Analysis of two-fluid plasma in the electromagnetic hydrodynamics approximation and discontinuous structures in their solutions

Various versions of equations of two-fluid plasma called the equations of electromagnetic hydrodynamics are considered. They are a generalization of the classical magnetic hydrodynamics equations obtained by adding dispersive terms. Application of finite-difference methods for solving these equations is analyzed. The Riemann problem is solved numerically, and various types of discontinuity structures that expand with time are considered. These are fast and slow magnetosonic structures and Alfven structures. In the case of moderate amplitudes, fast and slow magnetosonic structures are typical in the theory of nondissipative structures. It is found that due to the disappearance of dispersion, short waves can overturn under certain initial conditions, which requires the analysis of discontinuous solutions or the inclusion of additional dissipative or dispersive terms into the equations. In the case when the fluid dynamic viscosity is added, a shock-type structure is discovered. The evolutionary nature of the discontinuity and the conditions on the discontinuity are studied.