Ion acoustic cnoidal waves and associated nonlinear ion flux in a warm ion plasma

Using periodic boundary conditions in the reductive perturbation method for ion acoustic cnoidal waves in a collisionless, unmagnetized plasma consisting of warm ions and hot isothermal electrons, evolution equations for the first order and second order potential are derived. Determining the nonsecular solution of these coupled equations, expressions for wave phase velocity and averaged nonlinear ion flux are obtained. Variations of wave phase velocity and averaged nonlinear ion flux are examined for different values of wave frequency and ion to electron temperature ratio (Ti/Te). It is found that wave phase velocity increases with an increase in wave amplitude for a given value of frequency and temperature ratio. But for a given wave amplitude, the wave phase velocity increases as the temperature ratio increases or wave frequency decreases. The averaged nonlinear ion flux associated with the propagation of large amplitude cnoidal waves in plasma is found to be negative, which corresponds to back flow of ions. The magnitude of the ion flux increases with increase in wave amplitude as temperature ratio or wave frequency increases