Non-physical Asymptotic Behavior in the Modified Form of the Gyrokinetic Poisson Equation Used in the Split-Weight Scheme

The split-weight scheme [1,2] is a commonly used numerical technique for treating kinetic electrons in magnetized plasmas, based on a splitting of the electron distribution function into adiabatic and non-adiabatic parts. For consistency with the original equations, the operator applied to the electrostatic potential in the Gyrokinetic Poisson equation must be modified to account for the adiabatic density contribution. In the absence of discrete effects, this modification to the operator is exactly accounted for in the dynamics of the non-adiabatic density. Numerically, however, this may not be the case, and problematic asymptotic behaviors may be forced on the solution due to the nature of the modified operator. Here, we present an asymptotic analysis of the modified form of the Gyrokinetic Poisson equation, suggesting the presence of non-physical boundary layers in the solution. We demonstrate how this behavior can show up in XGC simulations when a newly developed axisymmetric solver is used, driving numerical instabilities. Finally, we explore mitigation methods.



[1] I. Manuilskiy and W.W. Lee, Phys. Plasmas 7, 1381 (2000)

[2] Y. Chen and S. Parker, J. Comput. Phys. 220, 839-855 (2007)