Gyrosymmetry: Global Considerations
Authors: J.W. Burby and H. Qin
Abstract:
In the guiding center theory, smooth unit vectors perpendicular to the magnetic field
are required to define the gyrophase. The question of global existence of these vectors
is addressed using a general result from the theory of principal circle bundles. It is
found that there is, in certain cases, an obstruction to global existence. In these cases,
the gyrophase cannot be defined globally. The implications of this fact on the basic
structure of the guiding center theory are discussed. In particular it is demonstrated
that the guiding center asymptotic expansion of the equations of motion can still
be performed in a globally consistent manner when a single global convention for
measuring gyrophase is unavailable. The key to this demonstration is thinking of
the asymptotic expansion as leveraging the globally defined zero'th order symmetry
associated to the magnetic moment.
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Submitted to: Physics of Plasmas (January 2012)
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Download PPPL-4723 (pdf 3.03 MB 27 pp)
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