TwoDimensional and ThreeDimensional BGK Waves
Abstract
Generalization of the BernsteinGreeneKruskal solution for a onedimensional collisionless plasma to two and threedimensional cases is demonstrated. For the case when the potential has the highest symmetry and has a single maximum at the center of the symmetry, explicit expressions for the trappedparticle distribution are obtained in terms of the potential and the other particle distribution functions for the untrapped particles. In particular, it is shown that when the distribution functions depend only on the particle energy, in the twodimensional case the trappedparticle distribution can be analytic as a function of energy, but is never analytic in the threedimensional case.
 Publication:

Journal of the Physical Society of Japan
 Pub Date:
 September 1976
 DOI:
 10.1143/JPSJ.41.1050
 Bibcode:
 1976JPSJ...41.1050K
 Keywords:

 Collisionless Plasmas;
 Electrostatic Waves;
 Plasma Oscillations;
 Plasma Potentials;
 Trapped Particles;
 Distribution Functions;
 Integral Equations;
 Isotropic Media;
 Poisson Equation;
 Vlasov Equations;
 Plasma Physics