THEORETICAL METHOD FOR PREDICTING THE PROPERTIES OF CYCLOTRON HARMONIC WAVES FROM THE PERPENDICULAR DISPERSION RELATION

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THEORETICAL METHOD FOR PREDICTING THE PROPERTIES OF CYCLOTRON HARMONIC

WAVES FROM THE PERPENDICULAR DISPERSION RELATION

Bertrand Lembège

To cite this version:

Bertrand Lembège. THEORETICAL METHOD FOR PREDICTING THE PROPERTIES OF CY- CLOTRON HARMONIC WAVES FROM THE PERPENDICULAR DISPERSION RELATION.

Journal de Physique Colloques, 1979, 40 (C7), pp.C7-615-C7-616. �10.1051/jphyscol:19797298�. �jpa-

00219287�

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JOUIWAL DE PHYSIQUE CoZZoqw C7, suppZ6ment au n07, Tome 40, JuiZZet 2979, page C7- 6 1 5

MEORETICAL METHOD FOR PREDICTING THE PROPERTIES tW CYCLOTRON HARMONIC WAVES FROM THE PERPENDICULAR DISPERSION RELATION

B. Lembege.

Space P Z c Z ~ ~ a Z V i ~ i o n Space Science Department, European Space Agency, ~ ~ ~ ~ d ~ i j k , fie NetherZands

A theoretical method is proposed

for predicting the properties of the back- ^+,2. ~ S O H ~

ward propagating cyclotron harmonic waves (CHW) from the simple dispersion curve for

&'4-

perpendicular propagation. This method is

i

i illustrated for the frequency range

3 0 -

1 < w/wC < 2, where w and w c are respec-

-

_w ^,^,^p ²

tively the wave and electron cyclotron ^wc ^t

i

frequencies and is applicable for any ,

plasma density conditions.

In previous experimental and theo-

2 1 a

retical study (LembBge, 1979), it was pro-

posed a new classification of properties

' [ ,

¹ ²

R e !KL Vr* Iwcl

of CHW both in the propagation and detec-

tion plane respectively described by the Figure 1 : Theoretical curves of the dispersion normalized wave vector

*

k p and the distance reZation i n the p e ~ e n d i c u l a r propagation for on vector

i?

; p is the electron gyroradius. example of dense pLasma (w /w J 2 = 13.02 ; t h e

P c

indexes 1 and 2 of P and P r e f e r t o the disper- This classification is based on the deter- c y l

?ion branches o f order 1 and 2

.

mination of two groups of values w/wc separated by a certain boundary value

(wcyl/wq) l. Knowing a given high value of other plasma densities. This is due to tbe (wp/wc)

,

where w is the plasma frequency, big variation of 61 with (w /wc) for mean

P P

and low plasma densities (Figure 2).

the dispersion curve for perpendicular propagation can be numerically determined

(Stix, 1962) ; consequently the value (W/W ) of its inflexion point P1 can be easily known. Then it was shown that the p1 value (w cyl/wc)l can be quickly defined from P1 by the numerical relation

(wcyl/wc).l = ( w / w ~ ) ~ ~

-

^where ^is

roughly constant for dense plasma condi- R C I ~ “ + ~ L ~ ; J

tions and equal to 0.145. This point Figure 2 : Theoretical curves of the f i r s t d i s - P cyl,l was shown to present particular

persion branch i n the perpendicuZar propagation characteristics and to divide the fre-

for ^(W/w ) 2 varying from i n f i n i t y t o very Zow quency range 1 < w/wc < 2 into two groups P c

values. The curve (CYL) (.-.-.) joins the d i f f e r e n t I and ^11. values of (wcy Z / ~ c ) Z . The curve (INTL) (---) joins

However, it can be shown that

t h e Zocations of t h e various i n f l e x i o n points PI.

although the classification into two groups I and I1 is always applicable for any plasma conditions, the previous principle of determination of the boundary value

( ~ ~ ~ cannot be simply extended to ~ / w ~ ) ~

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19797298

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Presently, the locations of P cyltl are determined for a large number of values of ( W / w ~ ) ~ from very low to infinite

P

plasma densities (Figure 2) ; each point P is numerically defined by the fre-

cylrl

quency w/wc for which the low damped part A1 of the polar curves kp has almost zero curvature with respect to the origin 0

(Figure 3) ; in this case A1 = Acyl ICyl.

Figure 3 : Sketch of the three kinds of polar curves of the real part of kp inside the frequency range 1 < w/wc < 2 (not to scale).

The ensemble of the points P

~ ~ 1 1 1 determines a curve (CYL) which is used as a reference curve ; this curve divides the plane (w/wc ; Re (k v /ac)) into two

I TH

areas I and I1 characteristic of the two groups previously defined (Figure 4 ) .

The present method consists of varying the ratio w/w represented by a

C

straight line (L) parallel to the axis Re (klvTH/wc) and noting where the line (L) intersects the curve (CYL). Three different frequencies ranges of w/wc, (a)

,

^{(b) and}

( c ) can be defined. It is shown that as a function of the ratio w/wc, the number of intersections between (L) and (CYL)

,

and various ranges of (w /wc) can be also

P

defined ; in each one of these ranges, the properties of CHW can be easily obtained using the characteristics of the groups I and 11. This method is shown to be extended to other dispersion branches of back- ward propagating CHW for perpendicular propagation.

References :

-

Lembsge (1979)

,

Antenna radiation pattern of cyclotron harmonic waves in a hot magnetoplasma, Rad. Science (to be published in May-June)

.

-

Stix (1962), Theory of Plasma waves, Mc Graw Hill, New York.

Figure 4 : Representation of the three characteristic frequency ranges (a), fb) and fc) of w/wc respectively defined by 12, 2.711, (1.71, 2.571 m d (2.57, 1 ) .