The effect of spatial dispersion on the stability of the plasma longitudinal oscillations

Demchenko, V. V.; El-Naggar, I.A.

doi:10.1016/0375-9601(72)90708-6

Cited by 10 publications

(6 citation statements)

References 3 publications

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“…Eq. (27) differs from (14) only in denominations. So all the qualitative conclusions obtained previously remain effective.…”

Section: The Instability Of Ion Acoustic Solitonmentioning

confidence: 99%

“…(9). Using relations (10)- (13), (9) To find the unstable regions and the characteristics of unstable oscillations let us use the method of parameter substitution already used in an earlier investigation of the stability of nonlinear longitudinal plasma oscillations [14]. Dropping the intermediate calculations (to be found in [15]) let us write out an expression for the increase coefficient* (q~~e "~ sin(nFx-tr), where n is an integer, ~ is the parameter to be determined) n F 2 2 2 2 1/2 2__ s2 c2…”

Section: P(~)) =---C + 8 ~Z N 1 (Kz E + M V~) Q-11 ~2 Q_ 12 ~)3mentioning

confidence: 99%

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Decay instability of ion-acoustic wave train (or soliton) and formation of the shock profile

Demchenko

Hussein

1973

Z. Physik

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The stability of a periodic ion-acoustic wave of a finite amplitude propagating in a nonisothermal plasma is investigated. It is demonstrated that such a wave is unstable with respect to the splitting into a large number of satellite waves with effective wave numbers different from the wave number of the initial wave. The phase velocity of the satellite waves differs therefore from that of the initial pulse. Hence, the satellite waves with bigger phase velocity will "overtake" the initial pulse and turbulize the upstream plasma. The scattering of ions and electrons by the fluctuations of electric field of turbulent oscillations will cause the energy dissipation of the initial ionacoustic wave translational motion and produce a collisionless shock wave.

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“…Eq. (27) differs from (14) only in denominations. So all the qualitative conclusions obtained previously remain effective.…”

Section: The Instability Of Ion Acoustic Solitonmentioning

confidence: 99%

Section: P(~)) =---C + 8 ~Z N 1 (Kz E + M V~) Q-11 ~2 Q_ 12 ~)3mentioning

confidence: 99%

Decay instability of ion-acoustic wave train (or soliton) and formation of the shock profile

Demchenko

Hussein

1973

Z. Physik

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“…= 0, i. e. if we allow for the non-linearity only through the terms (vV)v, Eq. ( 14) yields (15) Expression (15) suggests that the ion oscillation amplitude increases infinitely when the frequency of the high-frequency field tends to that of the plasma natural oscillations w^ {v-*l). Therefore, the non-linear terms (vV)v arising in the equations of motion do not restrict the amplitude increase in the region of the first hybrid resonance.…”

Section: Parametric Instability In the Region Of The First Hybrid Res...mentioning

confidence: 99%

“…We have made use of this method earlier[ 15] in studying the effect of strictional non-linearity on longitudinal oscillations in the vicinity of plasma resonance.…”

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confidence: 99%

Parametric instability in the region of low-frequency hybrid resonances

Demchenko¹,

El-Naggar

1973

Nucl. Fusion

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The non-linear longitudinal oscillations of a homogeneous plasma embedded in a weakly inhomogeneous magnetic field in the presence of an external high frequency field are investigated. The non-linearity of oscillations is manifested in two ways: (a) allowance for the terms (V⃗∇)V⃗ in the equations of motion and (b) dependence of the plasma natural oscillation frequency on the displacement amplitude (or, otherwise, the loss of isochronity). It is demonstrated that the terms (V⃗∇)V⃗ do not restrict the amplitude increase in the regions of hybrid resonances. The non-linear terms arising in the equations of motion governed by the inhomogeneity of B⃗0, item (a), restrict the oscillation amplitude in the resonant areas and, item (b), lead to a parametric build-up of oscillations. The conditions for the parametric instability and the growth rates of unstable oscillations are determined.

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“…In this case, Eq. ( 4) can be re-written as (5) where </ > are the roots of the equation P(</>) = 0. Using the substitution Y = [(</> -<£ 3 )/(</> 2 -<j> 3 )] 1/2 , the solution of Eq.…”

mentioning

confidence: 99%