The formation of current layers in slowly evolving, low- beta, nearly ideal magnetohydrodynamic plasmas

Details The formation of current layers in slowly evolving, low- beta, nearly ideal magnetohydrodynamic plasmas The formation of current layers in slowly evolving, low- beta, nearly ideal magnetohydrodynamic plasmas

Jul 1999

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1999phdt.........2a&link_type=abstract

Thesis (PhD). UNIVERSITY OF CALIFORNIA, LOS ANGELES, Source DAI-B 60/01, p. 236, Jul 1999, 141 pages.

Mathematics

Logic

2

Magnetic Null, Heating, Alfven Resonance

Scientific paper

This dissertation addresses where current sheets may form in strongly magnetized, tenuous, nearly ideal, magnetohydrodynamic plasmas which have tangled magnetic field lines, and which are stressed slowly compared to their Alfvén wave crossing times. These plasmas are often anomalously hot. These current sheets are of interest since many such plasmas (e.g., the plasma at the center of the galaxy, the galactic halo, and stellar coronae) are believed to be heated by the formation of current sheets that serve as the sites for magnetic reconnection and the conversion of magnetic energy into heat. Unlike in two dimensions, current sheets in three dimensions are subject to strong topological constraints. These constraints are inherently nonlocal, which makes this problem difficult to treat with standard analytical tools. A novel technique has been developed which uses the correspondence between the formation of current sheets in equilibrium plasmas and the existence of zero- frequency shear Alfvén modes to determine where current sheets may form. For the special case of line- tied potential fields, no current sheets may form in the plasma except for the special case of a purely two- dimensional X-point geometry. A numerical study has been made of whether global, low- frequency modes can exist in a bounded, three-dimensional magnetic field geometry with a magnetic null. No evidence for such a mode was found. Current sheets may form where the magnetic field makes a closed curve, such as a null-null loop. Statistical properties of magnetic nulls have been examined in a simple random magnetic field model that is formed from a collection of randomly directed plane waves that have a power-law wavenumber spectrum. The density of nulls has been computed in this model field. Nulls have been shown to form clusters; the fractal dimensions of the clusters of nulls have been computed. Such a plasma would be anticipated to form a hierarchy of current sheets along the null-null loops when the plasma is distorted. This may provide a mechanism for heating these plasmas.

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