Gyrokinetic Landau collision operator in conservative form*

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 current density and preserves the conservative form as the divergence of this current density. The operator contains both test-particle and field-particle contributions, and finite gyroradius effects are evaluated in either Bessel function series or gyrophase integrals. While equivalent to the gyrokinetic Fokker-Planck form with the Rosenbluth potentials [B. Li and D. R. Ernst, Phys. Rev. Lett. 106, 195002 (2011)], the gyrokinetic Landau form explicitly preserves the symmetry between test-particle and field-particle contributions, thus automatically satisfies the conservation laws and H-theorem. The operator in conservative form is being implemented in the gyrokinetic GENE code with a finite-volume method that preserves the discrete conservation laws. The gyrophase integrals for finite gyroradius effects can be pre-computed with an adaptive integration program. While model field terms may conserve the first three velocity moments, their local effects in velocity space have little connection with the exact Landau operator, altering classical transport.