Transport coefficients for an equal-mass plasma in a uniform magnetic field

1993 ◽  
Vol 50 (1) ◽  
pp. 125-144 ◽  
Author(s):  
S. Y. Rassak-Abdul ◽  
E. W. Laing
Keyword(s):  
Magnetic Field ◽  
Heat Flux ◽  
Electric Current ◽  
Uniform Magnetic Field ◽  
Transport Coefficients ◽  
Parallel Transport ◽  
Equal Mass ◽  
Particle Species ◽  
Hall Parameter ◽  
Fokker Planck Equations

Cross–field transport coefficients for the electric current and heat flux have been calculated for an equal–mass plasma for various values of the Hall parameter Ωr in the range Ωr ≥ 1. Coefficients have also been calculated for parallel transport. These have been obtained using the linearized Fokker–Planck equations for both particle species, taking advantage of the mass symmetry, which leads to remarkable cancellations in the collision terms.

Transport coefficients for a two-temperature equal-mass plasma in a uniform magnetic field

1994 ◽  
Vol 52 (2) ◽  
pp. 309-319 ◽  
Author(s):  
S. Y. Abdul-Rassak ◽  
E. W. Laing
Keyword(s):  
Magnetic Field ◽  
Heat Flux ◽  
Electric Current ◽  
Uniform Magnetic Field ◽  
Transport Coefficients ◽  
Equal Mass ◽  
Temperature Ratio ◽  
Fokker Planck Equations ◽  
Two Temperature ◽  
Fokker Planck

Transport coefficients for electric current and heat flux have been calculated for a two-temperature equal-mass plasma for several values of the temperature ratio R in the range 1 < R ≤ 100. Transport coefficients have been obtained using the linearized Fokker—Planck equations.

Electrically driven cylindrical free shear flows under an axial uniform magnetic field

2021 ◽  
Vol 57 (2) ◽  
pp. 229-250
Keyword(s):  
Magnetic Field ◽  
Electric Current ◽  
Applied Field ◽  
Uniform Magnetic Field ◽  
Shear Flows ◽  
Hartmann Number ◽  
Induced Magnetic Field ◽  
Free Shear Layers ◽  
Moderate Magnetic Field ◽  
Almost All

We consider a mathematical model of two-dimensional electrically driven laminar axisymmetric circular free shear flows in a cylindrical vessel under the action of an applied axial uniform magnetic field. The mathematical approach is based on the studies by J.C.R. Hunt and W.E. Williams (J. Fluid. Mech., 31, 705, 1968). We solve a system of stationary partial differential equations with two unknown functions of velocity and induced magnetic field. The flows are generated as a result of the interaction of the electric current injected into the liquid and the applied field using one or two pairs of concentric annular electrodes located apart on the end walls. Two lateral free shear layers and two Hartmann layers on the end walls and a quasi-potential flow core between them emerge when the Hartmann number Ha >> 1. As a result, almost all injected current passes through these layers. Depending on the direction of the current injection, coinciding or two counter flows between the end walls are realized. The Hartmann number varies in a range from 2 to 300. When a moderate magnetic field (Ha = 50) is reached, the flow rate and the induced magnetic field flux cease to depend on the magnitude of the applied field but depend on the injected electric current value. Increasing magnetic field leads only to inner restructuring of the flows. Redistributions of velocities and induced magnetic fields, electric current density versus Hartmann number are analyzed. Figs 18, Refs 21.

Model Fokker—Planck Equations: Part 3. Application to transport phenomena

1967 ◽  
Vol 1 (3) ◽  
pp. 327-339 ◽  
Author(s):  
J. P. Dougherty ◽  
S. R. Watson ◽  
M. A. Hellberg
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Strong Magnetic Field ◽  
Transport Phenomena ◽  
Transport Coefficients ◽  
Planck Equation ◽  
Fokker Planck Equation ◽  
Complete Set ◽  
Fokker Planck Equations ◽  
Fokker Planck

The Chapman—Enskog expansion is applied to the model Fokker—Planck equation for a plasma, derived in part 2. It is shown that the complete set of transport coefficients can be calculated without further approximations. Results are derived first in the absence of any external magnetic field. The transport coefficients are also derived when there is a strong magnetic field, in which case they become anisotropic.

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