Nonlinear interactions of positive and negative energy modes in rarefied plasmas (I)

doi:10.1016/0003-4916(69)90178-X

Annals of Physics

Volume 55, Issue 2, November 1969, Pages 207-247

https://doi.org/10.1016/0003-4916(69)90178-X Get rights and content

Abstract

The nonlinear interactions of electrostatic modes in a plasma are studied within the framework of the weak-turbulence approximation. It is shown that the multi-wave interaction (resonant mode-mode coupling) can be explosively unstable when, for Σ_j=1ⁿ k_j = 0 and Σ_j=1ⁿω_kj = 0, we also have S₁ = S₂ = … = S_n, where $S_{j} = (∂ϵ ∂ω_{kj}) /| ∂ϵ ∂ω_{kj} |$ , n being the number of interacting waves and ϵ the dielectric constant.

Significant examples are analyzed with special consideration for that of a plasma with a loss-cone distribution in a strong magnetic field B. This in fact can have positive and negative energy modes, for which unstable three-wave interactions can occur with growth rates which are appreciable for rather modest intensities. The modes considered are of flute type, with k · B = 0, so that convection along the lines of force does not affect the validity of the above results. A nonlinear mechanism of the type analyzed here can provide a possible explanation of the bursts of radiation often associated with low-density mirror confined plasmas.

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^☆: The present manuscript and a companion one dealing primarily with nonlinear Landau damping have been condensed in the paper “Nonlinear Interactions of Positive and Negative Energy Modes in Plasmas” presented at the Third Conference on Plasma Physics, Novosibirsk, USSR, August, 1968.

^†: Present address: Massachusetts Institute of Technology, Cambridge, Mass.

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Nonlinear interactions of positive and negative energy modes in rarefied plasmas (I)☆

Abstract

J. Appl. Phys.

Zh. Eksperim. i Teor. Fiz.

Soviet Phys.—JETP

Appl. Phys. Letters

Zh. Eksperim. i Teor. Fiz.

Soviet Phys.—JETP

Phys. Fluids

Zh. E.T.F. Pism'a Letters

Soviet Phys.—JETP

The Theory of Plasma Waves

Plasma Turbulence

Nucl. Fusion, Suppl. Pt 2

Zh. Eksperim. i Teor. Fiz.

Soviet Phys.—JETP