Theory and observations of the interaction between magnetohydrodynamic waves and shocks

The interaction between interplanetary shocks or planetary bow shock and upstream magnetohydrodynamics (MHD) waves (hereafter referred to as wave-shock interactions) is of fundamental importance to plasma physics. Linear waves and shocks, which are supported by MHD framework, are ubiquitous in almost all plasma environments. A thorough understanding of the interaction between linear waves and shocks is useful not only for heliophysics and astrophysics but also for other applications such as inertial confinement fusion. We revisit the theoretical problem of shock-wave interaction based on the linearized boundary conditions of MHD. The shock is regarded as an ideal discontinuity and individual wave modes are considered to impact the shock from upstream. The wavevectors and amplitudes of the downstream transmitted waves are calculated. We further develop a method to apply the theory directly to in-situ heliospheric shock observations. The validity of the method is demonstrated through the example of a fast-forward interplanetary shock observed at 1 AU.