Topology in Electromagnetics is a chapter in Frontiers in Electromagnetics, edited by Douglas H. Werner and Raj Mittra (The Institute of Electrical and Electronics Engineers, Inc., 2000).
The link to the book is:
http://www.amazon.com/Frontiers-Electromagnetics-Series-Microwave-Technology/dp/0780347013
Physics Letters A Vol. 262, pp. 257-260 (1999)
Coauthor: Charles Nissim-Sabat
Comment on an article by Van Flandern on the speed of gravity. Van Flandern argues that the speed of gravity must be greater than 2 X 10^10 c. We show this is not the case.
J. Phys. A: Math. Gen. 31 (1998) 7077-7094 (PDF)
The topology assumed by most authors for a spacelike hypersurface in a spacetime containing a monopole is generally Euclidean 3-space minus the origin; save for the spherical surface isolating the monopole, this space is unbounded. For such a topology, a consistency relation of de Rham’s theorems shows that a single isolated monopole cannot exist. Monopoles, with charge +/- m, if they exist at all, must occur in pairs having opposite magnetic charge. An extension of de Rham’s theorems to non-Abelian monopoles which are generalizations of Dirac monopoles (those characterized by the first homotopy group of G, the fundamental group of the gauge group G) is made using the definition of an ordered integral of a path-dependent curvature over a surface. This integral is similar to that found in the non-Abelian Stokes theorem. The implications of de Rham’s theorems for non-Abelian monopoles are shown to be similar to the Abelian case.
Helicity and Electromagnetic Field Topology is a chapter in Advanced Electromagnetism: Foundations, Theory and Applications, edited by Terence W. Barrett and Dale M. Grimes (World Scientific, 1995).
Link to the book:
http://books.google.com/books/about/Advanced_Electromagnetism.html?id=lA8tgLMRu2kC
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)