Magnetic Dipole Equilibrium Solution at Finite Plasma Pressure

Abstract

A realistic equilibrium with finite plasma pressure is derived for a plasma confined by the magnetic field of a point dipole. The low and high pressure forms of the solution are explicitly displayed. The energy principle is used to demonstrate the interchange stability of the equilibrium solution for arbitrary pressures and shows that it remains stable as the plasma pressure increases. [S0031-9007 (99)08794-3] PACS numbers: 52.55.Hc, 52.35.Bj

Equilibrium of a gravitating plasma in a dipolar magnetic field

“…Here we extend the results of Ref. 3 for a plasma equilibrium in a dipolar magnetic field to the case of an arbitrary β plasma in a gravitational field (see Figure).…”

“…Discussions. Interestingly, for β >>1 we find that |α|= β −1/2 <<1 with and without the effects of gravity and toroidal plasma rotation [3,4]. However, contour plots of the flux functions, described by r ψ (µ)∝ (H(µ)) 1/α , are very different since a large 1/|α| power strongly magnifies even the small differences between the H(µ) that correspond to the different cases (see [4]).…”

Axisymmetric Plasma Equilibrium in Gravitational and Magnetic Fields

“…From the force balance equation across the magnetic field lines and Ampere's law, we obtain the Grad-Shafranov equation (6) where is an adjustable parameter which plays the role of an eigenvalue to find a solution of Eq. (5) (see, e.g., [13]), while and are normalization constants such that . One can show that ansatz (6) is compatible with Eq.…”

Magnetohydrodynamic stability in a levitated dipole

“…For the magnetospheric problem it is necessary to consider rotation, anisotropy (p ⊥ = p ) as well as the boundary condition where the field lines enter the conducting regions near the planetary poles. Chan et al[7] utilize a low beta equilibrium expansion in the ballooning calculation and their results are suspect at high beta [8].…”

“…For the magnetospheric problem it is necessary to consider rotation, anisotropy (p ⊥ = p ) as well as the boundary condition where the field lines enter the conducting regions near the planetary poles. Chan et al[7] utilize a low beta equilibrium expansion in the ballooning calculation and their results are suspect at high beta [8].As a laboratory approach to controlled fusion a circular magnet that is located within a plasma will generate a dipole configuration. To avoid losses on supports the ring needs to be superconducting and be magnetically levitated within the vacuum chamber.…”