Determination of maximum electric field amplitude sustained by electron acoustic solitary waves in an unmagnetized plasma with kappa-distributed electrons

Abstract

This manuscript investigates the maximum electric field amplitude sustained by nonlinear electron acoustic waves, without losing their initial structure, and propagating in an unmagnetized homogeneous plasma comprising cold inertial electrons, hot kappa-distributed electrons, and stationary ions. Using nonlinear fluid Maxwell’s equations in one dimension, traveling wave solutions have been derived in the wave frame, and negative potential solitary structures have been observed. Furthermore, a pseudo-potential method has been employed to determine the maximum electric field amplitude as a function of the dimensionless Mach number (M), initial density ratio of hot to cold electron species (Rn=nh0nc0), and spectral index (κ) of the hot electron species velocity distribution function. We find that at this maximum electric amplitude, the density of the cold electron fluid becomes singular and thus can be called the wave breaking limit [J. M. Dawson, Phys. Rev. 113, 383 (1959)]. Density singularity is an artifact of the cold fluid plasma model and actually diminishes if one introduces a nonzero temperature to the cold inertial electrons. In that case, we find that the maximum electric field amplitude gets modified and follows the same scaling as the ratio of cold to hot electron species temperature (σ=TecTeh), as obtained by Coffey [Phys. Fluids 14, 1402 (1971)], with electron thermal velocity derived for the wave breaking limit of electron plasma waves in a warm plasma.