Automation of The Guiding Center Expansion

Abstract

We report on the use of the recently-developed Mathematica package \emph{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 non-unique 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 $e_1,e_2$ 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.

34 pages

References in corpus (2)

• Gyrosymmetry: Global Considerations
• VEST: abstract vector calculus simplification in Mathematica

Cited by in corpus (15)

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• Isodrastic Magnetic fields for suppressing transitions in guiding-centre motion
• Equivalence of two independent calculations of the higher order guiding center Lagrangian
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