Automation of The Guiding Center Expansion

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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 ... continued below

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Burby, J. W.; Squire, J. & Qin, H. March 19, 2013.

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Description

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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  • Physics of Plasmas (March 2013)

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  • Report No.: PPPL-4861
  • Grant Number: DE-ACO2-09CH11466
  • DOI: 10.2172/1072363 | External Link
  • Office of Scientific & Technical Information Report Number: 1072363
  • Archival Resource Key: ark:/67531/metadc840022

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Office of Scientific & Technical Information Technical Reports

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Office of Scientific and Technical Information (OSTI) is the Department of Energy (DOE) office that collects, preserves, and disseminates DOE-sponsored research and development (R&D) results that are the outcomes of R&D projects or other funded activities at DOE labs and facilities nationwide and grantees at universities and other institutions.

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  • March 19, 2013

Added to The UNT Digital Library

  • May 19, 2016, 9:45 a.m.

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  • July 11, 2016, 4:09 p.m.

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Burby, J. W.; Squire, J. & Qin, H. Automation of The Guiding Center Expansion, report, March 19, 2013; Princeton, New Jersey. (digital.library.unt.edu/ark:/67531/metadc840022/: accessed November 23, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.