Particle-in-cell (PIC) simulation is an important tool for studying laser-plasma interactions. Unlike classical algorithms based on the discretization of differential (or integral) equations of motion,  the symplectic algorithm derives its numerical schemes from discretization and variational formulation of the system's Hamiltonian, thereby avoiding the accumulation of numerical errors over time. This algorithm demonstrates its unique advantages, including long-term energy conservation, high-resolution simulation of dense plasmas, and high-accuracy modeling of relativistic particles, making it a promising candidate for the simulation of plasma physics processes characterized by long durations, high plasma densities, or strong relativistic effects. SymPIC^[1] is an open-source symplectic electromagnetic fully kinetic PIC code which has been used to  simulate tokamak plasmas on the world's leading supercomputers. Based on SymPIC, we have tested the feasibility of applying symplectic algorithms to the simulation of intense laser interactions with solid plasma and obtained preliminary results. In several tests, SymPIC has demonstrated its ability to accurately model several physical processes and to reproduce the same results with classical PIC codes such as Smilei. In the future, we aim to utilize SymPIC to conduct large-scale, long-term, and high-accuracy simulations for specific laser-plasma interactions driven by  kJ-ps laser beams or the ps-scale prepulse of 10PW lasers.

[1] https://github.com/JianyuanXiao/SymPIC

laser-plasma interactions,particle-in-cell algorithm