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Major Goals:
I. Revisit the basic concept of magnetic
helicity and its conservation properties in realistic geometries,
as well as its extensions to 2-fluid plasmas. Some ambiguities
still exist for gauge-invariant definitions of magnetic helicity
in realistic geometries, such as in the case where magnetic
field lines intercept a surface enclosing a doubly-connected
volume. Examples include a sub-volume of toroidal laboratory
plasmas, accretion disks, and spherical shell of the solar convection
zone. This first goal is to establish a realistic formalism
of gauge-invariant definitions of magnetic helicity in such
cases and to examine its conservation properties in laboratory
plasmas. Possible extensions of such definitions to a 2-fluid
plasma model will be attempted.
II. Determine role of conservation and
transport of magnetic and kinetic helicities during magnetic
self-organization processes. Although conservation of magnetic
helicity has been one of fundamental assumptions in the theories
of magnetic self-organization, its physical significance has
never been clear. There have been also arguments that fast dynamo
processes observed during self-organization are necessarily
accompanied by transport of magnetic helicity over space. This
goal is to establish clear physics understanding of exact roles
played by the helicity conservation properties and its flux
during relaxation processes. Assessments of roles by kinetic
helicities in more general cases will be made whenever possible.
III. Assess applicabilities of physics
understandings gained in achieving Goals#1&2 to astrophysical
circumstances, such as solar dynamo activity and accretion disk
dynamics. An example case is that a finite helicity flux
either in radial outward direction or through the equator plane
may be required to explain the fast dynamo phenomena on the
sun (the solar cycles). This goal is to address the key questions
like (1) Are the concepts of magnetic helicity (or other helicities)
really useful in understanding dynamics of these astrophysical
systems, and (2) if yes, how.
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