Gerald E. Marsh

World Publishing Co. Pte. Ltd. 1996

After an introductory chapter concerned with the history of force-free magnetic fields, and the relation of such fields to hydrodynamics and astrophysics, the book examines the limits imposed by the virial theorem for finite force-free configurations. Various techniques are then used to find solutions to the field equations. The fact that the field lines corresponding to these solutions have the common feature of being “twisted”, and may be knotted, motivates a discussion of field line topology and the concept of helicity. The topics of field topology, helicity, and magnetic energy in multiply connected domains make the book of interest to a rather wide audience. Applications to solar prominence models, type-II superconductors, and force-reduced magnets are also discussed. The book contains many figures and a wealth of material not readily available elsewhere.

(Force-Free Magnetic Fields at Amazon)

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)].

J. Appl. Phys. Vol. 68, p. 3818 (1990) (PDF)

The general approach to cylindrically symmetric force-free magnetic fields first introduced by Lüst and Schlüter [Z. Astrophys. Vol. 34, 263 (1954)], is restricted to cylindrically symmetric fields, and subsequently used to determine a set of solutions to the force-free field equations with non-constant alpha. The first element of the set is the well known constant a solution of Lundquist [Ark. Fys. Vol. 2, 361 (1951)]. These solutions may have practical applications with respect to high-temperature superconductors.

Applied Physics Communications Vol 8, p. 227 (1988)
Coauthor: Robert Piacesi
[A shortened version of this article also appeared in Physics & Society (January 1989)]

Markov processes represent a powerful method for quantifying questions related to the survivability of strategic nuclear forces. This paper gives an elementary introduction to Markow processes and chains followed by a simple anti-submarine warfare example in which the scenario of a surveillance-surge attack is treated as a steady state Markov process.

(MS Word Document)

Physics Today Vol. 40, p. 36 (August 1987) Part 1(PDF) Part 2 (PDF)
Coauthor: Jack Evernden

Failure to account properly for geological and seismological differences between the US and Soviet test sites has led to overestimates of Soviet tests and to incorrect claims of Soviet cheating on the treaty limit of 150 kilotons.

Reviews of Scientific Instruments, Vol 48, p. 841 (1977)

The accelerator, magnetic shielding-equipotential grading system, and voltage divider chain of the University of Chicago 1-MV STEM are described. A dynamical analysis of the system is presented in addition to a discussion of the problem of “electron loading” encountered while conditioning the accelerator tube.

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