Nonlinear waves in a low-density plasma with a strong magnetic field

Abstract

The nonlinear evolution of waves in a low-density plasma in a strong magnetic field is investigated on the basis of the Chew-Goldberger-Low approximation. The nonlinear effects are found to be essentially different for the magneto-acoustic and Alfvèn modes. For the magnetic-acoustic mode, waveform distortion occurs at order ε² (where ε is a measure of the linear wave amplitude) and shock formation occurs over a time-scale of order ε-^-1. For the Alfvén wave, modulation occurs at order ε ³ and shock formation over a time-scale of order ε-^-2. The nature of the waveform distortion is qualitatively different for the two modes.