Effect of Ion Motion on Breaking of Longitudinal Relativistically Strong Plasma Waves: Khachatryan mode revisited.

Effect of ion motion on the spatio-temporal evolution of a relativistically strong space charge wave, is studied using a 1-D fluid simulation code. In our simulation, these waves are excited in the wake of a rigid electron beam propagating through a cold homogeneous plasma with a speed close to the speed of light. It is observed that the excited wave is a mode as described by Khachatryan [Phys. Rev. E 58, 7799 (1998)] whose profile gradually sharpens and the wave eventually breaks after several plasma periods exhibiting explosive behaviour. It is found that breaking occurs at amplitudes, which is far below the breaking limit analytically derived by Khachatryan [Phys. Rev. E 58, 7799 (1998)]. This phenomenon of wave breaking, at amplitudes well below the breaking limit, is understood in terms of phase mixing of the excited wave. It is further found that the phase mixing time (wave breaking time) scales inversely with the energy density of the wave.