THE BOHM-TYPE THERMAL LOSSES FROM A HIGH- PLASMA

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THE BOHM-TYPE THERMAL LOSSES FROM A HIGH- PLASMA

P. Chebotaev, G. Vekstein

To cite this version:

P. Chebotaev, G. Vekstein. THE BOHM-TYPE THERMAL LOSSES FROM A HIGH- PLASMA.

Journal de Physique Colloques, 1979, 40 (C7), pp.C7-537-C7-538. �10.1051/jphyscol:19797260�. �jpa- 00219246�

JOURNAL DE PHYSIQUE CoZZoque C7, suppzdment au n07, Tome 40, JuiZZet 1979, page C7- 537

THE BOHM-TYPE THERMAL LOSSES FROM A HIGH- PLASMA

P.Z. Chebotaev, G.E. Vekstein.

I n s t i t u t e of NucZear Physics, Novosibirsk, U. S. S.R.

Current i n t e r e s t t o the p r o p e r t i e s of a high-

P

plasma i s i n i t i a t e d by a number of proposals t o use such a plasma i n t h e f u s i o n systems. Most o f t e n discussed pos- s i b i l i t y is the so-called uwallls ( o r %on- magneticss ) confinement of a plasma with density t'L>

loq7

~ m ' ~ / I ,2/, I n t h i s con- finement method t h e only r o l e of the mag- n e t i c f i e l d is t o reduce transverse t h e n -

both i n t h e numerical s t u d i e s / 6 / and i n the experiments / 7 / . So, a t i n i t i a l moment a hot plasma with density

no ,

temperature

T,

and magnetic f i e l d

H,

f i l l s the tube of r a d i u s

R

with cold walls. The mag- n e t l a a t i o n parameter of a plasma

s,

^=-

(q,,r:)~>I ,

i t s thermal conductivity )t,-..cT,

/eH,s, .

From the heat t r a n s p o r t e qua t ion

a 1 conductivity, while the mechanical

- S?'(nT)--L'o_r(:n~v-.kX)

( I )

a

%t - r It- 3r

equilibrium o f a plasma is provided by ri-

and the pressure homogeneity condition i t g i d walls. So, t h e "wallv confinement al-

follows t h a t the whole energs f l u x lows us t o r e d u c e the requirements t o t h e

magnetic f i e l d s t r e n g t h i n the s o l e n o i a a l plasma systems and t o o b t a i n j3 = 30+300.

Even more

p

(of the order of 10 3 ) may be a t t a i n e d i n the emploding l i n e r devices with

n

^z 7 01'+7 020 ~ m ' ~ / 3 / . Ifleanwhile, the dynamics of high-? plasma cooling possess- e s some d i s t i n c t i v e f e a t u r e s /4/. The rea- son is t h a t the plasma k i n e t i c pressure must be homogeneous during the cooling process. Due t o t h i s , a hot plasma begins t o flow t o t h e walls and t h e high-density near-wall l a y e r is formed, A s a r e s u l t , t h e cooling time of such a plaama can be s i g - n i f i c a n t l y decreased /5/.

I n our communication we s h a l l consid- e r the cooling of a hot magnetized plasma coming i n t o contact with a cold wall. A s i m i l a r problem has been r e c e n t l y solved

I n the cold .near-wall l a y e r , where

T44T,

and the thickness of which A < <

R ,

we have

9

^{a const. A t} the same time,W = 0 a t the w a l l , s o the convective h e a t f l u x is small here. and

A s the thermal conductivity ^a2 depends on the magnetic f i e l d , eq.(2) must be solved together with the equation f o r the magnet- i c f i e l d v a r i a t i o n /8/:

A d e t a i l e d a n a l y s i s of eqs.(2-3) w i l l be presented elsewhere. Here we r e s t n i c t our- s e l v e s only t o a q u a l i t a t i v e explanation.

In a hot region the magnetic f i e l d i s f r o z e n i n t o t h e plasma and takes out with

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19797260

i t t o t h e walls. If t h e w a l l is p e r f e c t l y conducting, then t h e t o t a l magnetic f l u x is conserved and t h e magnetic f i e l d in- c r e a s e s i n t h e near-wall l a y e r . I n t h i s

"

^@

case t h e plasma cooling time i s

%-R/jCo& ,

by a f a c t o r of

S:

s m a l l e r than t h a t f o r t h e low-pressure ( p d < j 1 plasma. I f t h e w a l l s a r e non-conducting, then t h e magnet-

i c f l u x takes out from t h e tube due t o the Nernst e f f e c t i n eq.(3) and t h e mag- n e t i c f i e l d n e a r w a l l remains of t h e o r d e r of i t s i n i t i a l value. A s a r e s u l t , t h e heat f l u x t o t h e w a l l i n c r e a s e s by a fac- t o r of fWH;Ti)o and

TE

reduces t o t h e Bohm-type v a l u e : 7,"

R ~ D , ; ) ; ~ , / c H, .

B r i e f l y i t may be explained i n a following way. Hot plasma c o o l s due t o a d i a b a t i c ex- pansion with a v e l o c i t y 'lYC

- q / K x ^,

^and

heat f l u x

q(t)

may be found by t a k i n g i n t o account t h e balance of p a r t i c l e s between a hot plasma and a near-wall l a y e r . It f o l - lows from eq.(2) t h a t t h e number of par-

2

t i c l e e i n a n e a r w a l l l a y e r

~ , ( t ) - a ~ k ~ ~ ~ ~ ~ ^{/ 4 ~}

B e c a u s e - ~ - n , ~ , ~ - g R / T ,

d ,

we determine

&

*

t h a t '12

I(+,

^?. no~o(~o)c,/t,\ ( 4 Such a dependence is v a l i d f o r

t

^STE

.

^NOW

f o r t h e cooling time

TE

we have:

h Cr

We have a l s o c a r r i e d out t h e nwneric- e l i n t e g r a t i o n of t h e complete s e t of plas- ma t r a n s p o r t equations, The plasma parame-

t e r s have been chosen c l o s e t o ,those of i m - ploading l i n e a r devices: tl, = 10 20 c ~ u - ~ ,

t-\,

=

= lo6 G,

T

= lo4 eV,

R

= 1 cm; t h e

The p r o f i l e s of temperature, d e n s i t y and magnetic f i e l d while cooling a r e shown i n Pig. I.

Fig. 1

The cooling time

TE

_{i s} p l o t t e d i n Pig.2 a s a f u n c t i o n of t h e magnetic f i e l d .

Fig. 2

It is seen t h a t t h i s dependence i s c l o s e t o t h e l i n e a r one t h a t corresponds t o t h e Bohm-type law,

Ref erencee :

/ I / Budker G.I. Proc. 6 t h Europ. Conf.,

~ o s c o w ,

2,

136, 1973.

/2/ Gross, R.A. Nuclear Fusion, 15,729,1975, /3/ Velikhov, E.P. Comments on Plasma

Physics, ?_, 171, 1972.

/4/ Vekstein, G.E. e t a l , Proc, 6 t h I A E A Gonf., Berchtesgaden, 1976 ,CX-35/E-21.

/5/ Vekstein,G.E. Sov.Phys., D o k l a d y , a , 295, 1977.

/6/ Jensen, B, P h y s . F l u i d s , ~ , 373, 1977.

Jablon, C., Longeon, R, Nuclear f i s i o n , 18, 775, 1978.

/7/ Feinberg,

-

B. Plasma Phys, ,l8,265,1976.

/8/ Braginsky, S.I. I n Reviews of Plasma Phys.,

1,

205, 1965.

w a l l s a r e considered t o be non-conducting,