Differential formulation of the gyrokinetic Landau operator

Abstract

Subsequent to the recent rigorous derivation of an energetically consistent gyrokinetic collision operator in the so-called Landau representation, this paper investigates the possibility of finding a differential formulation of the gyrokinetic Landau collision operator. It is observed that, while a differential formulation is possible in the gyrokinetic phase space, reduction of the resulting system of partial differential equations to five dimensions via gyroaveraging poses a challenge. Based on the present work, it is likely that the gyrocentre analogues of the Rosenbluth-MacDonald-Judd potential functions must be kept gyroangle dependent.

arXiv comment11 pages

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• Metriplectic foundations of gyrokinetic Vlasov-Maxwell-Landau theory
• Scattering Theory in Noncanonical Phase Space: A Drift-Kinetic Collision Operator for Weakly Collisional Plasmas