A covariant treatment of relativistic plasma oscillations in the presence of an external magnetic field

1969 ◽  
Vol 47 (10) ◽  
pp. 1057-1060 ◽  
Author(s):  
Kwok-Kee Tam ◽  
John O'hanlon
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Relativistic Plasma ◽  
Covariant Theory ◽  
Plasma Oscillations ◽  
Component Plasma

A covariant theory of plasma oscillations for a many-component plasma in the presence of an external magnetic field is formulated.

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.

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.

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.

A covariant treatment of relativistic plasma oscillations

1968 ◽  
Vol 46 (16) ◽  
pp. 1763-1767 ◽  
Author(s):  
Kwok-Kee Tam
Keyword(s):  
External Field ◽  
Infinite Number ◽  
Relativistic Plasma ◽  
Covariant Theory ◽  
Plasma Oscillations

A covariant theory of plasma oscillations in the absence of an external field is formulated by considering a plasma as the limit of an infinite number of relativistic streams.

Stability of an anisotropic relativistic plasma in a magnetic field

1968 ◽  
Vol 2 (2) ◽  
pp. 157-165 ◽  
Author(s):  
J. Skilling
Keyword(s):  
Magnetic Field ◽  
Boltzmann Equation ◽  
Supernova Remnants ◽  
Large Scale ◽  
Cosmic Ray ◽  
Relativistic Plasma ◽  
Relativistic Boltzmann Equation ◽  
Two Component ◽  
Component Plasma ◽  
The Stability

The collisionless relativistic Boltzmann equation is used to investigate the stability of a large-scale two-component plasma containing numerically small anisotropic relativistic populations. Although most permitted waves are stable, Alfvén type waves are found to be unstable whenever the anisotropy exceeds O(v A/c). Growth times are estimated as days for supernova remnants and millennia for cosmic ray protons.

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