Author: Guangye Chen
Requested Type: Pre-Selected Invited
Submitted: 2018-03-01 12:08:44
Co-authors: Luis Chacon
Los Alamos National Laboratory
P.O. Box 1663
Los Alamos, NM 87545
Particle-in-cell (PIC) algorithms are widely used for first-principles simulations of plasmas. Classical PIC employs an explicit advance for the Vlasov-Maxwell system, and is subject to both temporal and spatial (aliasing) instabilities. Gyrokinetic PIC eliminates some of these constraints by averaging the governing equations over the gyroperiod, but the resulting system is rigorous only in the low- regime with sufficiently smooth gradients. Implicit PIC holds promise for significant speedups when compared to classical PIC while remaining valid in all regimes of a collisionless plasma.
Implicit PIC has been explored before, but traditionally suffered from severe numerical heating. In this presentation, we discuss a multi-dimensional, nonlinearly implicit, conservative electromagnetic PIC algorithm, specifically using the Darwin approximation . The approach solves the numerical heating issue, and is free from the so-called cancellation problem of semi-implicit Darwin schemes, delivering both accuracy and efficiency for multiscale plasma kinetic simulations. The formulation conserves exactly total energy, local charge, canonical momentum in the ignorable directions, and preserves the Coulomb gauge exactly. Key to the performance of the algorithm is a moment-based fluid preconditioner, featuring the correct asymptotic limits for large domains (MHD limit) and small electron mass (ambipolar response). The formulation has been recently extended to curvilinear meshes  and arbitrary perfect-conductor boundaries , opening the possibility of accurate body-fitted implicit PIC simulations. The superior accuracy and efficiency properties of the scheme will be demonstrated with various numerical examples.
 G. Chen, L. Chacón, Comput. Phys. Comm. 197, 73-87 (2015).
 L. Chacón and G. Chen, J. Comput. Phys., 316, 578-597 (2016)
 L. Chacón and G. Chen, J. Comput. Phys., submitted (2018)