The curl (or exterior) derivative carries special import for
electromagnetism. It links the magnetic field to its vector potential, and to
the time derivative of the electric field. In perfectly conducting plasmas,
conforming to the Lorentz force, it produces an eigenstructure: a magnetic
vector surface which is toroidal.
Additionally, linkage of closed magnetic flux loops indicates
differential addition to the gauge component of the vector potential. Meanwhile,
vector field paths on surface manifolds introduce geometric phase via parallel
transport. These manifolds, and geometric phase in general, are characteristic
of magnetic contributions, especially along closed or periodic paths. An
approach to adapt these attributes to pico-scale fields will be outlined.
Selected math aspects will be presented.
Alan Craig was research professor of physics at Montana State University from
1999-2012. His investigations
encompassed applications of cryogenic rare-earth spectroscopy and quantized
silicon nanospheres, mode-locked fiber laser concepts for spectroscopy, and
initiation of experimental work on optical lattice plasmas susceptible to
surface plasmon polariton excitations.
Recently, as an extrapolation of conceptualizing nano-structural
resonances, he has studied the theory of stable (eigen-) structures in flows of
the magnetic vector potential and of plasmas, and their implications for
to joining the university, Dr. Craig served as program manager for Optical
Information Processing (i.e. optical computing and memory) at the Air Force
Office of Scientific Research, preceded by a stint as a laboratory scientist at
the Naval Research Laboratory. His
doctorate was awarded in 1984 from the Optical Sciences Center at the
University of Arizona, following completion of a B.S.E.E. degree in Electrical
Engineering and Physics at Princeton.