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The initial value problem in Lagrangian drift kinetic theory

Published online by Cambridge University Press:  23 May 2016

J. W. Burby
J. W. Burby*
Affiliation:
Courant Institute of Mathematical Sciences, New York, NY 10012, USA
*
†Email address for correspondence: [email protected]
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Abstract

Existing high-order variational drift kinetic theories contain unphysical rapidly varying modes that are not seen at low orders. These unphysical modes, which may be rapidly oscillating, damped or growing, are ushered in by a failure of conventional high-order drift kinetic theory to preserve the structure of its parent model’s initial value problem. In short, the (infinite dimensional) system phase space is unphysically enlarged in conventional high-order variational drift kinetic theory. I present an alternative, ‘renormalized’ variational approach to drift kinetic theory that manifestly respects the parent model’s initial value problem. The basic philosophy underlying this alternate approach is that high-order drift kinetic theory ought to be derived by truncating the all-orders system phase-space Lagrangian instead of the usual ‘field$+$particle’ Lagrangian. For the sake of clarity, this story is told first through the lens of a finite-dimensional toy model of high-order variational drift kinetics; the analogous full-on drift kinetic story is discussed subsequently. The renormalized drift kinetic system, while variational and just as formally accurate as conventional formulations, does not support the troublesome rapidly varying modes.

Type
Research Article
Information
Journal of Plasma Physics , Volume 82 , Issue 3 , June 2016 , 905820304
Copyright
© Cambridge University Press 2016 

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