Speaker
Description
Plasma discontinuities such as shocks and contact surfaces play a crucial role in space and astrophysical plasmas, governing energy conversion, wave-flow interactions, and momentum transport. While the classical Rankine-Hugoniot (RH) conditions are traditionally formulated in primitive magnetohydrodynamic (MHD) variables, this representation obscures the underlying wave content of discontinuities and their characteristic propagation directions.
In this work, we derive the complete set of Rankine-Hugoniot jump conditions expressed entirely in terms of the recently introduced Q-variable formalism, a wave-aligned generalization of Elsasser variables applicable to Alfvenic, fast, slow, and kink-like disturbances. By reformulating the ideal MHD equations in a shock-comoving frame and applying the thin-shock limit, we obtain explicit jump relations for mass, momentum, magnetic flux, and energy in terms of the $Q^{\pm}$ variables. We demonstrate analytically that this Q-based Rankine-Hugoniot system exactly reproduces the classical MHD jump conditions, confirming the full consistency and completeness of the formalism.
Beyond this equivalence, the Q-variable formulation offers a physically transparent and characteristic-aligned interpretation of MHD discontinuities. When the parameter $\alpha$ is chosen consistently with the relevant characteristic speed, the Q-variables isolate oppositely propagating wave contributions across the shock. This allows shocks to be interpreted as nonlinear interactions between counter-propagating modes and naturally accommodates one-directional propagation limits. The resulting framework clarifies the role of individual wave modes in shock structure, energetics, and transmission.
These results establish a theoretical foundation for analysing wave-shock interactions directly in wave variables and are particularly relevant for applications to solar-wind turbulence, magnetospheric plasmas, and next-generation global MHD models that incorporate wave-driven dynamics.