Small amplitude electron-acoustic double layers and solitons in fully relativistic plasmas of two-temperature electrons

A Korteweg-de Vries (KdV) equation for fully relativistic one dimensional plasmas of arbitrarily large streaming speed and temperature is derived by using the reductive perturbation method. For plasmas with more than two species of particles, the coefficient representing quadratic nonlinearity in KdV can vanish at critical values of certain parameters. To describe the nonlinear evolution at this critical parameter, a modified KdV (mKdV) equation that contains a cubic nonlinear term is obtained. Furthermore, a mixed mKdV equation pertaining to parameters in the vicinity of the critical values is also derived, in which the quadratic and cubic nonlinearities are both present. As an illustration of the results, the mixed mKdV equation is applied to a plasma comprised of cold ions and electrons having cold (T=0) and finite temperature components. For warm temperature T << m(e)c(2), it is found that electron-acoustic nonlinear waves in the shape of double layer (kink) and solitary waves can exist, which have phase speed root 3T/(4+a)m(e) in the rest frame of plasma, where alpha is the polytropic index of the equation of state of the warm electrons. The thickness of the transitional layer of the kink structure is of the order of Debye length lambda(D). For extremely high temperature T >> m(e)c(2), it is also found that double layer and soliton-type solutions can exist with phase speed root alpha-1c, which is equal to the well known relativistic sound speed c/root 3 for alpha=4/3. The thickness of the transition layer scales as delta similar to T-1/4, which is different from the T << m(e)c(2) case. (C) 2009 American Institute of Physics. [DOI: 10.1063/1.3121242]