Gyrokinetic Landau collision operator in conservative form

Pan, Qingjiang; Ernst, Darin R.

doi:10.1103/physreve.99.023201

Gyrokinetic Landau collision operator in conservative form

Journal Article · Thu Feb 07 23:00:00 EST 2019 · Physical Review E

DOI:https://doi.org/10.1103/physreve.99.023201· OSTI ID:1609272

Pan, Qingjiang ^[1]; Ernst, Darin R. ^[2]

Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States); DOE/OSTI
Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)

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.

View Accepted Manuscript (DOE)

Research Organization:: Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)

Sponsoring Organization:: USDOE Office of Science (SC)

Grant/Contract Number:: FC02-08ER54966

OSTI ID:: 1609272

Alternate ID(s):: OSTI ID: 1493960

Journal Information:: Physical Review E, Journal Name: Physical Review E Journal Issue: 2 Vol. 99; ISSN PLEEE8; ISSN 2470-0045

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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