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

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 Alfvén modes. For the magnetic-acoustic mode, waveform distortion occurs at order ² (where is a measure of the linear wave amplitude) and shock formation occurs over a time-scale of order ^–1. For the Alfvén wave, modulation occurs at order ³ and shock formation over a time-scale of order ^–2. The nature of the waveform distortion is qualitatively different for the two modes.