Nonlinear Dynamics of Relativistically Intense Cylindrical and Spherical Plasma Waves

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.