An energy- and momentum-conserving (gyro)kinetic Lenard-Bernstein collision operator in helical, open-field line continuum simulations*

The Lenard-Bernstein collision operator (LBO) has been implemented in Gkeyll for use in a Vlasov-Maxwell system and in a gyrokinetic system. Gkeyll is a continuum plasma physics code that uses a modal discontinuous Galerkin (DG) computational method. A novel calculation employing a DG weak form of division is used for the fluid velocity and thermal velocity moments that appear in the LBO, in order to conserve particles, momentum and kinetic energy. Simple 1x-2v and 1x-3v tests demonstrate an evolution to the correct steady state. Furthermore, the gyrokinetic LBO in Gkeyll has been tested in up to 3x-2v dimensions. Building upon work by E. Shi [1,2], simulations with open, helical field lines are performed in different parameter regimes, including the Texas Helimak experiment and the scrape-off layer of NSTX. These results are compared with turbulence measurements from the Helimak.

[1] Shi, E. L., et al. (2017). J. Plasma Phys., http://doi.org/10.1017/S002237781700037X

 [2] Shi, E.L., Princeton Ph.D. (2017), arXiv:1708.07283v1