2 research outputs found
An energy- and charge-conserving, nonlinearly implicit, electromagnetic 1D-3V Vlasov-Darwin particle-in-cell algorithm
A recent proof-of-principle study proposes a nonlinear electrostatic implicit
particle-in-cell (PIC) algorithm in one dimension (Chen, Chacon, Barnes, J.
Comput. Phys. 230 (2011) 7018). The algorithm employs a kinetically enslaved
Jacobian-free Newton-Krylov (JFNK) method, and conserves energy and charge to
numerical round-off. In this study, we generalize the method to electromagnetic
simulations in 1D using the Darwin approximation of Maxwell's equations, which
avoids radiative aliasing noise issues by ordering out the light wave. An
implicit, orbit-averaged time-space-centered finite difference scheme is
applied to both the 1D Darwin field equations (in potential form) and the 1D-3V
particle orbit equations to produce a discrete system that remains exactly
charge- and energy-conserving. Furthermore, enabled by the implicit Darwin
equations, exact conservation of the canonical momentum per particle in any
ignorable direction is enforced via a suitable scattering rule for the magnetic
field. Several 1D numerical experiments demonstrate the accuracy and the
conservation properties of the algorithm.Comment: 24 pages, 4 figure
A multi-dimensional, energy- and charge-conserving, nonlinearly implicit, electromagnetic Vlasov-Darwin particle-in-cell algorithm
For decades, the Vlasov-Darwin model has been recognized to be attractive for
particle-in-cell (PIC) kinetic plasma simulations in non-radiative
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. Here, we explore a fully implicit PIC algorithm for the Vlasov-Darwin
model in multiple dimensions, which overcomes many difficulties of traditional
semi-implicit Darwin PIC algorithms. The finite-difference scheme for Darwin
field equations and particle equations of motion is space-time-centered,
employing particle sub-cycling and orbit-averaging. The algorithm conserves
total energy, local charge, canonical-momentum in the ignorable direction, and
preserves the Coulomb gauge exactly. An asymptotically well-posed fluid
preconditioner allows efficient use of large time steps and 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. We demonstrate the accuracy and efficiency properties of the
algorithm with various numerical experiments in 2D-3V.Comment: 35 pages, 6 figure