Published online by Cambridge University Press: 13 March 2009
Following the method developed by Bernstein, Greene & Kruskal we obtain expressions for the distribution function of the trapped particles for a collisionless plasma, for cases when the plasma is unbounded and bounded (in a cylindrical waveguide). Figures are drawn showing the relationship between the width and amplitude of the solitary BGK wave for various cases. Analytic expressions depicting this relationship are also derived.