The stabilization of a viscous interface stressed by an oscillating magnetic field is investigated. Account is taken of the influence of free-surface currents on the effective solidly rotating fluid column. Only azimuthal modes are considered in the linear perturbation. The dispersion relation with or without free-surface currents is obtained in the form of a linear Mathieu equation with complex coefficients. It is found that there is a nonlinear relation between the surface current density and both the stratified viscosity and the stratified azimuthal magnetic field. The surface currents disappear on the interface of the fluid column when the stratified magnetic field has the value of unity. At this value, a coupled parametric resonance occurs in the absence of angular velocity. The magnetic field plays a stabilizing role. This role increases with increasing surface currents. The angular velocity plays a destabilizing role, while the field frequency plays a stabilizing role and acts against the angular velocity. The stratified viscosity plays a damping role in the presence of the surface current density, while, in the absence of a surface current, it plays two opposite roles corresponding to the presence or absence of the field frequency. A set of graphs are used to illustrate the relation between the presence of free-surface currents and both the viscosity and the azimuthal magnetic field.

In recent years, numerical solutions of the equations of compressible magnetohydrodynamic (MHD) flows have been found to contain intermediate shocks for certain kinds of problems. Since these results would seem to be in conflict with the classical theory of MHD shocks, they have stimulated attempts to reexamine various aspects of this theory, in particular the role of dissipation. In this paper, we study the general relationship between the evolutionary conditions for discontinuous solutions of the dissipation-free system and the existence and uniqueness of steady dissipative shock structures for systems of quasilinear conservation laws with a concave entropy function. Our results confirm the classical theory. We also show that the appearance of intermediate shocks in numerical simulations can be understood in terms of the properties of the equations of planar MHD, for which some of these shocks turn out to be evolutionary. Finally, we discuss ways in which numerical schemes can be modified in order to avoid the appearance of intermediate shocks in simulations with such symmetry.

The path is sought in the temperature–density plane that allows desired plasma burning conditions to be reached in the shortest possible time. This task is undertaken using the tools of classical variational analysis. The derived expression of Euler's equation is found to be degenerate. Ways to overcome such an impasse are examined, and eventually the solution is obtained. Illustrative applications to the OMITRON proposed ignition experiment are presented, which make reference to the Lackner–Gottardi and ITER-P89 scalings for the energy confinement time.

By means of the cold-electron fluid equations, we deduce a new strongly nonlinear surface solitary-wave solution for a semi-infinite plasma.