A GENERALIZED OHM'S LAW OF UNSTEADY STATE IN PARTIALLY IONIZED GASES

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A GENERALIZED OHM’S LAW OF UNSTEADY STATE IN PARTIALLY IONIZED GASES

Lu Quan-Kang

To cite this version:

Lu Quan-Kang. A GENERALIZED OHM’S LAW OF UNSTEADY STATE IN PAR- TIALLY IONIZED GASES. Journal de Physique Colloques, 1979, 40 (C7), pp.C7-517-C7-518.

�10.1051/jphyscol:19797250�. �jpa-00219235�

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J O U R Z U DE PHYSIQUE CoZZoque C7, suppZdment au n07, T o m 40, JuiZZet 1979, page C7- 517

A GENERALIZED OHM'S LAW OF lJNSTEADY STATE IN PARTIALLY IONIZED GASES

Lu Quan-Kang.

Fudan University, Shanghai.

A generalized O h m ' s law i n f u l l y ionized gases has been given by spitze:;

and n s i m i l a r law of steady s t a t e i n p a r t i a l l y ionized gases has bsen derfved

by

owli in&'

and mdaMosr3J

We have d e r i v e

4

a generalized ^.ohm*$

l a w 6f unsteady s t a t e i n p a r t i a l l y ionized

gases, proviaed t h a t t h e i o n i z a t i o n and recombinat;fon processes have reached t h e dynamic e q u i l i b r i d f ' It i s

n e J j

-

neat z e ne

+ $ t t & t - & J x i -

; I t ; ( ~ t 4 ~ ^.A

is t h e i o n i z a t i o n &eLree, a _antia, _{a r e} t h e e l e c t r o n . a n d itom number ' d e n s i t y r e s p e c t i v e l y , $ i s t h e mean c o l l i s f o n f requency between an e l e c t r o n and an i o n ,

y,ls- t h e mean colLIsioxi f repuency between

tun e l e c t r o n and a n atom, 9; i s t h e mean collisAon Prequencg between an i o n and'mn atom, V ' i t h 5 veloc%<y of a plawna mass element,

4

i s t h e r e l a t i v e mean v e l o c i t y ef i o n s 'w&tB r e s p e c t t 6 t h e pla- mess element,"j i s t h e e l e c t r o n c u r r e n t d e n s i t y ,

-8 i s t h e e l e c t r o n charge, q , a n d & ; a r e t h e eIec t r o n and Ian- cycJotron frequency r e s p e c t i v e l y , % and B a r e t h e e l e c t r i c and magnetic f i e l d s t r e n g t h r e s p e c t i v e l y , c i s

t h e l i g h t v e l o c i t y ' i n f r e e space,P i s t h e p r e s s u r e of plasma, and Pe i k t h e p a r t i a l p r e s s u r e of t b e - e l e c t r o n gas

.'

When Ko -'I-q , ( 1 1 -reduces t o a more conve- n i e n t form. It i a

- = - net

fi a' at v ' t ~ + f x $ - & ~ x B - ~ r + ae A ^{A - L} ^a

The p h y s l c a l meaning of i n t e g r a l terms 3.n (2) can be shown by t h e f a l l o w i n g i n t e g r a t i o n :

i''[lf$cp$$df]xt

f.f

^(1- I'*) (3)

-- A

where, ~ $ 1 i s sbme midfile-value of

v

i n t h e i n t e r v a l -(O,%)

.

^{I n}^{( 3)}^;t h e ~rbi8dle- Viirue thearem has been ^ased. It i s obvious, from ⁽2) and ⁽a ) , t h a t t h e . r e l a x h t i o h processes of n e u t r a l p a r t i c l e s 2drtic.i- PatIng t h e whole movement 6f plUmZI e l e - ment i s expressed by t h e i n t e g r a l terms i n O b i r s l a w .

I n t h e l1mttSng case:r-o

i

^f.6. V r W o )

,

by u s i n g Ohm* s 14w f'2) and Maxwell @.quato iefis, "it Wg -be -@b%rineti' that t h e s p e e B of Illf v&nt s wave i s Vi

&

afld- I$ not ^,V,

,

where'% is the Alfren bpeed. The p h y s i c a l reason of t h i s r e s u l t fs ' ~ b v i o u s . As ^96-0

,

the n e u t r a l atcoms don't p a r t i c i p a t e i n t h e o s c i l S a t i o n s In BLfras wave.

S,imi&%rly

,

i f we use ( 2 ) i n s t e a 8 of

x C G X B = O

,

t h e d i s p e r s i o n r e l a t i o n of wgnetohydromagnetic ^wavei s

where

A -

^!-d^i~

o( ptiw

i s t h e angle between t h e wave v e c t o r 2 k and t h e a p p l i e d magnetic f i e l d , ^d1s t h e a n g u l a r f requencg, and Pg i s t h e sound v e l o c i t y .

As 'A+@, ( 4 ) retitices t o ' t h e resu1e.s glven b y BXfvBn a d Fiilthammar.

When t h e plasma d e v i a t e s t o %he n l u t r a - l i t y , t h e form of generalifeti Ohm's law h a s 3 0 be c o r r e c t e d . The form o f [ I ) becomes

nec nec

where ne'

c P

m e ( u t 4 )

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19797250

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where

9,

i s t h e e l e c t r i c charge d e n s i t y sf plasma.

When t h e p l a s m approaches the s t e a d y s t a t e , ( 5 ) reduces t o t h e form given by

A M ~ U M O B :

4 a

0 vpe+nel$ + ~ $ x i ' ) - ~ ~ x ~ -$(x+*e)(j-&v)

+ ~ a C P P +1+ -. ( 6)

B K; e ~ J X B +$,F]xZ

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.

X S p i t z e r Jr. ,Phys. of ' F u l l y I o n i z e d

M s B s , - 'Tnt;ePsclence ^,119561, ( 2)

.

^T.G. ^Cawling; Magzietohydradynsmics,

I n t e r s c i e n c e , ( l 9 5 7 l .

( 3)

.

l\1.d6iHo~, flMM 25 (1961) 611, ( 4 ) .

7

=PI.Un, -&ctn P h y s s a S i n i c a

26

197'it) 417'.

(5). Hi Alfv6n dad C-G FLlthammslr

,

CoSnical E l e c t r o d ~ n a m i c s , ^the Clarandon P r a s s (1963)

.