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

作者：Misra Amar Prasad^*; Shukla Padma Kant

来源：Physics of Plasmas, 2011, 18(4): 042308.

DOI：10.1063/1.3574752

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 Schrodinger-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, beta proportional to lambda(C)n(0)(1/3) (where lambda(C) is the reduced Compton wavelength and n(0) is the particle number density) associated with the UR pressure of degenerate electrons, shifts the stable (unstable) regions at n(0) similar to 10(30)cm(-3) to unstable (stable) ones at higher densities, i.e., n(0) greater than or similar to 7 x 10(33). It is also found that the higher the values of n(0), 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.

• 出版日期2011-4