THEORY OF STABILITY OF LARGE AMPLITUDE PERIODIC (BGK) WAVES IN COLLISIONLESS PLASMAS,
Abstract
A method is developed for examining the stability of a large amplitude periodic (BGK) wave, Eo, in a collisionless plasma. Vlasov's equation is integrated by the method of characteristics to yield a polarization charge density response, linear in a small-amplitude field El, but nonlinear in Eo. The susceptibility linking charge density response El is expressed in terms of the exact orbits of trapped and untrapped particles in the field Eo, distributed in energy according to the assumed BGK distribution function, fo. These susceptibilities couple the Fourier components of El in the usual mode-coupling fashion, but trapping effects are now included. For fields Eo which are not too large, the mode-coupling problem reduces to finding the zeroes of a 2 x 2 or 3 x 3 determinant. Distribution functions which are localized at the bottom of the potential energy troughs of Eo give identically the growing side-band instability of Dawson, Kruer, and Sudan. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 01, 1969
- Accession Number
- AD0691747
Entities
People
- Martin V. Goldman
Organizations
- University of California, Los Angeles