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.

11 pages

References in corpus (2)

• Linearized model Fokker-Planck collision operators for gyrokinetic simulations. I. Theory
• A note on Coulomb collision operator in curvilinear coordinates