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Some properties of solitary BGK waves in a collisionless plasma

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.