Hydromagnetic discontinuities from the evolution of nonlinear Alvén waves

Abstract

To study the large‐amplitude Alfvén waves that are frequently observed in the solar wind, the nonlinear equations of electron and ion fluids coupled to Maxwell equations have been solved to obtain the relationships between the fluid density and magnetic field for finite amplitude Alfvén waves in the cold plasma limit. Two regimes of the parameter ωc/Ω (ratio of characteristic frequency to the ion Larmor frequency) are examined. When ωc/Ω = 0, we obtain an exact simple wave solution for the linearly polarized Alfvén wave, and recover the earlier results of [Montgomery, 1959a]. For finite ωc/Ω geometric optics approximation which is valid for large wave numbers yields a new relationship which involves elliptically polarized Alfvén waves. Both of these waves can be shown to evolve into shocks.