Enhancement of cyclotron absorption of plasma oscillations excited by powerful radio wave below multiple electron gyroharmonics

Adv. Space Res. Vol. 29, No. 9, pp. 1379-1384,2002 0 2002 COSPAR. Published by Elsevier Science Ltd. All rights reserved Printed in Great Britain 0273-l 177/02 $22.00 + 0.00

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PII: SO273-1177(02)00191-6

ENHANCEMENT OF CYCLOTRON ABSORPTION OF PLASMA OSCILLATIONS EXCITED BY POWERFlTL RADIO WAVE BELOW MULTIPLE ELECTRON GYROHARMONICS V.V.Vas’kov Jnstitntc

qf Terrestrial Magnetism. Ionosphere and Radio Wave Propqqation HAN (IZMJRAN). Troitsk. Moscow Region I421 90. Russia

ABSTRACT Theoretical research of increase in the cyclotron absorption of upper-hybrid plasma oscillations generated by a powerful radio wave is presented. Such increase occurs at pump frequencies below the harmonic of electron gyrofrequency due to the transformation of the plasma wave energy into a large wave number region which is formed in a magnetized ionospheric plasma under the action of the spatial dispersion. We suppose that proposed mechanism can result in the experimentally observed effect of additional ionosphere ionization appearance belotv the el&tron gvroharmonics and can lead to corresponding asymmetry in the effects of ionosphere artificial airglow and plasma noise enhancement caused by accelerated electrons. 0 2002 COSPAR. Published by Elsevier Science Ltd. All rights reserved.

INTRODUCTION It is known that the interaction of a powerful radio wave with the ionosphere can result in the production of suprathermal electrons with energy more then ionization potential of neutral particles (I2 - 15) eV and consequently in additional ionization of ionospheric plasma by accelerated electrons. Electron acceleration is connected to the cvclotron absorption of plasma oscillations generated by a powerful radio wave due to its scattering by art&&al magnetic field aligned irregularities created in the pump wave upper-hybrid resonance (UHR) region co;@ = co<;- ~6, 1where w, is the frequency of powerful radio wave. w,, = (4~’ electron

plasma

geomagnetic

frequency,

field B

gyroharmonics

N

is the electron

density,

w,, = eB (m,c)

Grach e/ al. (1997) has shown that additional

in the case of negative

frequency

is the electron

ionization

N/m,)’

” is the

gyrofrequency

in the

appeared near the 4-th and 6-th

shift with respect to gyroresonance

(w,, -

FIW~~ ) <

0 (the

references According

to the previous papers about additional ionization of the ionosphere are given in the cited articles). to Vas’kov er nl. (1999), such an asymmctrp of the effect may be caused by the influence of an

additional

second region II for the upper-hybrid

plasma oscillations

with a great wave vector component

k

2 pii

in the orthogonal to the magnetic field direction w:here heavy cyclotron absorption takes place. This region is created in magnetized plasma under the action of the spatial dispersion for the waves \\-ith large wa+e numbers in addition to the first region I containing

the plasma oscillations

\vith small wave numbers

k < pi:

and relativel)

weak cyclotron absorption. In this case the process of the electron acceleration looks as follows. At first; the pump wave excites comparatively long wave plasma oscillations in the region I due to the scattering by the irregularities. The excited oscillations are pumped over f?om the region I into the region II because of the induced scattering by ions. Thereafter they diffuse over this region due to multiple scattering by magnetic field aligned artificial irregularities and induced scattering by resonant particles and eff&ntly give up their energy to the electrons owing to the cyclotron absorption. Below calculation of this process is presented for the conditions when the diffusion of the plasma oscillations along the spectrum of wave numbers both in the first and in the second region is going on only

1379

V. V. Vas’kov

1380

due to the multiple scattering b!; irregularities. In addition to Vas’kov et ~71.(1999) in this paper the spectra of excited plasma waves in both regions are calculated taking into account the possibility of waves pumping over back from the region II into the region I. For simplicity wc consider mainly the vicinity of gyroharmonics with large numbers II =5 and 6, as the plasma oscillations cyclotron absorption in the region I in this case turns to be small and generation of the accelerated electrons takes place only in the region Il. DISPERSION PROPERTIES OF PLASMA WAVES Let us take into account that the processes of’ excitation and pumping over change the plasma wave frequency w z co,, only slighti\,. Therefore. we will consider the dispersion

properties

of these waves near the UHR point

where they arc excited. The dispersion relation for plasma waves in the region I near this point at rs >> o,,

can be

written in the following form (Grach. 1985) + 4’ + 3(x + .YY

vz x=k_?p;,, where

+p=o,

v^oi?q

v=w/u,,, ~=7;,i(ml,cz) ,

y=k,;p;,,

E’(w, k) = ReE(Lc), k) is the real part of longitudinal

orthogonal

(1)

to the magnetic

field B components

radius of the electrons with the temperahIre

dielectric

of the wave vector

71, A small parameter

fimction:

.

k

k,. k

pNv = (71, m,

are the parallel

wi,)’

’

and

is the Larmour

,8 - 10. 7 is included into the right hand side of

Eq. (1). This parameter takes into account the effect of small transverse

corrections

in the area x-/?“,

y 5

y -+ 0

in the region 1 are small: x 5 1 12,

The imaginaq

E” = Im E(O, k) equals to the sum of two terms: E” = E: + &f.

part of the dielectric function

1 ‘3 for CUDS ;o:~ =

v2 -

One can see that the wave vector components

first term c,” describes the c?;clotron absorption of plasma waves in the n-th gyroharmonic

J,(x)

Maxwellian.

The

vicinity

(2)

x+y

where

1

is the n-th order Bessel function

of the imaginaF

argument.

The second term &: describes the plasma wave collisional

.$ = v, tr) where vt, is the frequency of the electron collisions

Hereafter the plasma is taken to be

damping.

In the region I it is equal to

with heavy particles (ions). According to Eq. (1,2)

the plasma wave cyclotron absorption decreases with the increasing of the frequency o , and in the conditions of the ionospheric experiment near the 5th and 6-th g!Tohannonics this absorption is less than the collisional one. In order to describe the plasma wave behavior in the additional region II we need use the general expression for the dielectric fimction &‘(a, k) in collisionlcss plasma (3)

The second, additional region of weakl\- damped plasma oscillations

arises due to a strong spatial dispersion

area of great x and small ,y << x at a small distance from the dimensionless to y = 0. The value

x,

can be found

near the n-th gyroharmonic

of the equation

t‘,, (x =

in the

x = x,,corresponding

x,, ) = 0, where the tinction

by Eq. (3) in the limit of y -+ 0 . qd.z, ) = 1. When we describe the function

E,,(X) = E’(x, y = 0) is determined y(x)

as a solution

wave number

(Fr - v) <<

general expression (3) and take &z,)

1 near the UHR point we need only retain the function

~(z,?)

in the

= 1 when m # n. As a result for y << x we obtain (4)

Cyclotron Absorption below Gyroharmonics The possibility

to expand

the coefficients

of the cyclotron absorption

in Eq. (4) in terms of a small incrcmcnt (Eq. (2)) in the region I1 with increasing J’

Equation (4) determines q(l/

fi)

calculated

is given by the cunc

behaviour

from the general

of the p(z)

expression

(3) for different

?x) H at x = x, :

propert?. of this function

in Figure I xc present the dispersion

1’. Note that near the electron

curves

g)roharmonics

b!, the curve ci _ in spite of the fact

x,, , R(x,)

can change significantI>, v+ith v. see the Table (all the cures 7 in Figure 1 and the Table arc calculated for the UHR point of the plasma wave wai8 “ii, = 17’ - I).

that the coefficient and parameters

K and parameters

12. The cuncs for v = 5.6 and

from Eq. (4) arises at (W - lT) 2 0.2 and incrcascs lvith decreasing

v = 5.4 in Figure parameters

K = (&,

(/ in Figure 1. Two-valued

For comparison.

(n - 11)< 0.1 these curves arc close to each other. The\ arc well approsimated

A deviation

A.x is based on a sharp increase

/? = ,I! (1~- 11)’ of / = K & . where

the dependence

- I= -1. This dependence

is caused by non-monotonous j?(t)

1381

1 illustrate

changing

the behaviour

for these cases are: xm =5.89.

K=0.0988.

&x,)=1.330

TABLE.

for v=5.4,

K -0.344.

of y(r)

away f?orn the gproharmonic

H(x,,)=O.576

for I’-5.6,

n=6.

IIW,,

The main

and x0, =10.373,

t1=5.

The Basis Parameters Chamctcrizing

the Dispersion Propcrtics of Plasma Waccs in Region II.

The effect of \veak collisions is described in the Bhatnagar-Gross-Crook approximation. The plasma \\aves collisional damping only slight11 varies in the region II. unlike the cyclotron absorption. Near the n-th gyroharmonic

at v, <
(Vas’kov ct nl., 1999). The relationship determined by the following parameter

bct\\ccn

This

Table

parameter

is also

given

Te = O.leV; .f,, = 1.33M~z;

in the

the collisional

for

the typical

ET, = (vc (r)Be)fi

and cyclotron

conditions

damping

of the

V) =

>> &(T,

in the region

ionospheric

is \\eak:

II is

esperimcnts

V@CUBB x (4.9, 7.7, 11). 10 c near 4-th. 5-th. and 6-th g!.roharmonics.

Dots on the curve in Figure 1 denote the limits of the area n-here the cyclotron absorption (in the case ()I -

v -II

respectively,. &:(k:

) < E:,,

0.05 - 0.20 this area is located at p < (7 - 5.4). IO ’ ).

MAIN RESULTS Let us tind the spectrum of plasma noises evcitcd b?, the powerful radio \\ave taking into account the noises pumping over into the region II due to the induced scattering b> ions. The induced scatbring is related to the interaction of resonant particles (ions) with the low frequcnc! beatings of the clcctric field occurring at the difference frequent!. for two waves (w, , k,) and (w,, k,) in the first and second regions, respectively. in the process of the pumping over the frequcnc) of the cscitcd oscillations becomes smaller b>, the quantity

&u-/k,-k,j(27;.m,) '' << a, (uhere considered

71, m2 are the ionic temperature

and mass. respectively)

case k, F k m = (xnl )’ ’ pne >r k, can be taken as a constant.

which in the

WC also take into account that the

process of cascade pumping over the plasma Lva1.cenergy bct\\esn t\vo regions bccomcs possible with the po\\erful radio leave intensit!. increasing. This process can lcad to the formation in the plasma \vave spectrum a great number of satellites

j,,, >> 1 with frequencies

~0’~’ = CO,,- (,j - I)c~‘w, where

o,, =

vi,coBe

is the powxful

radio wave

1382

V. V. Vas’kov

frequency. The set of equations describing the plasma wave energy losses distribution considered case takes the formt see Vas’kov ef al. ( 1999) :

in the satellites

for the

(6) j22,

at

(7)

where we introduce the spectral function of energy losses qy) and integral wave intensity

H(‘j (in the orthogonal

to magnetic field direction) in the j-th satellite equal

(8) Here W;” is the energy density of the plasma waves in the satellite proportional spectral

density

coefficients

a

; yk

is the linear

LI(~’ in Eq.(7) are the rnkn

weight factor - k:

decrement

of the plasma

value of 2s”(ki )(k’ lkf)

The normalization

x=(klipB,)‘,

orthogonal

to the magnetic

&“=E:),andeven

As before, the subscripts oscillations

field B

j=2o

of the electric field amplitude

Therefore,

-totheregionII(k,

is different

Corn that used in

to draw the plasma wave electrostatic

=kzl.. x=(kZipHc)‘.

1, 2 refer to the regions I. II, respectively. c’(cL)~‘),k) = 0 where

variable.

The orthogonal

The longitudinal

the

along the spectrum u-ith the

Odd j = 2a - 1 refer to the satellites in the region I (k,

wave vector kL is used as an independent

from the dispersion relation

wave damping.

a Aer averaging

(Vas’kov et nf., 1999) by the factor 2. The factor kl lk is introduced component

to their electric field fluctuation

kflk’=l component

component

field

= k,, _

) E”=.$). of the plasma

k,, should be found

Q(” = CLI,)can be taken in the considered

approximation

0.8

0.6

0.4

0.2

0.0

-1

-0.4

-0.2

0.0

0.2

0.4

Fig. 1. Dispersion curves JJ of t in the region II near the UHR point of the plasma waves.

0

5

10

15

20

25

30

Fig. 2. Behavior of coefficient c2 describing the cyclotron portion S of energy losses in the region II.

Cyclotron Absorption

(we assume that ftiiJ) = o,, in all the functions

below Gyroharmonics

except coefficient

1383

I;‘ depending

on ( (uil’ - w”-” )). The spectrum

of the plasma waves is taken axially symmetric. The right-hand side of Eq. (6) for the first satellite contains a source term describing the coherent excitation of plasma waves due to the polarization of elongated irregularities in the field of the powerful radio wave. This ternI, i.e. the parameters

Q,, , k,?, are given in (Vas’kov et. LxI.~1999). The

second term in Eq. (6): (7) is responsible for the nonlinear interaction between adjacent satellites at the expense of the induced scattering of the waves by ions. The coefficient 11 (at F = 1.75 ) is equal to the maximum of the matrix element describing

this process for the optimum

in nearly one-temperature

ionospheric

2, = (SW / k_.,)(m,

value of the parameter

plasma. We kept in mind that the plasma wave excitation

the UHR point of the powerful radio wave N = N,

= nre (w,: - w,&) ‘4~‘.

2T)“’

2 1,3

takes place near

We also took into account that the

scale of the region II is small: Ak f << k f, due to a sharp increase of the cyclotron absorption.

characteristic

The third term in Eq. (6) (7) describes plasma waves diffiision along the spectrum as a result of the multiple scattering by artificial small scale irregularities (Grach. 1985). It can be expressed in terms of the energy flux of in the wave vector space Pi’) = 8

plasma oscillations region

(q::‘).

1 (see Eq. (1)) near the UHR point of a plasma

According to (Vas’kov, 2000) the flux PIL” in the wave with a frequency

~1)>> uHe takes the form (9)

where b2 =< l&VI’ > Ni << 1 is the relative mean-square

density perturbation

in the small scale irregularities,

equation (1) in the limit of /? + 0 : J’ W’

and y is one of two roots of the dispersion

= (1 - 6x T Jm)

The transition from yi” to y(‘) is performed with regard to the continuity of the function Pi,:’ in the merging point of the roots x = I/ 12. The homogeneous that are independent boundaries determine a w+‘)

of the region the spectral

= a,

smoothI!, (12(i)=

of ,j derived

Calculations increases

x = 0, y’ ” = l/3.

q;:’

of energy losses

with

the

parameter

solution

C;

from

WC obtain

roots y”.“’ of the dispersion Dependence are determined

of the normalized

to

allows

{=(1-12x)“’

us to

factor and to find the constant the coefficient

C, = 2.60

In

c, = a, 12~:. particular,

to 12” = 0 is valid. This solution

C“‘) are the normalization

spectral function

up

/{if’ = 0 at the

of this equation

6,” = &I; = cmat

ci = 1

of Eq. (7) corresponding

equation.

conditions

c, = 1.25, 1.45, 1.98, 2.36, 2.54, 2.57, 2.59.

q;;;2/ = cCjj(1 +<‘exp[-2(1To], - j +q(.‘.‘:i &IL ’

q;;; +:;?

Solution

except for normalization

show that for weak cyclotron absorption

0.1, 0.2, 0.5, 1.0, 2.0, 3.0, 5.0

(; 2 I/ 4 the asymptotic

and

qii,‘ and the energy flux

equations (7). (9) with coefficients

in such way must satisfy the homogeneous

1: x = 0, y(l) = 0.

function

differential

/ 6.

for

For large

has the foml:

n ~1 lere the signs (T ) refer to the

constants.

qit”’ on k2, and the coefficient

u”~:

in a similar way. The equation (7) regarding Eq. (4), (5) and the expression

= a2 in the region II

for the energy flux Pi_],’ __

(Vas’kov, 2000) for S << 1 can be reduced to the following form: c

lL

l+J+$xp(-h/q)

where

C, = a2 /(2&;,$),

approximation indicated

J2 --q/.ij d$ ! qZi

=0

q = &(?E,,(x,,)/&)\&\/&,

for the function

y(x)

above, such approximation

near x = x,

at

(10)

j=20.

h = H(r,)/(&S)>>

1.

Here

vve used

We also took the value &:s and parameter

absorption

/ q) away from the point x = x,, , y = 0, The variable

with an accuracy of a factor close to 1 determined

bv the spatial dispersion.

linear

y as constant.

is good enough because of a sharp increase in the cyclotron

plasma waves &z(k2 L) = .$, y Jblrl exp(-h

the

Solution of the homogeneous

As of

q is found equation

I384

V. V. Vas’kov

( 10) \+iith the boundap

conditions

hcav? cyclotron absorption

d4i.i’ / dy = 0 at 9 --+ 0 and the fimction

One can see that the correlation

in the region of

cZ in relation to y and h

(c3 - I) - In y and more rough

(L’, - 1) 2 In y h are valid. The relative portion of the plasma wave energy which is spent for the

acceleration calculation

decreasing

q >> h In y . allows us to calculate as before the coefficient

Figure 2 presents the results of these calculations. estimation

y:i,

of electrons

in the region II is given by the relationship c2

of the coefficient

.s = (c, - 1) c2

Note that the results of

for the region II don’t depend on plasma wave distribution

in the region I and

therefore remain valid near the 4-th and 3-rd gyrohannonics too. According to our calculation (see Table and Figure 2) the cyclotron portion s of energy losses in the region II decreases with the gyroharmonic number n and with increasing the shift (11-by) from the electron gyroharmonic toward lower frequencies. This decreasing is connected

to the growth of parameter

absorption

near the boundaT

B(x,,) /In y which characterized

the bandwidth

of the region II. In the case II = 6; 6 = 10.’

s = 0.26

and 0.13

v = 5.95 and 5.8, respectively.

According

takes place ashen the frequency

v z v,) passes the center of the interval between the adjacent gyroharmonics

csample

s = 0.029

for 1/= 5.4).

to our approximation,

we obtain

of the weak cyclotron

It is related to the restructuring

0 < (v - n) < 0.5, i.e. above electron gyroharmonics \vith ~r(k,

further decrease in the acceleration of the dispersion

which are accompanied

curves

by the enlargement

y(x)

for

of electrons (for

in the case

of the bandwidth

) < E!,, (see Figure 1 and its discussion). a “j it is easy to find the integral energy losses Q”’ = fqt’d’k.

Using Eq. ($7) and coefficients satellite and region. In accordance QrJ in ionospheric

experiments

to estimation

of Vas’kov ef al. (1999) the intensity Q,, >> AQ = a,a, /D

is well above threshold:

in each

of plasma waves excitation

where a,.? = ~E:~,~c,.~ . In this

case the total energy losses Q,>, in each region (I and II) is around 50% of the full flux of the energy Q, , spent by the powertil radio wave for the excitation of plasma oscillations (as this takes place, the electric field intensity in the first region is substantially higher than in the second one ow-ing to the relationship E: << 6: ). In order to see this.

one

(Q”’ lK”’

can

integrate

Eq.

(6,7)

z 2~:~) and expressions

11hen C,,, / A(,, >> 1 the frequency frequencies

\\ here

of individual

AQ = a,cr, ID,

stimulattcd electromagnetic can occur 26f

over

d’k

and

obtain

CQ,“’ = Q,,, PC’ I) -0”“’

the

relations

= a,a, / 1)

Q”’ /Ii”’

= a"' for

j 2 2

Hence it follows that in the case

spectrum of total energ?’ losses in each region after the averaging

over the

satellites takes the following form

Aa = (co,,- w) , 2k.1 = 1.3 k ~,~Jm emission,

at the odd satellite

frequencies

= CSWK = (10 - 30) KHz. This conclusion

REFERENCES Grach,S.M., Elcctromagnctic

At the same time in the spectrum

produced due to the plasma \\ave conversion

Radiation

of

,f ‘2g” = J;,-

2&j”(o - 1) _ arranged

one by one at a distance

is the direct result of satellite approximation

Artificial

Ionospheric

of the

in the region I, some maxima

Plasma Turbulence,

used in this paper.

Rcrdiophys. Quantum

I”;lccrron..28, N 6, 684-693 in Russian? 1985. Grach.S.M.. G.P.Komrakov, M.A.Yurishev, B.Thide, T.B.Lcyser, and T.Carozzi, Multifrequency Doppler Radar Observations of Electron Gyroharmonic Effects During Electromagnetic Pumping of the Ionosphere, I’/~x Rev. Mt.. 78, 883-886, 1997. Vas’kov.V.V., S.A.Pulinets, and N.A.Ryabova. Cyclotron Absorption of Plasma Oscillations Exited by Powerful Radio Wave in the Vicinity of Multiple Electron Gyroharmonics. Geomagn. Acron.. 39, N 4. 44-52 in Russian, 1999. Vas’k0v.V.V.. The Effect of Spatial Dispersion on the interaction of Short Wave Oscillations with Small Scale Plasma Inhomogeneities, Radiophys. QurrvlrumElectron., 43, N 4, 3 1O-324 in Russian. 2000.