Stationary solutions of the Vlasov–Poisson system for two-component plasma under an external magnetic field in a half-space

2017 ◽  
Vol 12 (6) ◽  
pp. 37-50
Author(s):  
Yu. Belyaeva
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Half Space ◽  
Stationary Solutions ◽  
Poisson System ◽  
Two Component ◽  
Component Plasma

scholarly journals On classical solutions to the first mixed problem for the Vlasov-Poisson system in an infinite cylinder

2019 ◽  
Vol 484 (6) ◽  
pp. 663-666
Author(s):  
Yu. O. Belyaeva ◽  
A. L. Skubachevskii
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Mixed Problem ◽  
Field Potential ◽  
Classical Solutions ◽  
Infinite Cylinder ◽  
Poisson System ◽  
Electric Field Potential ◽  
Vlasov Equations ◽  
Component Plasma

The first mixed problem for the Vlasov-Poisson system in an infinite cylinder is considered. This problem describes the kinetics of charged particles in a high-temperature two-component plasma under an external magnetic field. For an arbitrary electric field potential and a sufficiently strong external magnetic field, it is shown that the characteristics of the Vlasov equations do not reach the boundary of the cylinder. It is proved that the Vlasov-Poisson system with ion and electron distribution density functions supported at some distance from the cylinder boundary has a unique classical solution.

The Normal Modes of Linearized Magnetohydrodynamics

1974 ◽  
Vol 52 (6) ◽  
pp. 509-515
Author(s):  
P. B. Corkum
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Normal Modes ◽  
Nonequilibrium Thermodynamic ◽  
Magnetohydrodynamic Equations ◽  
Minimal Set ◽  
Special Cases ◽  
Component Plasma ◽  
Phenomenological Coefficients ◽  
Central Purpose

The central purpose of this paper is to derive a general set of magnetohydrodynamic equations for a two component plasma in an external magnetic field and to find the eigenmodes of the linearized equations. The magnetohydrodynamic equations are derived from nonequilibrium thermodynamic principles. It is pointed out that a minimal set of phenomenological coefficients are found in this manner. The magnetohydrodynamic equations are linearized and then solved for the magnetohydrodynamic eigenmodes in the two special cases of the wave vector k parallel and perpendicular to the external magnetic field.

A novel method of inversion for a class of matrices: application to calculation of two-component plasma viscosities in a magnetic field

1990 ◽  
Vol 68 (7) ◽  
pp. 1072-1076
Author(s):  
Byung Chan Eu
Keyword(s):  
Magnetic Field ◽  
Transport Coefficients ◽  
Homogeneous Magnetic Field ◽  
Neumann Series ◽  
Neutral System ◽  
High Dimensions ◽  
Two Component ◽  
Component Plasma ◽  
Novel Method ◽  
Class Of Matrices

To calculate transport coefficients for a plasma in a magnetic field in a linear approximation it is necessary to invert matrices of fairly high dimensions. In this paper we present a novel method of inverting matrices involved in such problems. The method requires a solution of an inhomogeneous matrix integral equation in the Neumann series and a resummation of the series obtained. It involves inversions of lower order matrices, which can be achieved easily. We then apply the method to calculate viscosities of a two-component plasma subject to a homogeneous magnetic field. The structure of the viscosity matrix (tensor) calculated thereby is shown to be the same as that of a neutral system with an axial symmetry; namely, it can be decomposed into a scalar, a 2 × 2 matrix, and a 3 × 3 matrix. The method developed here can be applied to calculate other transport coefficients of the two-component plasma. Keywords: mathematical method, viscosity, plasmas, transport coefficients, kinetic theory.

scholarly journals Generalized Buneman Dispersion Relation in the Longitudinally Dominated Magnetic Field

2011 ◽  
Vol 2011 ◽  
pp. 1-6 ◽  
Author(s):  
Martin Bohata ◽  
David Bren ◽  
Petr Kulhánek
Keyword(s):  
Magnetic Field ◽  
Dispersion Relation ◽  
Plasma Physics ◽  
Plasma Jet ◽  
Background Plasma ◽  
Magnetized Plasmas ◽  
Beam Plasma ◽  
Two Component ◽  
Component Plasma

The generalized Buneman dispersion relation for two-component plasma is derived in the case of nonzero pressure of both plasma components and longitudinally dominated magnetic field. The derived relation is also valid for other field configurations mentioned in the paper. It can be useful in a variety of plasma systems, for example, in the analyses of plasma jet penetrating into background plasma, in beam-plasma physics, and in tests of various magnetohydrodynamics (MHD) and hybrid numerical codes designed for the magnetized plasmas.

Waves in Multicomponent Vlasov Plasmas with Anisotropic Pressure

1967 ◽  
Vol 22 (12) ◽  
pp. 1927-1935 ◽  
Author(s):  
Frank G. Verheest
Keyword(s):  
Magnetic Field ◽  
Dispersion Relation ◽  
External Magnetic Field ◽  
Small Amplitude ◽  
Anisotropic Pressure ◽  
Moment Equations ◽  
Component Plasma ◽  
General Dispersion ◽  
Ion Species ◽  
Constant External Magnetic Field

This is a study of the dispersion formulas for small amplitude waves in a fully ionized N-component plasma, in the presence of a constant external magnetic field. The number of ion species (whether positively or negatively charged) is left general. From a BOLTZMANN-VLASOV equation for each component of the plasma the first three moment equations are taken. The lowtemperature approximation is used to close the set of equations. This set is then solved together with the equations of MAXWELL to obtain a general dispersion relation, a determinant of order 3N. This relation is studied for the principal waves, and various compact formulas are derived. They are shown to include several known results, when applied to plasmas of the usual compositions. Their general form makes them suitable for various physical approximations.

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