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 Hydromagnetic Stability of a Current Layer

1955 ◽  
Vol 8 (3) ◽  
pp. 319 ◽  
Author(s):  
RE Loughhead
Keyword(s):  
Magnetic Field ◽  
Normal Modes ◽  
Marginal Stability ◽  
Current Layer ◽  
Special Cases ◽  
Uniform Current ◽  
A Current

The hydromagnetic stability of a uniform current flowing along a magnetic field and confined within a pair of parallel planes is discussed by the method of normal modes. The condition for marginal stability is derived and discussed with reference to two special cases.

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.

scholarly journals Spin models in complex magnetic fields: a hard sign problem

2018 ◽  
Vol 175 ◽  
pp. 07026 ◽  
Author(s):  
Philippe de Forcrand ◽  
Tobias Rindlisbacher
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Partition Function ◽  
External Field ◽  
Potts Model ◽  
Cluster Algorithm ◽  
Spin Models ◽  
Sign Problem ◽  
Special Cases ◽  
Severe Sign

Coupling spin models to complex external fields can give rise to interesting phenomena like zeroes of the partition function (Lee-Yang zeroes, edge singularities) or oscillating propagators. Unfortunately, it usually also leads to a severe sign problem that can be overcome only in special cases; if the partition function has zeroes, the sign problem is even representation-independent at these points. In this study, we couple the N-state Potts model in different ways to a complex external magnetic field and discuss the above mentioned phenomena and their relations based on analytic calculations (1D) and results obtained using a modified cluster algorithm (general D) that in many cases either cures or at least drastically reduces the sign-problem induced by the complex external field.

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 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.

Factorization of the evolution operator for a spin–orbit coupled system in an external magnetic field for an arbitrary L and

1976 ◽  
Vol 54 (23) ◽  
pp. 2295-2305
Author(s):  
R. Bogdanović ◽  
M. A. Whitehead ◽  
M. S. Gopinathan
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Evolution Operator ◽  
Coupled System ◽  
Projection Operators ◽  
Spin Orbit ◽  
Group Representations ◽  
Special Cases ◽  
The Matrix ◽  
Strong External Field

The evolution operator of the spin–orbit coupled system in an external magnetic field is factorized according to the operator equation:[Formula: see text]where HSO is the spin–orbit coupled Hamiltonian and HZ is the Zeeman Hamiltonian. The preceding equation is expressed in matrix form using the theory of the O(4) group representations. For the special case of [Formula: see text], an explicit form of the matrix C(t) is found. The operator corresponding to the matrix C(t) is found in a closed form using the projection operators constructed in the Appendix. Two special cases, corresponding to a weak and a strong external field, are considered, and possible applications of the results obtained are indicated.

Exact nonlinear wave solutions of the incompressible magnetohydrodynamic equations in a non-uniform magnetic field

1989 ◽  
Vol 42 (2) ◽  
pp. 247-256 ◽  
Author(s):  
Hiromitsu Hamabata ◽  
Tomikazu Namikawa
Keyword(s):  
Magnetic Field ◽  
Incompressible Fluid ◽  
Uniform Magnetic Field ◽  
Magnetohydrodynamic Equations ◽  
Wave Solutions ◽  
Laboratory Plasmas ◽  
Special Cases ◽  
Circular Magnetic Field ◽  
Incompressible Magnetohydrodynamic Equations ◽  
Nonlinear Wave Solutions

Exact wave solutions of the nonlinear magnetohydrodynamic equations for a highly conducting incompressible fluid within an axisymmetric container are obtained. It is shown that there are four types of exact wave solutions with large amplitude in a non-uniform magnetic field. These solutions are very useful because they can be expressed in terms of arbitrary scalar functions and they are applicable to astrophysical and laboratory plasmas as well as the earth's core. The solutions also include as special cases the nonlinear Alfvén waves in a uniform magnetic field and in a circular magnetic field found respectively by Walén (1944) and by Namikawa & Hamabata (1987, 1988).

Sign in / Sign up

Export Citation Format

Share Document