Nonlinear periodic ion acoustic waves in a relativistic plasma with isothermal electrons and cold ions

Propagation of nonlinear ion acoustic waves in a relativistic electron-ion plasma is studied using the covariant formulation. Ions are assumed cold and a polytropic equation of state of the form p = Cn^Γ is assumed for electrons with Γ = 1 (isothermal case). The continuity, momentum and energy equations for electrons and ions are transformed to a special frame of reference via Lorentz-transformation. In the said frame of reference, all physical quantities are time independent. The well-known Sagdeev potential (or pseudopotential) technique is used to investigate the effect of changes in polytropic index Γ, electron temperature T_e0 and phase speed of wave V_p on the wave amplitude. It is found that ion acoustic waves can propagate in the relativistic plasma only if the following condition (γ_V − eϕ/m_ic²)² > 1 is satisfied (where γ_V=1/√1−V_p/c² is defined, ϕ is the electrostatic potential, m_i is the ion mass and c is the speed of light). Maximum value of the amplitude (ϕ′_m) attained by the wave before collapsing, is also derived. It is also found that an increase in temperature T_e0 (or V_p) increases the maximum possible wave amplitude of the nonlinear wave whereas, increasing V_p results in decreasing ϕ′_m. (author)