Modulational instability and nonlinear evolution of two-dimensional electrostatic wave packets in ultra-relativistic degenerate dense plasmas

Abstract

We consider the nonlinear propagation of electrostatic wave packets in an ultra-relativistic (UR) degenerate dense electron–ion plasma, whose dynamics is governed by the nonlocal two-dimensional nonlinear Schrödinger-like equations. The coupled set of equations is then used to study the modulational instability (MI) of a uniform wave train to an infinitesimal perturbation of multidimensional form. The condition for the MI is obtained, and it is shown that the nondimensional parameter, β∝λCn01/3 (where λC is the reduced Compton wavelength and n0 is the particle number density) associated with the UR pressure of degenerate electrons, shifts the stable (unstable) regions at n0~1030cm-3 to unstable (stable) ones at higher densities, i.e., n0>̃7×1033. It is also found that the higher the values of n0, the lower is the growth rate of MI with cut-offs at lower wave numbers of modulation. Furthermore, the dynamical evolution of the wave packets is studied numerically. We show that either they disperse away or they blowup in a finite time, when the wave action is below or above the threshold. The results could be useful for understanding the properties of modulated wave packets and their multidimensional evolution in UR degenerate dense plasmas, such as those in the interior of white dwarfs and/or pre-Supernova stars.