Application to radiation acoustics of the Whitham method for analysing wave phenomena in magnetised plasma

The exact governing equation of radiative acoustics in radiating grey gas is derived in this work, taking into account the influence of the transverse magnetic field. The radiative MHD is described by three equations of hydrodynamics and two equations of radiation momentum with extensive use of the formalism of radiative thermodynamics. In order to describe the propagation of linear radiative magneto-acoustic perturbation waves with scattering and attenuation, radiation-thermal dissipation conditions, radiation drag force, and magnetic force and Joule heat are introduced into these equations. The Eddington approximation is used, which allows us to study the modes of radiative magneto-hydrodynamic waves in two asymptotic cases - optically thin and thick gas.
The exact governing equation derived in this paper allows, using the heuristic Whitham method, to obtain a set of approximate governing equations of lower order, each of which is part of a reliable approximation to the exact equation in a certain region of the independent time variable. The relatively simple form of such equations allows, without formally solving the full problem, to investigate the physical processes occurring in each radiative magneto-hydrodynamic linear travelling wave.