Theory of Stability of Large Periodic Plasma Waves | CU Experts

A method is developed for examining the stability of a large-amplitude periodic Bernstein-Greene-Kruskal wave, E0, in a collisionless plasma. Vlasov's equation is integrated by the method of characteristics to yield a polarization charge density response ρ1, linear in a small-amplitude field E1, but nonlinear in E0. The susceptibility linking ρ1 and E1 is expressed in terms of the exact orbits of trapped and untrapped particles in the field E0, distributed in energy according to an assumed Bernstein-Greene-Kruskal distribution function f0. These susceptibilities couple the Fourier components of E1 in the usual mode-coupling fashion, but trapping effects are now included. For fields E0 which are not too large, the mode-coupling problem reduces to finding the zeroes of a 2 × 2 or 3 × 3 determinant. Trapped electron distribution functions which are localized at the bottom of the potential energy troughts of E0 give the growing side-band instability of Kruer, Dawson, and Sudan.

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