ABOUT THE GENERATION OF A "RESULTANT DRIFT INWARDS" FROM THE BOUNDARY OF A D-T-PLASMA BY ELECTROMAGNETIC FIELDS

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ABOUT THE GENERATION OF A ”RESULTANT DRIFT INWARDS” FROM THE BOUNDARY OF A

D-T-PLASMA BY ELECTROMAGNETIC FIELDS

F. Manfred

To cite this version:

F. Manfred. ABOUT THE GENERATION OF A ”RESULTANT DRIFT INWARDS” FROM THE

BOUNDARY OF A D-T-PLASMA BY ELECTROMAGNETIC FIELDS. Journal de Physique Col-

loques, 1979, 40 (C7), pp.C7-527-C7-528. �10.1051/jphyscol:19797255�. �jpa-00219240�

JOURNAL DE PHYSIQUE CoZZoque C7, suppZ6ment au n07, Tome 40, JuiZZet 1979, page

C7- 527

ABOUT THE GENERATION OF: A "RESULTANT DRIFT INWARDSw FROM THE BOUNDARY A D-T-PLASMA BY ELECTROMAGNETIC FIELDS

F. Manfred.

VoB, Seppeistr. 25, D-8 Miinchen.

tion of useful B(t1- and E(t)-fields for

A b o u t t h e g e n e r a t i o n o f a r e s u l t a n t d r i f t t h e r e s u l t a n t d r i f t .

i n w a r d s f r o m t h e b o u n d a r y of a

pla plasma

For generating the resultant drift the

b y e l e c t r o m a g n e t i c f i e l d s . fields B(t) and E(t) must both have terms

with cos@t,see equs.(*) and (**).That is

A i m :

T h e

E

- d r i f t a t t h e b o u n d a r y o f a possible,if the two fields ~ ( t ) and it)

c y l i n d r i c a l p l a s m a s h a l l

be

u s e d t o g e n e - are themselves built up by two fields:

r a t e a r e s u l t a n t d r i f t i n w a r d s f r o m t h e ~ ( t )

=

~ ~ ( t ) + ~ ~ ( t ) and

b o u n d a r y o f t h e p l a s m a . E(t) = El(t) + E2(t) .

1 ) The f o r m o f e q u a t i o n s f o r t h e m o t i o n Thereby should be at the boundary,where

of a c h a r g e i n a n E - B - f i e l d the resultant drift should exist,

a ) i n x - y - z - c o o r d i n a t e s , for example: B,(t)>> B2(t) with

b)

i n r - 6 - z - c o o r d i n a t e s . El(t)<< E2(t).

F o r a c y l i n d r i c a l p l a s m a w i t h a d i a m e t e r Then the resultant drift is produced by of s e v e r a l c e n t i m e t e r s o r e v e n meters t h e the two fields

e q u a t i o n s o f m o t i o n i n x - y - z - c o o r d i n a t e s ~ ( t ) = ~ ( ( t ) and E ( t ) Q E2(t), c a n f o r m a l l y b e t r a n s f ormed i n t h o s e f o r which fields are generated with desired x - f - ~ ~ o o r d i n a t e s Dy r e p l a c i n g

x b y

r and phase by currents in two separate coils y b y $ , i f t h e m a g n e t i c f i e l d

B

z i s s t r o n g wound around the cylindrical plasma.

e n o u g h o r , w h a t i s i n e f f e c t t h e s a m e , t h e The figures 5 till

8

show with the aid of g y r a t i o n r a d i i

are small.

T h e r e e x i s t s t h e n a d r i f t i n a s m a l l vo- l u m e , w h i c h i s a n a l o g o u s t o t h a t i n x-y-z- c o o r d i n a t e s f o r E = c o n s t . a n d B = c o n s t ..

S e e f i g u r e s

1

a n d

2.

2 ) T h e s o l u t i o n o f t h e e q u a t i o n s of m o t i o n w i t h a t i m e d e p e n d e n t m a g n e t i c f i e l d

B ( t )

=

Bo

+

B1.coSWt a n d t h e e l e c t r i c f i e l d s

(.) E $ ( t

) = E o v o - t

+ E

s i n & a n d

16

E

r ( t ) = E O r c o S W t

+

E l r s i n O t .

The f i g u r e s

3 a n d 4

show t h e

f i r s t

terms of t h e s o l u t i o n v r ( t ) a n d v ( t 1 , w h i c h

have nonlinear terms with sinwt,caused by #

the timedependent magnetic field BlcosWt.

The upper long expressions . a r e achieved bv the series development of

. JL,

e l

,

sinWt

c s l +

ⁱ

cu

⁴

s i n ~ t for Id<<

^{I .}

T h e lower expressions are achieved' with the aid of the saddle point method with

Fourier-Bessel-series calculated fields E(r,t) and B(r,t).By appropriate choise of the radius of the coil the electric field E(r,t) is generated in such a form, that only in the middle of the plasma,r=O, and at thB boundary

E

vanishes,see' fiyu- res 5 till 7..This E-field E2 is surely greater than that E l in fig. 8 near the zero-point of E1.In the opposite the mag- netic field in fig.8 can be built up gre- ater than that of the figures 5 tjll 7 near the zero-point o f E l in fiy.8,which lies nearly at r=l,l m.When the plasma reaches from r=O ti14 ne.arly r=l,l m,at the boundary of the plasma the desired E2(t)-,Bl(t)-field can established,which causes the desired resyltant drift.

The fig.9 shows appropriate parts of the field curves f o r E and

B.

4)Equations for E (t) and Er(t) in the

plasma. 4

the collision frequency V # 0,here for sim- If you set in v r and vo from fig.3 a n d 4 plicity with v = ~ . T h e constant terms in into the equatidns for Er

the expression for v r represent in a fiy.10,so you yet differential a n d Eb ^{equations from}

timedependent field B(t),E(t)

( * )

the with periodic coefficients because of the resbltant d r i p : sinwt-terms,which can cause instabili-

1 Eo

(**I

^{V @ -}

x - r ^, if 4Uf2<4fi

02.

ties.lf you s e r a ,=O,the equation of

U u

3)The calculation and graphic representa- fig.10 for E (t) with the terms

A

and T

t

is establish

d.

35

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19797255

If further the frequency of the elec- tromagnetic field,the plasma-frequencies W p s , s = e , d , t and the cyclotron-frequencies

AOs are chosen so,that they make the term A(1,what should be possible,then the wave length of

E/

in the plasma should nearly the same as in the vacuum.By this selection of the frequency w it should be possible to generate in the plasma fields E(t) and B(t),which give the resul- tant drift from the boundary inwards and suppress otherwise possible instabilities.

f&&t*)- $yJ

+,

l-c [ ~ w i + d ~ ) ! d ( ! J ~ ~ . t , $ ~ , ( + ) ]

+i-:. ^*Lj -* ("2- &:J4

+(/I] + d $ , i d c [ 8 , ~ g 4 j *; EA~! +

" m, ( " l d y

+ . t . e f - f * r ~ . + l ~ ~ . + ) + d,n.~ r

r n. tt tu'-&4 u .t

!,

^+."i

fig

.4

fig

.8

f i g . 9