Freak waves in a plasma having Cairns particles

The probability of the existence of the ion-acoustic rogue waves in a plasma composed of warm ions and non-Maxwellian (nonthermal or Kappa) electrons is investigated in the framework of the modified Korteweg-de Vries (mKdV) equation. Using the reductive perturbation method, the Korteweg-de Vries (KdV) equation is derived. After numerical analysis, it is found that the present plasma system populated with nonthermal (Cairns) electrons leads to generation of compressive and rarefactive pulses, in contrast to the case of Kappa distribution. Thus, only for the nonthermal populated electrons, there is a critical value of the nonthermal parameter at which the coefficient of the nonlinear term of the KdV equation vanishes. In this case, we derived the modified KdV (mKdV) equation to describe the evolution of the system. To investigate the rogue waves propagation in our system, the mKdV equation should transfer to the nonlinear Schrodinger equation (NLSE). Our results provide a better understanding of observations in space plasmas which indicate the existence of nonthermal particles.