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

## TL;DR

This study uses 1-D fluid simulations to analyze how ion motion affects the evolution and breaking of relativistically strong plasma waves, revealing wave breaking below theoretical limits due to phase mixing.

## Contribution

It revisits Khachatryan's mode, demonstrating wave breaking at lower amplitudes than previously predicted, and links wave breaking time to wave energy density.

## Key findings

- Wave profile sharpens and breaks after several plasma periods.
- Wave breaks at amplitudes below Khachatryan's analytical limit.
- Wave breaking time scales inversely with wave energy density.

## Abstract

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.