i t s

c a l c u l a t i o n a r e n o t very v a l i d .

The sharp i n c r e a s e of power i n p u t and o f t h e t r a n s p o r t c o e f f i c i e n t s and o t h e r r e l a t e d phenomena described i n r e f . 1-3 and i n t h i s paper seems t o

show some i n t e r e s t i n g p o s s i b i l i t i e s f o r a p p l i c a t - i o n s of t h e TDDs and demonstrate t h e very m u l t i - d i s c i p l i n a r y c h a r a c t e r of t h i s f i e l d . We a r e hopeful t h a t t h e development of t h e TDD probl&n

presented i n t h i s paper w i l l s t i m u l a t e f u r t h e r i n v e s t i g a t i o n of t h e n o n - s t a t i o n a r y non-equilibrium k i n e t i c s o f t h e TDDs.

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