Gyrokinetic Landau collision operator in conservative form

Qingjiang Pan and Darin R. Ernst
Phys. Rev. E 99, 023201 – Published 8 February 2019

Abstract

A gyrokinetic linearized exact (not model) Landau collision operator is derived by transforming the symmetric and conservative Landau form. The formulation obtains the velocity-space flux density and preserves the operator's conservative form as the divergence of this flux density. The operator contains both test-particle and field-particle contributions, and finite Larmor radius effects are evaluated in either Bessel function series or gyrophase integrals. While equivalent to the gyrokinetic Fokker–Planck form with Rosenbluth potentials [B. Li and D. R. Ernst, Phys. Rev. Lett. 106, 195002 (2011)], the gyrokinetic conservative Landau form explicitly preserves the symmetry between test-particle and field-particle contributions, which underlies the conservation laws and the H theorem, and enables discretization with a finite-volume or spectral method to preserve the conservation properties numerically, independent of resolution. The form of the exact linearized field-particle terms differs from those of widely used model operators. We show the finite Larmor radius corrections to the field-particle terms in the exact linearized operator involve Bessel functions of all orders, while present model field-particle terms involve only the first two Bessel functions. This new symmetric and conservative formulation enables the gyrokinetic exact linearized Landau operator to be implemented in gyrokinetic turbulence codes for comparison with present model operators using similar numerical methods.

  • Figure
  • Received 3 November 2018

DOI:https://doi.org/10.1103/PhysRevE.99.023201

©2019 American Physical Society

Physics Subject Headings (PhySH)

Plasma Physics

Authors & Affiliations

Qingjiang Pan* and Darin R. Ernst

  • Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA

  • *panqj@psfc.mit.edu
  • dernst@psfc.mit.edu

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Issue

Vol. 99, Iss. 2 — February 2019

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