Real Spatial Shapes and Phase Space Structures of 3-D Nonlinear Electrostatic Plasma Wave

Abstract

3-D nonlinear electrostatic plasma wave is periodic along its longitudinal direction. By strictly analyzing a universal equation set of charged particles system, we find that such a longitudinal periodicity has a severe constraint on the transverse shape of a 3-D electrostatic structure. Only few allowed transverse shapes could warrant the longitudinal periodicity. This longitudinal periodicity in real space shapes can lead to a corresponding periodic structure in phase space.