scholarly journals The Existence of Non-unique Steady State Solutions to the RMF Current Drive Equations

1985 ◽  
Vol 38 (2) ◽  
pp. 157 ◽  
Author(s):  
WN Hugrass
Keyword(s):  
Magnetic Field ◽  
Steady State ◽  
Initial Boundary ◽  
Skin Depth ◽  
Current Drive ◽  
Rotating Magnetic Field ◽  
Electron Mass ◽  
Plasma Cylinder ◽  
Initial Boundary Value ◽  
Steady State Solutions

It is shown that the value of the d.c. current driven in a plasma cylinder by means of a rotating magnetic field (RMF) is not unique for R/o ;;:; 6 and eB",/vel m ~ R/o, where R is the radius of the plasma cylinder, a is the classical skin depth, Vel is the electron-ion momentum transfer collision frequency, B", is the magnitude of the rotating magnetic field, e is the electron charge and m is the electron mass. This effect is predicted using three distinct approaches: (i) a steady state analysis which ignores the second and higher harmonics of the fields and currents; (ii) a qualitative model which utilizes the analogy between the RMF current drive technique and the operation of the induction motor; (iii) a solution of the initial boundary value equations describing the RMF current drive in cylindrical plasmas.

Steady-state solutions for the penetration of a rotating magnetic field into a plasma column

1981 ◽  
Vol 26 (3) ◽  
pp. 441-453 ◽  
Author(s):  
Ieuan R. Jones ◽  
Waheed N. Hugrass
Keyword(s):  
Magnetic Field ◽  
Steady State ◽  
Plasma Column ◽  
Skin Effect ◽  
Rotation Frequency ◽  
Rotating Magnetic Field ◽  
Electron Current ◽  
Plasma Cylinder ◽  
Resistive Plasma ◽  
Steady State Solutions

The penetration of an externally applied rotating magnetic field into a plasma cylinder is examined. Steady-state solutions of an appropriate set of magneto-fluid equations show that, provided the amplitude and rotation frequency of the field are suitably chosen, the penetration is not limited by the usual classical skin effect. The enhanced penetration of the rotating field is accompanied by the generation of a unidirectional azimuthal electron current which is totally absent in a purely resistive plasma cylinder.

A numerical study of the generation of an azimuthal current in a plasma cylinder using a transverse rotating magnetic field

1981 ◽  
Vol 26 (3) ◽  
pp. 455-464 ◽  
Author(s):  
W. N. Hugrass ◽  
R. C. Grimm
Keyword(s):  
Magnetic Field ◽  
Numerical Study ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Threshold Value ◽  
Rotating Magnetic Field ◽  
Plasma Cylinder ◽  
Initial Boundary Value ◽  
Azimuthal Current ◽  
Cylindrical Plasma Column

The generation of a steady azimuthal current in a cylindrical plasma column using a rotating magnetic field is numerically investigated. The mixed initial-boundary-value problem is solved using a finite difference method. It is shown that substantial azimuthal current can be driven provided that the amplitude of the rotating magnetic field is greater than a certain threshold value which depends on the plasma resistivity.

Bounds for the solution of a non-linear parabolic initial-boundary value problem

1977 ◽  
Vol 82 (1) ◽  
pp. 131-145
Author(s):  
M. R. Carter
Keyword(s):  
Steady State ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Initial Boundary Value Problems ◽  
The Past ◽  
Existence And Stability ◽  
Image Position ◽  
Initial Boundary Value ◽  
Steady State Solutions

A number of papers have appeared over the past decade or so which study questions of the existence and stability of positive steady-state solutions for parabolic initial-boundary value problems of the general form

scholarly journals MATHEMATICAL MODELLING OF AN ELONGATED MAGNETIC DROPLET IN A ROTATING MAGNETIC FIELD

2012 ◽  
Vol 17 (1) ◽  
pp. 47-57 ◽  
Author(s):  
Andrejs Cebers ◽  
Harijs Kalis
Keyword(s):  
Magnetic Field ◽  
Mathematical Modelling ◽  
Numerical Solutions ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Rotating Magnetic Field ◽  
Singularly Perturbed ◽  
Actual Shape ◽  
Initial Boundary Value ◽  
Magnetic Droplet

Dynamics of an elongated droplet under the action of a rotating magnetic field is considered by mathematical modelling. The actual shape of a droplet is obtained by solving the initial-boundary value problem of a nonlinear singularly perturbed partial differential equation (PDE). For the discretization in space the finite difference scheme (FDS) is applied. Time evolution of numerical solutions is obtained with MATLAB by solving a large system of ordinary differential equations (ODE).

scholarly journals Effect of the Motion of Ions on the Penetration of a Rotating Magnetic Field into a Plasma Cylinder

1998 ◽  
Vol 51 (5) ◽  
pp. 859 ◽  
Author(s):  
W. N. Hugrass
Keyword(s):  
Magnetic Field ◽  
Equations Of Motion ◽  
Current Drive ◽  
Rotating Magnetic Field ◽  
Simplified Model ◽  
Plasma Cylinder ◽  
Cylindrical Plasma ◽  
Nonlinear Mechanism

A simplified model for the rotating magnetic field (RMF) current drive in an infinitely long cylindrical plasma is considered. The model allows for motion of both the electron and ion fluids in the z and θ directions. It is assumed that equilibrium is satisfied on the average and hence the r components of the equations of motion are not considered. It is shown that the motion of the ion fluid does not introduce any significant modifications to the nonlinear mechanism for the penetration of the RMF into the plasma.

Analytical solutions for the current driven by a rotating magnetic field in a cylindrical plasma with azimuthal field

1988 ◽  
Vol 40 (1) ◽  
pp. 109-126 ◽  
Author(s):  
Peter A. Watterson
Keyword(s):  
Magnetic Field ◽  
Skin Depth ◽  
Current Drive ◽  
Rotating Magnetic Field ◽  
Toroidal Field ◽  
High Resistivity ◽  
Axial Field ◽  
Low Resistivity ◽  
Cylindrical Plasma ◽  
Synchronous Rotation

The generation of steady currents by a rotating magnetic field (RMF) in a cylindrical plasma permeated by a steady azimuthal (or toroidal) magnetic field is studied analytically. Solutions are presented for the following limiting cases:(1) high resistivity, when the penetration of the RMF and current drive are confined to a skin depth layer;(2) low resistivity and weak toroidal field (small compared with the RMF), when the RMF fully penetrates the plasma and the toroidal current is that due to nearly synchronous rotation of the electron fluid with the RMF;(3) low resistivity and intermediate toroidal field (comparable to the axial field associated with synchronous current), when the toroidal current is a significant fraction of its synchronous value, but large oscillating fields are generated; and(4) strong toroidal field, when the RMF fully penetrates the plasma but current is only driven in a boundary layer at the plasma edge.The applicability of these solutions is governed by the relative sizes of three dimensionless parameters.

Formation and steady-state maintenance of field reversed configuration using rotating magnetic field current drive

2002 ◽  
Vol 9 (1) ◽  
pp. 185-200 ◽  
Author(s):  
H. Y. Guo ◽  
A. L. Hoffman ◽  
R. D. Brooks ◽  
A. M. Peter ◽  
Z. A. Pietrzyk ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Steady State ◽  
Current Drive ◽  
Rotating Magnetic Field ◽  
Field Reversed Configuration
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