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 Integral Equations for Problems on Wave Propagation in Near-Earth Plasma

Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1395
Author(s):  
Danila Kostarev ◽  
Dmitri Klimushkin ◽  
Pavel Mager
Keyword(s):  
Magnetic Field ◽  
Integral Equations ◽  
Field Potential ◽  
Low Frequency ◽  
Fredholm Equation ◽  
Compression Waves ◽  
Parallel Component ◽  
Electric Field Potential ◽  
The Magnetic Field ◽  
Low Frequency Waves

We consider the solutions of two integrodifferential equations in this work. These equations describe the ultra-low frequency waves in the dipol-like model of the magnetosphere in the gyrokinetic framework. The first one is reduced to the homogeneous, second kind Fredholm equation. This equation describes the structure of the parallel component of the magnetic field of drift-compression waves along the Earth’s magnetic field. The second equation is reduced to the inhomogeneous, second kind Fredholm equation. This equation describes the field-aligned structure of the parallel electric field potential of Alfvén waves. Both integral equations are solved numerically.

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.

Far-Field Potential of a Test Charge in an Inhomogeneous and Magnetized Plasma

1974 ◽  
Vol 52 (3) ◽  
pp. 281-283 ◽  
Author(s):  
P. K. Shukla ◽  
K. H. Spatschek ◽  
M. Y. Yu
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Inhomogeneous Plasma ◽  
Field Potential ◽  
Magnetized Plasma ◽  
The Other ◽  
Far Field ◽  
Homogeneous Plasma ◽  
Test Charge ◽  
Stationary Test

It is shown that a stationary test charge in a magnetized inhomogeneous plasma has a far-field potential which falls off as the inverse cube of the distance between the test charge and an observer who is located in a direction perpendicular to both the density gradient and the external magnetic field. On the other hand, the effect of an external magnetic field parallel to the velocity of a slowly moving test charge in a homogeneous plasma is shown to be insignificant.

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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