Automation of The Guiding Center Expansion
Authors: J. W. Burby, J. Squire and H. Qin
Abstract:
We report on the use of the recently-developed Mathematica package VEST (Vector
Einstein Summation Tools) to automatically derive the guiding center transformation.
Our Mathematica code employs a recursive procedure to derive the transformation
order-by-order. This procedure has several novel features. (1) It is designed
to allow the user to easily explore the guiding center transformation's numerous nonunique
forms or representations. (2) The procedure proceeds entirely in cartesian
position and velocity coordinates, thereby producing manifestly gyrogauge invariant
results; the commonly-used perpendicular unit vector fields e1, e2 are never even introduced.
(3) It is easy to apply in the derivation of higher-order contributions to
the guiding center transformation without fear of human error. Our code therefore
stands as a useful tool for exploring subtle issues related to the physics of toroidal
momentum conservation in tokamaks.
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Submitted to: Physics of Plasmas (March 32013)
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Download PPPL-4861 (pdf 544 KB 26 pp)
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