SPECTRUM OF CHARGE EXCHANGE NEUTRALS FROM ROTATING PLASMA

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HAL Id: jpa-00219228

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Submitted on 1 Jan 1979

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SPECTRUM OF CHARGE EXCHANGE NEUTRALS FROM ROTATING PLASMA

M. Ryutova

To cite this version:

M. Ryutova. SPECTRUM OF CHARGE EXCHANGE NEUTRALS FROM ROTATING PLASMA.

Journal de Physique Colloques, 1979, 40 (C7), pp.C7-503-C7-504. �10.1051/jphyscol:19797244�. �jpa- 00219228�

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JOURNAL DE PHYSIQUE CoZloque C7, suppZdment au n07, Tome 40, JuiZZet 1979, page C7- 503

SPECTRUM OF CHARGE EXCHANGE NEUTRALS FROM ROTATING PLASMA

M.P. Ryutova.

I n s t i t u t e o f NucZem Physics, Novosibirsk, U.S.S.R.

I n r o t a t i n g plasma experiments ( s e e , e.g., /I-3/) i t o f t e n happens t h a t t h e

i o n s a r e produced i n a device only due t o i o n i z a t i o n of n e u t r a l g a s i n t h e crossed e l e c t r i c and magnetic f i e l d s (and. t h e r e

a r e no o t h e r ion s o u r c e s , say, e x t e r n a l i n j e c t i o n ) . Since t h e i o n s produced from cold n e u t r a l p a r t i c l e s by t h e e l e c t r o n impact have a n e g l i g i b l y small energy a t t h e i n i t i a l moment, t h e i r f u r t h e r motion is described by t h e formulae: _{- ,}

.

V,

"tlr15io~L(t -to)

H (1

1

V\p 2

'*

^{\ ~ 0 5}

~ ~ ( t - t ~ ) - i]

where

E

(r) i s a r a d i a l e l e c t r i c f i e l d ,

H

is a homogeneous magnetic f i e l d ( d i r e c t e d

t h e f a s t n e u t r a l a r i s e s , which h a s j u s t t h e same momentum a s t h e i n i t i a l ion. I n a s u f f i c i e n t l y dense plasma, t h e f a s t n e u t r a l has some p r o b a b i l i t y t o be i o n i - zed a g a i n by e l e c t r o n impact o r by charge exchange w i t h plasma i o n before r e a c h i n g t h e plasma boundary ( i n both c a s e s t h e i n i t i a l momentum of t h e i o n appeared is n e a r l y t h e same a s t h e n e u t r a l momentum).

T h i s l e a d s t o t h e formation of t h e i o n s w i t h non-zero i n i t i a l v e l o c i t i e s . We c a l l

them "second generation" i o n s ( i n c o n t r a s t t o t h e " f i r s t generation" i o n s which a r e produced by e l e c t r o n impact i o n i z a t i o n from cold . n e u t r a l s and move according t o ^eq.(?)).

a l o n g t h e z-axis, s e e ~ i g . l ) ,

aL

i s Lar- Let u s f i r s t c o n s i d e r t h e p r o p e r t i e s mor frequency of i o n s - It i s assumed t h a t of charge exchange n e u t r a l s produced from

t h e Larmor r a d i u s of ion equal t o ~ E / H W L t h e first g e n e r a t i o n ions. Using eq.(?), 5s n e g l i g i b l e a s compare3 t o t h e s c a l e - i t i s easy t o show t h a t t h e d i s t r i b u t i o n

l e n g t h of a r a d i a l e l e c t r i c f i e l d which f u n c t i o n of f a s t n e u t r a l s r e g i s t e r e d by is u s u a l l ~ O f t h e o r d e r of t h e Plasma ra- _a d e t e c t o r w i l l ^bet h e following:

d i u s . Since t h e i o n i z a t i o n moments

to

a r e d i s t r i b u t e d randomly, t h e d i s t r i b u t i o n of i o n s over t h e phaselysbJL(t-Qis a l s o random.

A s seen from e q s . ( l ) , t h e a b s o l u t e value of i o n v e l o c i t y V ( ~ J Z

J '

l i e s w i t h i n t h e l i m i t s from z e r o

( \ Y =

0

,

2a)

t o V O ( ~ ) = ~ G / E [ ~ ) / H \

( y = $

1-

On t h e o t h e r hand, i n o f f - a x i s measu- remente of charge exchange n e u t r a l s (Fig.1) t h e n e u t r a l s w i t h maximum energy exceeding

max

^r" W ~ k ) ( w h e r e ~ , [ r ) s

~ ~ . l ( r ) / 2 )

a r e o f t e n

where no\r) and n(7) a r e t h e d e n s i t i e s of n e u t r a l s and i o n s r e s p e c t i v e l y ,

a,(w)

is t h e resonant charge exchange c r o s s sec- t i o n , n ( r ) = c € ( r ) / r ~ i s t h e a n g u l a r d r i f t frequency, and $3 i n ( 2 ) i s considered a s a f u n c t i o n o f W , d e f i n e d by t h e following r e l a t i o n s h i p :

det'ected, while a t s m a l l e n e r g i e s the s p e - From formulae (2) and ( 3 ) i t f o l l o w s ctrum of n e u t r a l s i s l i m i t e d n o t by z e r o a n important f o r t h e experiment conclu- but by a f i n i t e q u a n t i t y which is l.5+2 s i o n t h a t i n t h e case of "hard-body" ro- times s m a l l e r t h a n ~ F W o L o 1x1 t h e

eme-

t a t i o n , w h e n n ( i ) = c ~ n i t ,

d ~ / d ~

is of t h e s e n t paper a simple e x p l a n a t i o n of t h e s e form of a d e l t a - f u n e t i o n : d l / d ~ c n

&[w- w&];

f e a t u r e s of t h e n e u t r a l spectrum i s g i v e n * d e v i a t i o n of

dr /dbf!

from SJ d e l t a - f u n c t ion A s i s w e l l known, i n a resonant charge i s a measure of plasma motion d e v i a t i o n exchange event of a f a s t i o n on a n e u t r a l

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19797244

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from hard-body r o t a t i o n .

The f o m of t h e f u n c t i o n

~ L / W

i n t h e c a s e s when A(r) monotonely i n c r e a s e s and monotonely d e c r e a s e s w i t h r a d i u s is shown

q u a l i t a t i v e l y i n Fig.2. The p e c u l i a r i t y of t h e case c o n s i s t s i n t h e presence of t h e r o o t s i n g u l a r i t y on t h e lower ( i n t h e first c a s e ) and upper ( i n t h e second c a s e ) ends of t h e i n t e r v a l where

dT/dw

d.if- f e r s from zero. This makes i t p o s s i b l e t o f i n d r e a d i l y t h e d i r e c t i o n of v a r i a t i o n of t h e f u n c t i o n fl \r) from experimental data.

Thus, c o n s i d e r a t i o n of t h e f i r s t ge- n e r a t i o n i o n s a l l o w s u s t o e x p l a i n t h e presence of a lower bound.ary of t h e energy spectrum of charge exchange n e u t r a l s , A s t o upper boundary, i n t h i s c a s e i t cannot of course l i e above m;%Wc(r).

For e x p l a n a t i o n of t h e f a s t n e u t r a l s formation we have t o i n v e s t i g a t e t h e d i s - t r i b u t i o n f u n c t i o n of t h e second genera- t i o n ions. The number of t h e s e i o n s is de- termined by t h e r a t i o of i o n i z a t i o n l e n g t h

hi

t o plasma r a d i u s

R .

Usually i n experiments t h e c o n d i t i o n

hi>>

i s f u l f i l - l e d ( t h e case when

hi4< R

is d i s c u s s e d i n

/+/I.

Let t h e n e u t r a l , produced a t r a d i u s from t h e i o n of first g e n e r a t i o n and moving a t t h i s moment a t a n a n g l e d w i t h r e s p e c t t o e l e c t r i c f i e l d , be ionized a g a i n a t r a d i u s C*

.

Then t h e v e l o c i t y of t h u s produced second g e n e r a t i o n i o n chan- g e s w i t h time according t o

"C

where ^I

n\r6)

u = J.& ^~1

^t-v?(r)[i

- = ] s i ~ i '

\y = W L ~ + ~ O n & t (5)

Using t h e s e formulae, one can f i n d t h e d i s t r i b u t i o n f u n c t i o n of n e u t r a l s , produced by charge exchange from second genera- t i o n ions. However, t h e s e c a l c u l a t i o n s a r e t o o cumbersome, and we s h a l l r e s t r i c t our- s e l v e s only by r e v e a l i n g of t h e maximum value of t h e energy of t h e second genera- t i o n ions. Prom e x p r e s s i o n s (4). one can s e e , t h a t t h e maximum (over y/ ) v a l u e of t h e i o n v e l o c i t y is

w

D e t e c t o r Fig. 1

Fig. 2

I n t h e c a s e of "hard-body" r o t a t i o n t h e second g e n e r a t i o n i o n s have t h e same d i s t r i b u t i o n f u n c t i o n a s t h e first genera- t i o n i o n s , i.e. a c c e l e r a t e d p a r t i c l e s do n o t appear. The most obvious s i t u a t i o n i n which a c c e l e r a t e d i o n s appear, i s t h e f o l - lowing:

vo(r)

is t h e non-decreasing func- t i o n of r a d i u s , ~z.(r) i s t h e d e c r e a s i n g one, Let, f o r example,

vo

^(I-) be independ- e n t of

r

( t o judge by t h e r e s u l t s : of t h e paper /3/, Vo can be c o n s t a n t in a q u i t e l a r g e region). Then, from eqs. (5)-(6) i t i s easy t o o b t a i n t h e maximum energy of t h e second g e n e r a t i o n i o n s , which i s e q u a l t o

w ~ C ~ + - @ J / Z ,

^i.e. i t i e about 5 t i m e s h i g h e r t h a n Wo

.

One can g i v e some examplee i l l u s t r a t i n g a n even more n o t i c e - a b l e g a i n ,

R e f e r e n c e s :

/I/ B.Lehnert, Wucl.Fusion,

2,

485, 1971.

/2/ B.W.James, S.W,Simpeon, Phys.Lett.,

-9 347, 1974.

/3/ V.B.Bocharov e t al., F i z i k a Plasmy, 4, 488, 1978 ( i n Ruesian).

/4/

-

D.D.Ryutov, T.Tange, F i z i k a Plasmy,

3,

920, 1977 ( i n Russian).

SPECTRUM OF CHARGE EXCHANGE NEUTRALS FROM ROTATING PLASMA

HAL Id: jpa-00219228

https://hal.archives-ouvertes.fr/jpa-00219228