Numerical Investigations of the Dynamics of Development of Two-Dimensional Perturbations in Magnetic Galathea Traps

Differential Equations - Studying the stability of traps for magnetic plasma confinement is one of the main tasks in solving the problem of controlled thermonuclear fusion. The main trends and...     

Acceleration of Plasma in Coaxial Channels with Preshaped Electrodes and Longitudinal Magnetic Field

The paper presents a mathematical model and results of numerical simulation of axisymmetric plasma flows in nozzle-type channels formed by two coaxial electrodes. Transonic accelerated flows, which are of interest for the development of plasma accelerators, are considered. The mathematical apparatus of the models are two-dimensional MHD problems solved numerically, the steady-state solutions of which are obtained in the process of relaxation. Some characteristics of the flow in narrow tubes between close trajectories are considered in the quasi-one-dimensional approximation. The main attention is paid to the influence of the longitudinal magnetic field and the curvilinear geometry of the electrodes on the properties of accelerated flows.     

A plasmastatic model of the galathea-belt magnetic trap

The mathematical apparatus of plasmastatics, which includes the MHD equilibrium equation and steady-state Maxwell equations, is reduced, in two-dimensional problems arising due to symmetry, to a single scalar second-order elliptic equation with a nonlinear right-hand side known as the Grad-Shafranov equation. In this paper, we numerically solve a series of boundary value problems for this equation that model equilibrium plasma configurations in the magnetic field of the belt-like galathea trap in a cylinder with two plasma embedded conductors. The mathematical model is outlined, the results of calculations of the magnetic field and plasma pressure in the cylinder depending on the parameters of the problem are presented, and the main integral characteristics of the trap are calculated. The existence and uniqueness of the solution is discussed; the limiting values of the maximal pressure at which there exists a solution of the equilibrium problem are found.     

Stability Issues in Two-Dimensional Mathematical Models of Plasma Equilibrium in Magnetic Galathea Traps

Differential Equations - Galathea traps for confining plasma in a magnetic field created by current-carrying conductors immersed in the plasma volume constitute a promising class of objects for...     

Steady-State MHD Flows in Nozzles with an External Longitudinal Magnetic Field

Steady-state MHD flows in channels of the nozzle type in the presence of an external longitudinal magnetic field can be divided into two significantly different classes. Subcritical flows, in which the Alfvén velocity calculated from the longitudinal magnetic field is less than the plasma velocity, have mainly the same properties as flows in a transverse magnetic self-field and their quantitative characteristics depend only slightly on the longitudinal magnetic field strength. Supercritical flows with the opposite inequality for the velocities correspond to strong longitudinal magnetic field. The main difference is the transitions between different forms of energy (kinetic, thermal, and electromagnetic). The present study contains a classification of possible flows, namely, sub- and supercritical and sub-, super-, and transonic flows with respect to the fast and slow magnetosonic and Alfvén velocities. Examples of these flows are given. The effect of the problem parameters on the flow properties is investigated.     

On the Stability of Plasma Equilibrium in the Neighborhood of a Straight Current Conductor

Computational Mathematics and Mathematical Physics - The article presents a mathematical model of an equilibrium magnetoplasma configuration in a plasma cylinder containing on its axis a conductor...     

Computation of axisymmetric MHD flows in a channel with an external longitudinal magnetic field

A numerical study of two-dimensional plasma flows in coaxial channels of plasma accelerators is presented. Two new results are obtained. First, for the computation of MHD problems belonging to the class under consideration, Zalesak’s method is used. It is based on an explicit finite difference scheme with flux correction. This method is free of space splitting, and, therefore, is well suited for parallel computations on multiprocessors. Second, the statement of the problem is extended so that the acceleration of the plasma by the azimuth magnetic self-field goes on in the presence of an external longitudinal field. The results of test computations demonstrate the efficiency of the method and made it possible to investigate the influence of the longitudinal field on the properties of the plasma flows.     

Hall effect in the MHD model of plasma channel flow

The steady flow regime with quasi-radial electric current and nonequipotential boundaries is obtained in calculating axisymmetric plasma flow in a coaxial channel with an azimuthal self-magnetic field. The calculations were carried out using the MHD model with allowance for the Hall effect. The regime obtained describes the flow in the stream core of the channel of a modern quasi-steady heavy-current plasma accelerator outside thin near-electrode layers. Estimates of the Hall corrections relating to these layers are given.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, pp. 56–65, September–October, 1995.