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A hybrid Maxwell solver for fully relativistic and electromagnetic (EM)particle-in-cell (PIC) codes is described. In this solver, the EM fields aresolved in $k$ space by performing an FFT in one direction, while using finitedifference operators in the other direction(s). This solver eliminates thenumerical Cerenkov radiation for particles moving in the preferred direction.Moreover, the numerical Cerenkov instability (NCI) induced by therelativistically drifting plasma and beam can be eliminated using this hybridsolver by applying strategies that are similar to those recently developed forpure FFT solvers. A current correction is applied for the charge conservingcurrent deposit to correctly account for the EM calculation in hybrid Yee-FFTsolver. A theoretical analysis of the dispersion properties in vacuum and in adrifting plasma for the hybrid solver is presented, and compared with PICsimulations with good agreement obtained. This hybrid solver is applied to both2D and 3D Cartesian and quasi-3D (in which the fields and current aredecomposed into azimuthal harmonics) geometries. Illustrative results for laserwakefield accelerator simulation in a Lorentz boosted frame using the hybridsolver in the 2D Cartesian geometry are presented, and compared against resultsfrom 2D UPIC-EMMA simulation which uses a pure spectral Maxwell solver, andfrom OSIRIS 2D lab frame simulation using the standard Yee solver. Very goodagreement is obtained which demonstrates the feasibility of using the hybridsolver for high fidelity simulation of relativistically drifting plasma with noevidence of the numerical Cerenkov instability.

computer physics communications

Mitigation of numerical Cerenkov radiation and instability using a  hybrid finite difference-FFT Maxwell solver and a local charge conserving  current deposit