ABOUT THE STATIONARY TURBULENCE REGIONS AND ANOMALOUS RESISTANCE IN THE MAGNETO-SPHERE PLASMA

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ABOUT THE STATIONARY TURBULENCE REGIONS AND ANOMALOUS RESISTANCE IN

THE MAGNETO-SPHERE PLASMA

A. Volosevich, M. Livshits, V. Liperovsky, G. Skuridin

To cite this version:

A. Volosevich, M. Livshits, V. Liperovsky, G. Skuridin. ABOUT THE STATIONARY TURBULENCE

REGIONS AND ANOMALOUS RESISTANCE IN THE MAGNETO-SPHERE PLASMA. Journal de

Physique Colloques, 1979, 40 (C7), pp.C7-625-C7-626. �10.1051/jphyscol:19797303�. �jpa-00219293�

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JOURNAL DE PHYSIQUE CoZZoque C7, suppZBment a u n07, Tome 40, J u i Z Z e t 1979, page C7- 625

ABOUT THE STATIONARY TURBULENCE REGIONS AND ANOMALOUS RESISTANCE IN THE MAGNETO-SPHERE PLASMA

A.V.

Volosevich,

M.A.

Livshits,

V.A.

Liperovsky

and G.A.

Skuridin.

I n s t i t u t e f o r Space Research, Ac. o f S c i . , U.S.S.R.

The s t r o n g l o n g i t u d i n a l c u r r e n t s , low frequency e l e c t r o s t a t i c waves of h i g h l e - v e l [I] and l o n g i t u d i n a l e l e c t r i c f i e l d s

due t o anomalous r e s i s t a n c e

[2]

a r e ays- t e m a t i c a l l y observed i n t h e E a r t h magneto- sphere plasma. So i t i s i n t e r e s t i n g t o con- s t r u c t even though rough semiempiric mo- d e l s t o d e s c r i b e t h e s t a t i o n a r y r e g i o n s of t h e wave e l e c t r o s t a t i c turbulence which

a h e r e

C s

, c o e f f i c i e n t 4/3 i s due t o t h e p r e s s u r e g r a d i e n t i n the equa- t i o n of motion. The t u r b u l e n t h e a t i n g of e l e c t r o n s znd i o n s can be roughly des- c r i b e d by t h e s e t of e q u a t i o n s assuming t h a t t h e turbulence

i s

weak and t h e d i - r e c t i o n a l v e l o c i t y vie= Z T T ; = ~ and tZ

=

c o n s t .

:

r e s u l t s i n anomalous r e s i s t a n c e . W e s h a l l - a n a ~ i u o = o =-A

IelEhC, 2 ,o

r

7;3&

f u r t h e r r e s t r i c t o u r s e l v e s t o t h e one-di- mensional model of t h e f a i r l y wide magne-

t i c f i e l d tube. Let t h e e l e c t r i c f i e l d be a l i g n e d i n a p o s i t i v e d i r e c t i o n of

Z

axis along t h e magnetic f i e l d tube, and Te=T,, *

T ~ = T ~ and the l o n g i t u d i n a l e l e c t r i c f i e l d E ,,

⁼

^Eb

^{i f}

^z

⁼^0.

The e q u a t i o n d e s c r i b - i n g t h e t u r b u l e n t h e a t i n g of e l e c t r o n 0 i s

The e q u a t i o n of motion i s

hQ2a - ^\e\n ^E ⁺ muon3*

at

9

where 3 * i s t h e c o l l e c t i v e c o l l i s i o n frequency, v0 i s t h e d i r e c t i o n a l velo-

c i t y .

I f the

c o n d i t i o n

B

> 1 3 ~ ~ 1 6 ~ 3 ~ ~ ~

Tc m;

i s f u l f i l l e d , t h e n t h e Sagdeev formula i s v a l i d f o r c u r r e n t i n the e l e c t r i c f i e l d i n t h e homogeneous plasma s t a t i o n a r ~ r e -

The c u r r e n t along t h e maanetic f o r c e tube

The s o l u t i o n of t h i s system w i t h

4 >>+: , t . = a ~ d ~ . ~ l $ t a k e t h e form:

TI IT: = 1 - 3 UP^'^

=

^0.

rs

( ~ 2 ) l ' ~

E/&, ==IT:) CAZT'~

Limiting of t h e magnetic tube l e n g t h L i s a s s o c i a t e d with t h e c o n d i t i o n of the i o n sound e x i s t e n c e , f o r example, T e a 6Ti

and

T*

= lo3 ev, Ti=leV,

-lo2 omm3,

e

- -

²

E

=

3.10 v/m, q

=

30 mp. the l e n g t h of t h e tube of t h e f i e l d a l i g n e d current;

w i t h t h e q u a s i - s t a t i o n a r y turbulence

For t h e p o t e n t i a l drop we have

t h a t

i s

equal- 380v f o r the above w r i t t e n parameters. The c o n d i t i o n of v a l i d i t y of t h e Sagdeev formula

E > E 2

i s f u l f i l l e d f o r the g i v e n example i n the upper p o l a r

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19797303

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ionosphere i f t h e e l e c t r o n temperature a r e not t o o h i g h Te<5.10 3 eV.

The o t h e r p o s s i b l e case o f q u a s i s t a t i o - n a r y regime w i t h E;<E<E2,

i s d i s c u s s e d i n [4]

.

The c o e f f i c i e n t ) l = $ i s due t o the p r e s s u r e gradient.The s a t u - r a t i o n mechanism a s s o c i a t e d w i t h t h e non- l i n e a r deca,v p r o c e s s S 7 S 1 + S " which

i s

f e a s i b l e when t h e wave spectrum c o r r e l a - t i o n broadenina i s taken i n t o account .The e q u a t i o n s f o r t h i s case [6]:

szq= ^lelnzr. ^E

⁺

^f ^hz%u.

where

i t i s

assumed t h a t

2T;d =

and n=n,=const,can be s o l v e d i n t h e sta-

V

x7'2+ 2

~ f

^;^COW+,

i

t i o n a r y case:

3

4%

=

(4-d2j'/3 ^A=

^e ⁵

E,

^>

r.2

-

These s o l u t i o n s a r e t r u e w i t h

A?

4

1

For example.the s t a t i o n a r y t u r b u l e n c e can e x i s t f o r 2 4 5 0 km, i n some l o c a l i z e d r e -

-

^L

g i o n when T*=5 keV, E-3-10 vIm.For f a i r l y s m a l l d i s t a n c e s d % 4< 1

, TL - i f t

and

T , ,

e l e c t r i c f i e l d i n s i g n i f i c a n t l y v a r y w i t h t h e d i c t a n c e . when

A s

~ 0 . 5 1 ,

TdT; - ^{6 ,}

t h u s , t h e magnetic f i e l d tube l e n g t h does not exceed

75

km w i t h the t u r b u l e n t r e - gime c 6 3

.

For t h e case o f e x t e r n a l t u r b u l i z a t i o n i f t h e r e

i s

a heat-remova1,in t h e s t a t i o - nary case we can f i n d t h e

A

(E,W).Tfie pro- blern of t h e anomalous r e s i s t a n c e due t o s t r o n g ion-sound t u r b u l e n c e produced by a n e x t e r n a l source was c o n s i d e r e d i n

[5] .

The s o l u t i o n of k i n e t i c e q u a t i o n made

i t

The c u r r e n t

i n

independent of t h e e l e c t - r i c f i e l d i f

E < d m i , !$

^C

^' ⁴⁰

From t h i s e x p r e s s i o n and t h e e q u a t i o n f o r t h e homogeneous s t a t e F , - \ e \ h ~ = 0

,

%= h~'3,

one c a n o b t a i n t h e c o l l i s i o n e f f e o l i v e frequency

9 =

lm

* Am,!%-

The s e t of e q u a t i o n d e s c r i b i n g t h e coor- d i n a t e dependence o f

h , ,

^E, ^{Te i n}

s t a t i o n a r y c o n d i t i o n s : 'no%,

does not have s o l u t i o n s i f n = c o n s t

F

Analogously, if

Ee E,

t h a n

4

⁼

^on ^cS& , hi =

^MI) i n t h e

Ru-

dakov-Korablev regime by n=const t h e r e a r e no s o l u t i o n . F o r f i n d i n g f u n c t i o n s

mental i n f o r m a t i o n about one of t h e s e f u n c t i o n s

i s

needed.

lie f e r e n G

I . R.K. F r e d e r i c k s e t a l . JGR, 1973,

E.

2133.

2. F.S. IuIoser. I n "UIagne t o s p h e r i c P a r t i - c l e s and F i e l d " . Holland, 1976.

3. R.S. Sagdeev. Proceedings o f Symposia i n Applied &Inthematics

18,

1967.

4.

V.N. Tsytovich. Plasma Phys. 1971,

2,

100.

5.

M.A. L i v s h i t s , B.A. Lipemvsky, V.Id.To mozov, V.IT. Tsytovich. The S t r o n g ion- a c o u s t i c Yurbulence and E l e c t r o n Spec-

t r u m

i n an E l e c t r i c F i e l d . Report on t h e 1 4 t h I n t .Conf. on Zhenomena i n i o n i z e d c a s e s .

6. V.A. Gudlsova e t

al.,

I n t l S t r u c t u r a magne to-ionoshernich a v r o r a l n i c h vos- muscheniiw

.

Iiauka, Leningrad, 1977,

P O 23-

p o s s i b l e t o f i n d t h e c u r r e n t of nonrun- away e l e c t r o n s :

jg= JJ, ^(q @)U;

d 3 = e f i + ( v