Theory and observations of the interaction between magnetohydrodynamic waves and shocks

The problem of wave-shock interaction is of fundamental importance to plasma physics. Linear waves and shocks that are supported by the magnetohydrodynamics model are ubiquitous in many plasma environments. We revisit the theoretical problem of shock-wave interaction based on linearized boundary conditions of magnetohydrodynamics. The shock is regarded as an ideal discontinuity and an individual wave mode is considered to impact the shock from upstream. Depending on the type of the shock, there may be waves transmitted downstream or reflected upstream. The wavevector and fluctuation amplitude of the transmitted or reflected waves are calculated. We show how compressible and incompressible waves can be generated or amplified at the shock, and how the shock front is perturbed. We also demonstrate through examples how the theory can be directly applied to in-situ heliospheric observations.