Generalized Ohm’s law and geometric optics: Applications to magnetosonic waves

A geometric optics analysis on the magnetohydrodynamics equations is performed when diffusion, Hall current and electron inertia are added as perturbations of the appropriate order. The first order approximation yields a transport equation along the rays that is of Korteweg–de Vries–Burgers type, whose coefficients may be explicitly found in terms of the main quantities at the original equilibrium. Using known results on traveling wave solutions of this equation, and assuming that we start from a constant equilibrium, we are able to discern which ones among the plasma parameters determine the shape of shocks, either monotonic or oscillatory. •The generalized Ohm’s law is studied using geometric optics methods.•The equation of magnetosonic waves is obtained.•This equation turns out to be of Korteweg–de Vries–Burgers type.•Its properties are studied and applied to real plasmas.