Compressive and Rarefactive Ion Acoustic Nonlinear Periodic Waves in Nonthermal Plasmas

Abstract

The ion acoustic nonlinear periodic (cnoidal) waves are studied in an unmagnetized plasma consisting of cold ions and nonthermal electrons following Cairns distribution. By employing reductive perturbation method, the nonlinear Korteweg-de Vries (KdV) and modified Korteweg-de Vries (mKdV) equations are derived, and their periodic wave solutions are obtained and analyzed numerically. It has been pointed that the KdV equation fails at plasma critical composition, and we have thus taken into account the higher order nonlinearity and derived the mKdV equation. In the latter case, the coexistence of compressive and rarefactive periodic wave structures is pointed out in the critical case. So far, this aspect has not been tackled at all in the nonthermal plasma literature on periodic waves. In the present work, it is the degree of nonthermality of electrons that is responsible for the rarefactive solutions. The present plasma model accounts for the cnoidal wave structures (Jovanovic and Shukla Phys. Rev. Lett. 84, 4373 2000) in the magnetosphere observed via FAST and POLAR spacecrafts.