A MATHEMATICAL MODEL FOR AN HOURGLASS MAGNETIC FIELD
- Department of Physics and Astronomy, Western University, London, Ontario N6A 3K7 (Canada)
Starting with a mathematical boundary value problem for the magnetic vector potential in an axisymmetric cylindrical coordinate system, we derive a general solution for any arbitrary current distribution using the method of Green's functions. We use this to derive an analytic form for an hourglass magnetic field pattern created by electrical currents that are concentrated near (but not confined within) the equatorial plane of a cylindrical coordinate system. Our solution is not characterized by a cusp at the equatorial plane, as in previous solutions based on a current sheet. The pattern we derive provides a very good fit to hourglass magnetic field patterns emerging from three-dimensional numerical simulations of core formation, and can in principle be used for source-fitting of observed magnetic hourglass patterns.
- OSTI ID:
- 22167421
- Journal Information:
- Astrophysical Journal, Vol. 767, Issue 1; Other Information: Country of input: International Atomic Energy Agency (IAEA); ISSN 0004-637X
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
GENERAL PHYSICS
79 ASTROPHYSICS
COSMOLOGY AND ASTRONOMY
AXIAL SYMMETRY
BOUNDARY-VALUE PROBLEMS
COMPUTERIZED SIMULATION
CUSPED GEOMETRIES
CYLINDRICAL CONFIGURATION
ELECTRIC CURRENTS
GREEN FUNCTION
MAGNETIC FIELDS
MATHEMATICAL MODELS
POTENTIALS
THREE-DIMENSIONAL CALCULATIONS