A PHYSICAL PICTURE OF THE HIGHER-ORDER LANDAU MODES OF ELECTRON PLASMA WAVE

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A PHYSICAL PICTURE OF THE HIGHER-ORDER LANDAU MODES OF ELECTRON PLASMA WAVE

S. Ikezawa, Y. Nakamura

To cite this version:

S. Ikezawa, Y. Nakamura. A PHYSICAL PICTURE OF THE HIGHER-ORDER LANDAU MODES OF ELECTRON PLASMA WAVE. Journal de Physique Colloques, 1979, 40 (C7), pp.C7-573-C7-574.

�10.1051/jphyscol:19797277�. �jpa-00219264�

JOURNAL DE PlfYSIQUE CoZZoque C 7 , suppZe'ment au n07, Tome 40, JuiZZet 1979, Page C7- 573

A PHYSICAL PICTURE OF THE MGHER-ORDER LANDAU MODES OF ELECTRON PLASMA WAVE

S. Ikezawa and Y. ~akamura'.

Chubu I n s t i t u t e o f TechnoZogy, Kasugai (Nagoya-Shigail 487, Japan.

y n s t i t u t e o f Space and AeromuticaZ Science, University o f Tokyo, 253, Japan.

Introduction: The higher-order Landau modes where v o l t

2=

( 2 k ~ ~ , ^2/m) 'I2. ^{o r w}

^{= O r}

^n=l

^I

~2

were theoretically analyzed by Derfler

&

and n23, the modes are named as the funda- simonen/l/ using a set of the plasma wave mental Landau node and the hic~her-order functions. In order to make clear the Landau modes, respectively.

meaning of the individual higher-order In the case o : the water-baq model, the Landau mode, we calculate the dispersion

relations of the electron wave in a two-

"axwellian plasma/2/ and also in a water- bag plasma/3-4/ for w/w,<l(w :electron

P

plasma frequency

j

, an5 co!lipar

t: i l ~ e ~ , ~ 2:i

the previous experiment/4/. It is found that the higher-order Landau mode strongly depends on the temperature in the high energy tail of the electron distribution.

Dispersion relations: In the case of -- the

-

a

-

, one dimension-

al distribution of electrons is written as,

F ( t , x , ~ ) = f ~ ~ ( ~ ) + f ~ ~ ( ~ ) + f ( t l ~ , ~ ) ,

(1) fol, 2=1,2 ( m / 2 ~ r k ~ ~ ,

2 )

112exp(-nv2/2k!21,2) n2/nl=a<<l, T~/T~'~>I.

f

denotes the perturbed distribution, and the subscripts I

&

2 denote the cold part

&

the hot part, respectively. The basic

equations are the Xaxwell equation approx- imated by the dipole excitation and the linearized-collisionless Eoltzmann equa-

distribution is composed by the Yaxwellian plus a water-bag due to the random motion of monoenerqetic electrons. The dispersion relation is shown as follows/3-4/;

k ; = (wgl/vB1) ' ^{z ' (w/knvOl) +(wpc/vc)}

^2/

[

(w/knvc) '-11,

where vc and wpc denote the truncated

~ r e l n c i t l 7 a n d the

~ \ ~ a t ~ r - h a ?

P I a9ma

+TP?IIP~PV.

The eqs.2 and

3

are calculated usinc the Newton-Raphson method for a=0.1 and b=

5 ( = ~ ~ / v ~ ~ ) = 4 - 5 0 , and shown in Fiqs.1 and 2,

C

respectively. One can see in Piq.l,the two- temperature(m0dified fundamental Landau) modes with 4Sbs22 merge into the 3rd-order Landau mode (a=0) . For 23cb~32, it merges

into the 4th-order Landau node, sequentigl- ly. However, as shown in "ig.2, the phase velocity can be varied arbitrarily with B in the case of the water-bau model.

Discussion: The experiment was performed using the chamber at the Institute of Space tion. using the ~ourier-Laplace trans'or- and Aeronautical Science, University of mation, the dispersion relation is given Tokyo/&/. Tith the hish anode voltage Vaof with the derivative of the nlasma dis!?er- the glow mode ~ l a s n a source, a typical

sion function

'2'

as follows; energy distribution and the dis2ersion re- k ~ 9 ~ p 1 / ~ e l )

' 3 '

I w / ~ ~ v ~ ~ ) + ( ~ ~ ~ / v ~ ~ )

? .

lation are shown in Fig.3. From the in-

2- 2

Z

' ^(w/knvg2)

~ p - ~ p l + ~ ~ 2 r

(2) serted fog., we obtain a=0.07 and

h=4

for the two-temperature model, and

B=10

for the

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19797277

water-bag.mode1. The dispersion relations observed agree with that of ehe two-tehper- ature model shown by

(3) &

(4) for b=4.

In summary, when the monoenergetic elec- trons are injected into the plasma for the non-?laxwelli.an experiment, they are assumed to be soon thermalized with the finite tem- perature T2 and contribute to the higher- order Landau mode. The authors thank Prof.

Y. Kawai of Kyushu University for discus- sion, and Prof. T. Okuda, Prof.

0 .

"iikami and Prof.A.Kimpara for encouragements.

This work was supported by Extra Research

Budget of Chubu Institute of Technology. I

References:

/l/.H.Derfler and

T.C.Shnen: Phys. Fluids z(1969) 269.

72, AX;- at~d?'I.Vm %l-t<XPTC;, 31~012 t19?1!

p.96.

/3/

J.P.Treguier and

D.Henry:

J. ?lama Phys. 13

(1975) 193.

/4/

Y.Kawai, Y.Nakamura, T.Itoh, T.Hara

and T.Kacvabe

;J. Phys.

Soc.

Japan 33-(1975)876.

Fig.2.Dispersion relation of the water-bag

?ode1 from

eq.3

06 i1 ^d2 63 ^6.4 6.5 0:6 0:7 .~ig.3.~omparison with the exneriment/4/.

k n l

km The inserted figure shows an energy

Fig.1. Dispersion relation of the two- distribution with T1=7eV, T2=28eV, temperature model from eq.2 a-0.07, and the truncated potential

Vc=7 OV .