Wave propagation and transformation in the frame of magnetohydrodynamics with a vortex electric field

Bright transient objects in different wave bands have been discovered in recent years. To explain these short (from ms to s), and very powerful events, different models, galactic and extragalactic, have been considered. One of the popular models is based on the suggestion of transformation of the magnetized plasma blob, presumably a magnetohydrodynamic (MHD) shock wave, moving with relativistic speed, into electromagnetic (EM) pulse after collision with some obstacle, or entering into media with different properties. Such transformation cannot be described in the frame of classical MHD equations, which don’t contain the displacement current and don’t include such transformation. Updating of the classic MHD equations by using of full set of Maxwell equations with displacement current, made recently by several authors, gave a possibility to describe hydrodynamic phenomena, together with electromagnetic ones by the same set of equations. Here we apply these equations for study of propagation of different waves with account of displacement current, and of transformation between different kinds of waves in the nonuniform media. We derive a dispersion equation describing a propagation of a weak linear wave in a uniform magnetized plasma, and consider in detail the cases with perpendicular and parallel motion to the magnetic field. It contains MHD, HD, Alfven and EM waves in the limiting cases, and some new types of behavior in a general situation. We consider a plasma with zero viscosity and heat conductivity, with a finite scalar electric conductivity. We have shown that the transformation of MHD into EM wave may happen only in a highly magnetized plasma, and have found the region of parameters, where no waves exist and only damping static perturbations may be present.