Statistics – Computation
Scientific paper
Mar 1987
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1987phdt.........1y&link_type=abstract
Ph.D. Thesis Stanford Univ., CA. Center for Space Science and Astrophysics.
Statistics
Computation
2
Astrophysics, Force-Free Magnetic Fields, Lorentz Force, Magnetic Field Configurations, Nonlinear Systems, Solar Physics, Accretion Disks, Computational Grids, Extragalactic Radio Sources, Finite Difference Theory, Iteration, Plasma Physics, Radio Jets (Astronomy), Solar Flares, Sunspots
Scientific paper
The problem concerned in this work is that of calculating magnetic field configurations in which the Lorentz force (vector)j x (vector)B is everywhere zero, subject to specified boundary conditions. The magnetic field is represented in terms of Clebsch variables in the form (vector)B = del alpha x del beta. These variables are constant on any field line. The most appropriate choice of boundary conditions is to specify the values of alpha and beta on the bounding surface. It is proposed that the field lines move in the direction of local Lorentz force and relax towards a force-free field configuration. This concept leads to an iteration procedure for modifying the variables alpha and beta that tends asymptotically towards the force-free state. This method is first applied to a simple problem in two rectangular dimensions; the calculation shows that the convergence of magnetic field energy to a minimum state (force-free) is close to exponential. This method is then applied to study some astrophysical force-free magnetic fields, such as the structures and evolution of magnetic fields of rotating sunspots and accretion disks. The implication of the results, as related to the mechanisms of solar flares, extragalactic radio sources and radio jets, are discussed.
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