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We introduce a quasi-static particle-in-cell (PIC) code -- WAND-PIC -- whichdoes not suffer from some of the common limitations of many quasi-static PICs,such as the need for a predictor-corrector method in solving electromagneticfields. We derive the field equations under quasi-static (QS) approximation andfind the explicit form of the "time" derivative of the transverse plasmacurrent. After that, equations for the magnetic fields can be solved exactlywithout using the predictor-corrector method. Algorithm design and codestructure are thus greatly simplified. With the help of explicit quasi-staticequations and our adaptive step size, plasma bubbles driven by the large beamcharges can be simulated efficiently without suffering from the numericalinstabilities associated with the predictor-corrector method. In addition,WAND-PIC is able to simulate the sophisticated interactions betweenhigh-frequency laser fields and beam particles through the method ofsub-cycling. Comparisons between the WAND-PIC and a first-principle full PICcode (VLPL) are presented. WAND-PIC is open-source, fully three-dimensional,and parallelized with the in-house multigrid solver. Scalability, timecomplexity, and parallelization efficiency up to thousands of cores are alsodiscussed in this work.

WAND-PIC: an accelerated three-dimensional quasi-static particle-in-cell code