Steady-state benchmarks of DK4D: A time-dependent, 
axisymmetric drift-kinetic equation solvera

Authors:   B. C. Lyons, S. C. Jardin, and J. J. Ramos

Abstract:   The DK4D code has been written to solve a set of time-dependent, axisymmetric, finite-Larmor-radius drift-kinetic equations (DKEs) for the non-Maxwellian part of the electron and ion distribution functions using the full, linearized Fokker-Planck-Landau collision operator. The plasma is assumed to be in the low- to finite-collisionality regime, as is found in the cores of modern and future magnetic confinement fusion experiments. Each DKE is formulated such that the perturbed distribution function carries no net density, parallel momentum, or kinetic energy. Rather, these quantities are contained within the background Maxwellians and would be evolved by an appropriate set of extended magnetohydrodynamic (MHD) equations. This formulation allows for straight-forward coupling of DK4D to existing extended MHD time evolution codes. DK4D uses a mix of implicit and explicit temporal representations and finite element and spectral spatial representations. These, along with other computational methods used, are discussed extensively. Steadystate benchmarks are then presented comparing the results of DK4D to expected analytic results at low collisionality, qualitatively, and to the Sauter analytic fits for the neoclassical conductivity and bootstrap current, quantitatively. These benchmarks confirm that DK4D is capable of solving for the correct, gyroaveraged distribution function in stationary magnetic equilibria. Furthermore, the results presented demonstrate how the exact drift-kinetic solution varies with collisionality as a function of the magnetic moment and the poloidal angle.
_________________________________________________________________________________________________

Submitted to:  Physics of Plasmas
_________________________________________________________________________________________________

Download PPPL-5143 (pdf 3.1 MB 37pp)
_________________________________________________________________________________________________