MAGNETIZED PLASMA PARAMETRIC RESONANCE IN NON-MONOCHROMATIC PUMP-WAVE

(1)

HAL Id: jpa-00219255

https://hal.archives-ouvertes.fr/jpa-00219255

Submitted on 1 Jan 1979

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

MAGNETIZED PLASMA PARAMETRIC RESONANCE IN NON-MONOCHROMATIC

PUMP-WAVE

Yu. Aliev, O. Gradov, Vivien Stefan

To cite this version:

Yu. Aliev, O. Gradov, Vivien Stefan. MAGNETIZED PLASMA PARAMETRIC RESONANCE IN

NON-MONOCHROMATIC PUMP-WAVE. Journal de Physique Colloques, 1979, 40 (C7), pp.C7-

557-C7-558. �10.1051/jphyscol:19797269�. �jpa-00219255�

(2)

JOURNAL DE PHYSIQUE CoZZoque C7, suppZ6ment au n07, Tome 40, JuiZZet 1979, page C7- 557

MAGNETIZED PLASMA PARAMETRIC RESONANCE IN N O N - M O m O M A T I C PUMP-WAVE

Yu. M. Aliev, O.M. Gradov and V. ~tefan".

P. N. Lebedev PhysicaZ ~ n s t i t u t e , Academy o f Sciences o f t h e U.S.S. R., Moscow, U.S.S.R.

% o r i s Kidric I n s t i t u t e o f Nuclear Sciences - Vinca, Beograd, YugosZauia.

Parametric effects of monochrorratic following expression for the ehreshold is pump-wave interacting with plasma, in pre- obtained

sent time, are well studied / I / . On the

other hand in all actual experiments dea- h ,-n,h= -r2.

4G.Tt=Te 2 ' 4iiUS-e ^{( 2 )}

ling with an interaction of the radio or laser radiation with plasma we have sig- nals duration of which is finite in time.

Some aspects of the theory of parametric resonance in non-monochromatic pump-wave for non-magnetized plasma are given in /2-4/. In this work we represent some as- pects of the finite-bandwidth parametric theory for magnetized plasma. It has been shown that the effect of finite-bandwidth leads to stabilization or facilitation of parametric qrowth of the turbulent noise.

We consider infinite, homogeneous, fully ionized, magnetized plasma inter- acting with the pump field

'Iere E ~ is the threshold for the ca ~ ~ , ~ ~ ~ se of monochromatic pump-wave. From (2) it

is evident that the existence of the dis- crete external pump-wave leads to the sta- bilization of plasma - the increasing of the threshold times is apparent. Note that the wave numbers of excited oscilla-

C

tions are the same as in che case of r.iono- chromatic pump-wave.

With decreasing of the pulse repeti- tion frequency the possibility for reso- nance A'J~~SL' can be encountered which lead, in both periodical and aperiodical case, to the ion-sound instabilities. In

( 1 ) this case the following expression for the

threshold is obtained.

where the amplitude and phase are assumed

to be slow varying compared with carrier ( \ \

^L:

-A 4

frequencydo, which is chosen so to be kL%; 2

near to the eiqen-frequencies of high-fre-

guency (dk>>&) magnetized plasma oscil- Here:

lations. We also consider a set of rectan- ~wnde

gular impulses with duration , ^repeti- B ⁿ⁼ ^+A%)@ Pkiwf@B,++~\ ^,x=

tion period T and peak intensity Eo. Note, that the conclusions presented below are valid for cases of any shape of Eo(t) and

(t) except the demand for the periodici- ty of Eo (t) and (t) with the period T that must be satisfied.

Let us consider the amplitude-modu- laked (+ (t) =b) pump wave with frequency ddso that (obdoe~'>Ris valid in the cane when the oscillation velocity of electrons is'significantly less than the thermal ve- locity VTt. ^In the case when the frequency of the pulse repetition ZZ=%/~ is much higher than all low eigen-frequencies of

the magnetized plasma oscillation (a>%)

in the case of periodical (A>o) ^{and ape-}

riodical (b~O,od&$) instability the

The remaininq notations are conventional.

The yrave numbers of excited oscillations are deftned from **hk%%*(l5** in the decay case

(

TadS ^or **A*-=%$$&** ^{in the}

nondecay case ( e>>@

'k

⁾ . The minimum thres hold value from ( 3 ) is reached if 'k = 1 and 2trT . In the meantime for the posi- tive mismatching ( 470) the threshold va lue (3) is higher than the value obtained by (2). It means that in the domain consi- dered-% for h > O the treshold value is defined by (2) and the wave number of oscillations satisfies A==(L3S in the decay case(OS~@) or ~ $ 1 ~ ¹ n the nondecay

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19797269

(3)

( d s ~ d ~

-b

⁾ case. In the same time for the negative mismatching ( ALO ⁾ ^{the reso-}

nances hs-nfi make possible excitations of ion-sound oscillations with the thres- hold value given by (3) which appears to be less than the corresponding value in the czse of aperiodical instabilities

A=-? .

With further decrease in the pulse repetition frequency a sitvat ion when

m%!hd$ can be reached (n- odd number).

In the nondecay case w h e n p > > a is satis- fied an excitation of two ion-sound modes can take place, with the threshold and in- crement, respectively.

From the expression (4) it is evi- dent that the threshold value of the non- decay instabilities is significantly less than the corresponding value in the case of monochromatic pump-wave. The optimum value for the pulse duration, in presence of which the threshold value (4) reaches ninimum, is defined from

The wave number appearinq in the right- hand side of (4) is fixed by &*$ . ^From

here it is evident that in the case of nonmonochromatic pump-wave the decay in- stabilities, which are absent in the case of monochronatic pump-wave, are possible if ALO is satisfied.

REFERENCES

/1/ V.P.Silin, "Parametric Effects of High Power Radiation on Plasma", Nauka, Moscow, 1973, Chapter 3

/2/ V.V.Pustovalov, V.P.Silin, A.A.Cherni- kov, Quantum Electronics (1978), s,&9

/3/ Yu.M.Aliev, O.M.Gradov, D.SGnder, Beitrage aus der Plasma Physik, B.17, H.6 (1977) 353

/4/ Yu.M.Aliev, A.A.Chernikov, O.M.Gradov,

V.V.Pustovalov, V.P.Silin, V.Stefan,

Eight European Conference on Control-

led Fusion and Plasma Physics, Con-

tributed papers, v.1 (1977) 146,

Prague

MAGNETIZED PLASMA PARAMETRIC RESONANCE IN NON-MONOCHROMATIC PUMP-WAVE

HAL Id: jpa-00219255

https://hal.archives-ouvertes.fr/jpa-00219255

Submitted on 1 Jan 1979

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

MAGNETIZED PLASMA PARAMETRIC RESONANCE IN NON-MONOCHROMATIC

PUMP-WAVE

Yu. Aliev, O. Gradov, Vivien Stefan

To cite this version:

Yu. Aliev, O. Gradov, Vivien Stefan. MAGNETIZED PLASMA PARAMETRIC RESONANCE IN

NON-MONOCHROMATIC PUMP-WAVE. Journal de Physique Colloques, 1979, 40 (C7), pp.C7-

557-C7-558. �10.1051/jphyscol:19797269�. �jpa-00219255�

JOURNAL DE PHYSIQUE CoZZoque C7, suppZ6ment au n07, Tome 40, JuiZZet 1979, page C7- 557

MAGNETIZED PLASMA PARAMETRIC RESONANCE IN N O N - M O m O M A T I C PUMP-WAVE

Yu. M. Aliev, O.M. Gradov and V. ~tefan".

P. N. Lebedev PhysicaZ ~ n s t i t u t e , Academy o f Sciences o f t h e U.S.S. R., Moscow, U.S.S.R.

% o r i s Kidric I n s t i t u t e o f Nuclear Sciences - Vinca, Beograd, YugosZauia.

Parametric effects of monochrorratic following expression for the ehreshold is pump-wave interacting with plasma, in pre- obtained

sent time, are well studied / I / . On the

other hand in all actual experiments dea- h ,-n,h= -r2.

4G.Tt=Te 2 ' 4iiUS-e ( 2 )

ling with an interaction of the radio or laser radiation with plasma we have sig- nals duration of which is finite in time.

We consider infinite, homogeneous, fully ionized, magnetized plasma inter- acting with the pump field

'Iere E ~ is the threshold for the ca ~ ~ , ~ ~ ~ se of monochromatic pump-wave. From (2) it

is evident that the existence of the dis- crete external pump-wave leads to the sta- bilization of plasma - the increasing of the threshold times is apparent. Note that the wave numbers of excited oscilla-

tions are the same as in che case of r.iono- chromatic pump-wave.

With decreasing of the pulse repeti- tion frequency the possibility for reso- nance A'J~~SL' can be encountered which lead, in both periodical and aperiodical case, to the ion-sound instabilities. In

( 1 ) this case the following expression for the

threshold is obtained.

where the amplitude and phase are assumed

to be slow varying compared with carrier ( \ \

-A 4

frequencydo, which is chosen so to be kL%; 2

near to the eiqen-frequencies of high-fre-

guency (dk>>&) magnetized plasma oscil- Here:

lations. We also consider a set of rectan- ~wnde

gular impulses with duration , repeti- B n= +A%)@ Pkiwf@B,++~\ ,x=

tion period T and peak intensity Eo. Note, that the conclusions presented below are valid for cases of any shape of Eo(t) and

(t) except the demand for the periodici- ty of Eo (t) and (t) with the period T that must be satisfied.

the magnetized plasma oscillation (a>%)

in the case of periodical (A>o) and ape-

riodical (b~O,od&$) instability the

The remaininq notations are conventional.

The yrave numbers of excited oscillations are deftned from hk%%*(l5 in the decay case

TadS or A*-=%$$& in the

nondecay case ( e>>@

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19797269

( d s ~ d ~

) case. In the same time for the negative mismatching ( ALO ) the reso-

nances hs-nfi make possible excitations of ion-sound oscillations with the thres- hold value given by (3) which appears to be less than the corresponding value in the czse of aperiodical instabilities

A=-? .

With further decrease in the pulse repetition frequency a sitvat ion when

m%!hd$ can be reached (n- odd number).

In the nondecay case w h e n p > > a is satis- fied an excitation of two ion-sound modes can take place, with the threshold and in- crement, respectively.

The wave number appearinq in the right- hand side of (4) is fixed by &*$ . From

here it is evident that in the case of nonmonochromatic pump-wave the decay in- stabilities, which are absent in the case of monochronatic pump-wave, are possible if ALO is satisfied.

REFERENCES

/1/ V.P.Silin, "Parametric Effects of High Power Radiation on Plasma", Nauka, Moscow, 1973, Chapter 3

/2/ V.V.Pustovalov, V.P.Silin, A.A.Cherni- kov, Quantum Electronics (1978), s,&9

/3/ Yu.M.Aliev, O.M.Gradov, D.SGnder, Beitrage aus der Plasma Physik, B.17, H.6 (1977) 353

/4/ Yu.M.Aliev, A.A.Chernikov, O.M.Gradov,

V.V.Pustovalov, V.P.Silin, V.Stefan,

Eight European Conference on Control-

led Fusion and Plasma Physics, Con-

tributed papers, v.1 (1977) 146,

Prague

4G.Tt=Te 2 ' 4iiUS-e ^{( 2 )}

gular impulses with duration , ^repeti- B ⁿ⁼ ^+A%)@ Pkiwf@B,++~\ ^,x=

in the case of periodical (A>o) ^{and ape-}

The yrave numbers of excited oscillations are deftned from **hk%%*(l5** in the decay case

TadS ^or **A*-=%$$&** ^{in the}

⁾ case. In the same time for the negative mismatching ( ALO ⁾ ^{the reso-}

The wave number appearinq in the right- hand side of (4) is fixed by &*$ . ^From