Nonlinear Dynamics of Relativistically Intense Cylindrical and Spherical Plasma Waves

TL;DR

This paper investigates the nonlinear evolution and wave breaking of relativistically intense cylindrical and spherical plasma waves, deriving a universal scaling law for wave breaking time and verifying it numerically.

Contribution

It provides an analytical expression for phase mixing time in relativistic plasma oscillations with geometric effects, validated by numerical simulations.

Findings

Wave breaking occurs via phase mixing at small amplitudes due to anharmonicity.

Wave breaking time scales inversely with the cube of initial wave amplitude.

Analytical scaling law is confirmed through numerical Dawson Sheet Model simulations.

Abstract

Spatio-temporal evolution and breaking of relativistically intense cylindrical and spherical space charge oscillations in a homogeneous cold plasma is studied analytically and numerically using Dawson Sheet Model [J.M. Dawson, Phys. Rev.113, 383(1959)]. It is found that cylindrical and spherical space charge oscillations break via the process of phase mixing at an arbitrarily small amplitude due to anharmonicity introduced by geometry and relativistic mass variation effects. A general expression for phase mixing time (wave breaking time) has been derived and it is shown that for both cases, it scales inversely with the cube of the initial wave amplitude. Finally this analytically obtained scaling is verified by using a numerical code based on Dawson Sheet Model.