April 4-6

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approvedsturdevant_sherwood.pdf2022-04-05 10:23:47Benjamin Sturdevant


Author: Benjamin J Sturdevant
Requested Type: Consider for Invited
Submitted: 2022-03-04 14:42:58

Co-authors: L. Chacon

Contact Info:
Princeton Plasma Physics Laboratory
P.O. Box 451
Princeton, NJ   08543

Abstract Text:
Finite-grid (aliasing) instabilities are known to place severe limitations on momentum-conserving particle-in-cell (PIC) methods applied to models including charge separation effects by requiring the resolution of the Debye length. Gyrokinetic models, on the other hand, generally 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 present our recent work showing that a simple reformulation of the discrete equations, making use of a co-located discretization of the continuity equation, eliminates this instability for all practical purposes [3]. Numerical dispersion analyses for both the original and reformulated schemes, including the effects of finite mean parallel velocity and finite-beta, have been performed. The reformulated scheme is shown to be numerically stable for stationary plasmas at any spatial resolution and for plasmas in which the electron mean parallel velocity is smaller than the electron thermal velocity (generally ensured by ambipolarity in plasmas of interest). This reformulation may be particularly useful for codes with complicated meshes, where high-order shape functions or energy-conserving schemes are difficult to implement. The analysis presented here may also be useful for explaining the success of previously considered methods to remove particle instabilities, such as the split-weight scheme [4].

[1] G. J. Wilkie, W. Dorland, Phys. Plasmas 23 (2016) 052111. doi:10.1063/1.4948493.
[2] B. F. McMillan, Phys. Plasmas 27 (2020) 052106. doi:10.1063/1.5139957.
[3] B. Sturdevant, L. Chacon, submitted to J. Comput. Phys.
[4] I. Manuilskiy, W. W. Lee, Phys. Plasmas 7 (5) (2000) 1381. doi:10.1063/1.873955.