A problem of propagation of very long planetary waves in the upper atmosphere of the Earth is investigated. A new exact solution of the magnetohydrodynamics equations of the ionosphere in the spherical coordinate system is found taking into account the Earth’s rotation and geomagnetic field. The general dispersion equation for the planetary waves in the E and F regions of the ionosphere is deri...

In this paper we describe and analyze a two-level method for discretizing the equations of stationary, viscous, incompressible magnetohydrodynamics. The MHD equations model the ow of a viscous, incompressible, electrically conducting uid, interacting with magnetic and electric elds. These arise in plasma physics, nuclear reactor technology, and geophysics. The suggested algorithm involves solvi...

For static reductions of isotropic and anisotropic Magnetohydrodynamics plasma equilibrium models, a complete classification of admitted point symmetries and conservation laws is presented. It is shown that the symmetry algebra for the isotropic equations is finite-dimensional, whereas anisotropic equations admit infinite symmetries depending on a free function defined on the set of magnetic su...

Variational principles for magnetohydrodynamics were introduced by previous authors both in Lagrangian and Eulerian form. In a previous work Yahalom & Lynden-Bell introduced a simpler Eulerian variational principles from which all the relevant equations of magnetohydrodynamics can be derived. The variational principle was given in terms of six independent functions for non-stationary flows and ...

Heisenberg spin equation equivalence to nonlinear Schrödinger equation recently demonstrated by Rogers and Schief , is applied to the investigation of vortex filaments in magnetohydrodynamics (MHD) dynamos. The use of Gauss-Mainard-Codazzi equations allows us to investigate in detail the influence of curvature and torsion of vortex filaments in the MHD dynamos. This application follows closely ...

We study the eeects of plasma viscosity on the dynamics of primordial magnetic elds by simulating magnetohydrodynamics in the early universe by appropriate non-linear cascade models. We nd numerically that even in the presence of large kinetic viscosity, magnetic energy is transferred to large length scales. There are indications, however, that the inverse cascade stops at a given time which de...

The excitations of nonlinear magnetosonic waves in the presence charged space debris objects low Earth orbital (LEO) plasma region are investigated by taking into account effects electron inertia framework classical magnetohydrodynamics (MHD); which is also referred to as inertial magnetohydrodynamics. found be governed a forced Kadomtsev–Petviashvili (KP) equation with forcing term representin...

High beta poloidal tokamaks can confine plasma pressures an order of magnitude higher than their low beta poloidal counterparts. The theoretical stability of these high beta poloidal magnetohydrodynamics equilibria was left unresolved for many years. Using modern computational tools, such configurations are now found stable to Mercier, resistive and high-n (ideal and resistive) ballooning crite...

The celebration of Allan Kaufman’s 80th birthday was an occasion to reflect on a career that has stimulated the mutual exchange of ideas (or memes in the terminology of Richard Dawkins) between many researchers. This paper will revisit a meme Allan encountered in his early career in magnetohydrodynamics, the continuation of a magnetohydrodynamic mode through a singularity, and will also mention...

Variational principles for magnetohydrodynamics were introduced by previous authors both in Lagrangian and Eulerian form. In this paper we introduce simpler Eulerian variational principles from which all the relevant equations of barotropic magnetohydrodynamics can be derived. The variational principle is given in terms of six independent functions for non-stationary barotropic flows and three ...