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A recently developed three-dimensional version of the quasistatic code LCODEhas a novel feature that enables high-accuracy simulations of the long-termevolution of waves in plasma wakefield accelerators. Equations of plasmaparticle motion are modified to suppress clustering and numerical heating ofmacroparticles, which otherwise occur because the Debye length is not resolvedby the numerical grid. The previously observed effects of premature wakechaotization and wavebreaking disappear with the modified equations.

LCODE: Quasistatic code for simulating long-term evolution of three-dimensional plasma wakefields