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

• Published in: Annals of physics 1969-11, Vol.55 (2), p.207-247
• Main Authors: Coppi, B, Rosenbluth, M.N, Sudan, R.N
• Format: Article
• Language: English
• ISSN: 0003-4916; 1096-035X
• DOI: 10.1016/0003-4916(69)90178-X

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=1 n k j = 0 and Σ j=1 n ω k j = 0, we also have S 1 = S 2 = … = 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.