Eliminating Finite-Grid Instabilities in Gyrokinetic Particle-in-Cell Simulations

Finite-grid (aliasing) instabilities place severe limitations on momentum-conserving particle-in-cell (PIC) methods applied to models with charge separation effects by requiring the resolution of the Debye length. Gyrokinetic models, on the other hand, enforce quasi-neutrality thereby removing the Debye length analytically. Recent studies with momentum-conserving PIC applied to gyrokinetic models, however, show that a manifestation of this instability exists in certain physical parameter regimes for arbitrary spatial resolution [1,2]. Here, we show that a simple reformulation of the discrete equations, using a co-located discretization of the continuity equation, eliminates this instability for all practical purposes. We perform numerical dispersion analyses for both the original and reformulated schemes, including the effects of finite drifts and finite beta. This reformulation may be useful for codes with complicated meshes, where high-order shape functions or energy-conserving schemes are difficult to implement. Finally, we demonstrate that our reformulation eliminates the finite-grid instability in an implicit electromagnetic version of the XGC code.

[1] G. J. Wilkie, W. Dorland, Phys. Plasmas 23 (2016) 052111

[2] B. F. McMillan, Phys. Plasmas 27 (2020) 052106