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Implicit particle-in-cell codes offer advantages over their explicitcounterparts in that they suffer weaker stability constraints on the need toresolve the higher frequency modes of the system. This feature may proveparticularly valuable for modeling the interaction of high-intensity laserpulses with overcritical plasmas, in the case where the electrostatic modes inthe denser regions are of negligible influence on the physical processes understudy. To this goal, we have developed the new two-dimensional electromagneticcode ELIXIRS (standing for ELectromagnetic Implicit X-dimensional IterativeRelativistic Solver) based on the relativistic extension of the so-calledDirect Implicit Method [D. Hewett and A. B. Langdon, J. Comp. Phys.\textbf{72}, 121(1987)]. Dissipation-free propagation of light waves intovacuum is achieved by an adjustable-damping electromagnetic solver. In thehigh-density case where the Debye length is not resolved, satisfactory energyconservation is ensured by the use of high-order weight factors. In this paper,we first present an original derivation of the electromagnetic direct implicitmethod within a Newton iterative scheme. Its linear properties are theninvestigated through numerically solving the relation dispersions obtained forboth light and plasma waves, accounting for finite space and time steps.Finally, our code is successfully benchmarked against explicit particle-in-cellsimulations for two kinds of physical problems: plasma expansion into vacuumand relativistic laser-plasma interaction. In both cases, we will demonstratethe robustness of the implicit solver for crude discretizations, as well as thegains in efficiency which can be realized over standard explicit simulations.

Particle-in-cell modelling of relativistic laser-plasma interaction with the adjustable damping, direct implicit method