A multidimensional, energy and chargeconserving, nonlinearly implicit, electromagnetic Vlasov–Darwin particleincell algorithm
For decades, the Vlasov–Darwin model has been recognized to be attractive for particleincell (PIC) kinetic plasma simulations in nonradiative electromagnetic regimes, to avoid radiative noise issues and gain computational efficiency. However, the Darwin model results in an elliptic set of field equations that renders conventional explicit time integration unconditionally unstable. We explore a fully implicit PIC algorithm for the Vlasov–Darwin model in multiple dimensions, which overcomes many difficulties of traditional semiimplicit Darwin PIC algorithms. The finitedifference scheme for Darwin field equations and particle equations of motion is space–timecentered, employing particle subcycling and orbitaveraging. This algorithm conserves total energy, local charge, canonicalmomentum in the ignorable direction, and preserves the Coulomb gauge exactly. An asymptotically wellposed fluid preconditioner allows efficient use of large cell sizes, which are determined by accuracy considerations, not stability, and can be orders of magnitude larger than required in a standard explicit electromagnetic PIC simulation. Finally, we demonstrate the accuracy and efficiency properties of the algorithm with various numerical experiments in 2D–3V.
 Authors:

^{[1]};
^{[1]}
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States). Theoretical Division
 Publication Date:
 Report Number(s):
 LAUR1521463
Journal ID: ISSN 00104655
 Grant/Contract Number:
 AC5206NA25396
 Type:
 Accepted Manuscript
 Journal Name:
 Computer Physics Communications
 Additional Journal Information:
 Journal Volume: 197; Journal Issue: C; Journal ID: ISSN 00104655
 Publisher:
 Elsevier
 Research Org:
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Sponsoring Org:
 USDOE National Nuclear Security Administration (NNSA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING; 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; Implicit particleincell; Energy conservation; Charge conservation; Canonical momentum conservation; Vlasov–Darwin; Multiscale; JFNK; Physicsbased preconditioner
 OSTI Identifier:
 1329577
 Alternate Identifier(s):
 OSTI ID: 1246662
Chen, G., and Chacón, L.. A multidimensional, energy and chargeconserving, nonlinearly implicit, electromagnetic Vlasov–Darwin particleincell algorithm. United States: N. p.,
Web. doi:10.1016/j.cpc.2015.08.008.
Chen, G., & Chacón, L.. A multidimensional, energy and chargeconserving, nonlinearly implicit, electromagnetic Vlasov–Darwin particleincell algorithm. United States. doi:10.1016/j.cpc.2015.08.008.
Chen, G., and Chacón, L.. 2015.
"A multidimensional, energy and chargeconserving, nonlinearly implicit, electromagnetic Vlasov–Darwin particleincell algorithm". United States.
doi:10.1016/j.cpc.2015.08.008. https://www.osti.gov/servlets/purl/1329577.
@article{osti_1329577,
title = {A multidimensional, energy and chargeconserving, nonlinearly implicit, electromagnetic Vlasov–Darwin particleincell algorithm},
author = {Chen, G. and Chacón, L.},
abstractNote = {For decades, the Vlasov–Darwin model has been recognized to be attractive for particleincell (PIC) kinetic plasma simulations in nonradiative electromagnetic regimes, to avoid radiative noise issues and gain computational efficiency. However, the Darwin model results in an elliptic set of field equations that renders conventional explicit time integration unconditionally unstable. We explore a fully implicit PIC algorithm for the Vlasov–Darwin model in multiple dimensions, which overcomes many difficulties of traditional semiimplicit Darwin PIC algorithms. The finitedifference scheme for Darwin field equations and particle equations of motion is space–timecentered, employing particle subcycling and orbitaveraging. This algorithm conserves total energy, local charge, canonicalmomentum in the ignorable direction, and preserves the Coulomb gauge exactly. An asymptotically wellposed fluid preconditioner allows efficient use of large cell sizes, which are determined by accuracy considerations, not stability, and can be orders of magnitude larger than required in a standard explicit electromagnetic PIC simulation. Finally, we demonstrate the accuracy and efficiency properties of the algorithm with various numerical experiments in 2D–3V.},
doi = {10.1016/j.cpc.2015.08.008},
journal = {Computer Physics Communications},
number = C,
volume = 197,
place = {United States},
year = {2015},
month = {8}
}