An energy- and charge-conserving, nonlinearly implicit, electromagnetic 1D-3V Vlasov–Darwin particle-in-cell algorithm

摘要: Abstract A recent proof-of-principle study proposes a nonlinear electrostatic implicit particle-in-cell (PIC) algorithm in one dimension (Chen et al., 2011). The employs kinetically enslaved Jacobian-free Newton–Krylov (JFNK) method, and conserves energy charge to numerical round-off. In this study, we generalize the method electromagnetic simulations 1D using Darwin approximation Maxwell’s equations, which avoids radiative noise issues by ordering out light wave. An implicit, orbit-averaged, time–space-centered finite difference scheme is employed both field equations (in potential form) 1D-3V particle orbit produce discrete system that remains exactly charge- energy-conserving. Furthermore, enabled exact conservation of canonical momentum per any ignorable direction enforced via suitable scattering rule for magnetic field. We have developed simple preconditioner targets waves skin currents, allows us employ time steps O ( m i / e c v T ) larger than explicit CFL. Several experiments demonstrate accuracy, performance, properties algorithm. particular, shown be second-order accurate, CPU speedups more three orders magnitude vs. an Vlasov–Maxwell solver are demonstrated “cold” plasma regime (where k λ D ≪ 1 ).