Magnetoacoustic nonlinear periodic (cnoidal) waves in plasmas

Abstract

Magnetoacoustic nonlinear periodic (cnoidal) waves and solitons are studied in magnetized electron-ion plasmas with inertial cold ions and warm electrons. Using the two fluid model, the dispersion relation of the magnetoacoustic waves is obtained in the linear limit and the wave dispersive effects appear through the electron inertial length. The well known reductive perturbation method is employed to derive the Korteweg-de Vries equation for magnetoacoustic waves in plasmas. The Sagdeev potential approach is used, and the cnoidal wave solution of magnetoacoustic waves is obtained under periodic boundary conditions. The analytical solution for magnetoacoustic solitons is also presented. The phase plane portraits are also plotted for magnetoacoustic solitons shown as a separatrix, and the cnoidal wave structure always lies within the separatrix. It is found that plasma beta, which depends on the plasma density, electron temperature, and magnetic field intensity, has a significant effect on the amplitude and phase of the cnoidal waves, while it also affects the width and amplitude of the magnetoacoustic soliton in plasmas. The numerical results are plotted within the plasma parameters for laboratory and space plasmas for illustration. It is found that only compressive magnetoacoustic nonlinear periodic wave and soliton structures are formed in magnetized plasmas.