THE STABILITY OF TWISTED MAGNETIC FIELDS IN A FLUID WITH FINITE TRANSPORT PROCESSES AND MASS MOTIONS. 1. GENERAL CONSIDERATIONS

Technical Report · Thu Jan 01 04:00:00 EST 1959

OSTI ID:4257082

Tayler, R J

The investigation of the stability of static plasma equilibrium configurations, when transport processes are neglected, can be reduced to the solution of a second order linear differential equation and a transcendental dispersion relation. Alternatively a variational procedure has been formulated. If the effects of finite electrical conductivity, viscosity, and thermal conductivity are introduced, a twelfth order (or in the case of an incompressible fluid a tenth order) differential equation has to be solved. It is shown that, for an incompressible fluid with constant isotropic transport coefficients, there is one simple configuration in which the tenth order equation can be solved completely in terms of Bessel functions. In this configuration a cylindrical column of fluid carries a uniform axial magnetic field and a uniform axial current and its mass motion consists of a uniform motion along the axis and a uniform angular velocity about the axis. The solution of the dispersion relation is still a serious problem; indication is given of a way in which this solution might be attempted. (auth)

• Research Organization: United Kingdom Atomic Energy Authority. Research Group. Atomic Energy Research Establishment, Harwell, Berks, England
• NSA Number: NSA-13-012768
• OSTI ID: 4257082
• Report Number(s): AERE-T/R-2787
• Country of Publication: United Kingdom
• Language: English

Related Subjects

ANISOTROPY
BESSEL FUNCTIONS
CONFIGURATION
CURRENTS
CYLINDERS
DIFFERENTIAL EQUATIONS
DISPERSION RELATIONS
ELECTRIC CONDUCTIVITY
ELEMENTARY PARTICLES
FIELD THEORY
FLUIDS
MAGNETIC FIELDS
MASS
MATHEMATICS
MOTION
PHYSICS AND MATHEMATICS
PLASMA
PRESSURE
ROTATION
STABILITY
THERMAL CONDUCTIVITY
TRANSPORT
VELOCITY
VISCOSITY