Gerald E. Marsh

Phys. Rev. B Vol. 50, p. 571 (1994) (PDF)

A heuristic model of flux flow and vortex cutting that does not imply a build up of longitudinal flux is given for type-II superconducting cylinders carrying a current in the presence of an axial magnetic field.

Phys. Rev. B Vol. 49, p. 450 (1994) (PDF)

For values of r greater than the coherence length, the axially symmetric Ginzburg-Landau equations are solved for a flux vortex carrying a longitudinal current. The field is not force-free, and it is shown that there are no regular solutions to the force-free field equations that decay exponentially with increasing penetration into a superconductor. It is also shown, in this approximation, that in the case of a vortex carrying a non-zero longitudinal current, the Ginzburg-Landau equations are equivalent to the radial pressure-balance equilibrium relation in ideal magneto-hydrodynamics. The techniques developed in this field to address stability issues can then be used to answer questions related to vortex stability.

Phys. Rev. E Vol. 47, p. 3607 (1993) (PDF)

Concepts from topology are increasingly finding utility in magnetohydrodynamics. This paper gives an example of how the connectivity of the domain and the gauge freedom of the vector potential can play an important role in computing the helicity of twisted magnetic fields used in several areas of astrophysics, particularly solar physics. By computing the relative helicity of a simple magnetic field configuration used to model solar prominences, it is shown that helicity can have a non-local character. This necessitates a reexamination of its conventional physical interpretation. The magnetic energy is also discussed.

Phys. Rev. A Vol. 46, p. 2117 (1992) (PDF)

This paper addresses the question of magnetic energy in multiply connected domains. It is shown that the magnetic energy must in general include a boundary term that is usually assumed to vanish. The physical interpretation of this term is discussed in terms of De Rham’s theorems.

Phys. Rev. A Vol. 45, p. 7520 (1992) (PDF)

The force-free magnetic field condition is expressed in terms of a flux function; alpha is then also a function of the flux function, and with suitable restrictions the resulting equations can be separated and solved. The case of spherical coordinates yields four sets of solutions which are shown to be dependent and equivalent to a simple generalization of those given by Chandrasekhar [Proc. Natl. Acad Sci. USA Vol. 42, 1 (1956)]. Similarly, the case of cylindrical coordinates results in a generalization of the solution given by Furth, et al. [Rev. Sci. Instrum. Vol. 28, 949 (1957)].

The utility of differential forms for understanding the origin of the self-dual gauge-field equations is illustrated by deriving the systems of linear partial differential equations introduced by Belavin and Zakharov and used in a different form by Ueno and Nakamura. The integrability condition for these systems of equations is then used to show their relation to a generalized form of the Ernst equation.

Physics Essays 3, 406-413 (1990)

Self-Dual Gauge Field Eqs