Exact nonlinear solutions for three-dimensional Alfven-wave packets in relativistic magnetohydrodynamics

We show that large-amplitude, non-planar, Alfven-wave (AW) packets are exact nonlinear solutions of the relativistic magnetohydrodynamic equations when the total magnetic-field strength in the local fluid rest frame (b) is a constant. We derive analytic expressions relating the components of the fluctuating velocity and magnetic field. We also show that these constant-b AWs propagate without distortion at the relativistic Alfven velocity and never steepen into shocks. These findings and the observed abundance of large-amplitude, constant-b AWs in the solar wind suggest that such waves may be present in relativistic outflows around compact astrophysical objects.

Automated summary

The study demonstrates that large-amplitude, non-planar Alfven-wave packets are exact nonlinear solutions of the relativistic magnetohydrodynamic equations when the total magnetic-field strength in the local fluid rest frame is constant. These constant-b AWs propagate without distortion at the relativistic Alfven velocity and never steepen into shocks, suggesting their presence in relativistic outflows around compact astrophysical objects.