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

TL;DR

This paper introduces a new implicit particle-in-cell code, ELIXIRS, for modeling relativistic laser-plasma interactions, demonstrating improved stability and efficiency over explicit methods, especially in high-density plasma scenarios.

Contribution

Development of the ELIXIRS code based on the relativistic direct implicit method with adjustable damping, enabling stable and efficient simulations of laser-plasma interactions.

Findings

Successful benchmarking against explicit PIC simulations.

Demonstrated robustness with coarse discretizations.

Showed efficiency gains over explicit methods.

Abstract

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