Conservative Finite-Difference Construction of the Relativistic Vlasov-Maxwell and Reduced Systems for Laser-Driven Kinetics*

Introducing a minimal numerical framework supporting intense laser-plasma kinetic interactions. The relativistic Vlasov-Maxwell Hamiltonian system is naturally constrained to simulate laser-driven ponderomotive effects on electron and ion kinetics along the direction of laser propagation, without discarding the impact of transverse momentum on longitudinal dynamics. Finite-differencing allows integration-by-parts but not generally an exact product rule. We found V-M algorithms exactly conserving particle number, momenta, enstrophy, and energy. Elective transverse projection to 1D costs the gamma factor its spatial independence, splitting the Poisson bracket subalgebra in the absence of a product rule into three orbits mapped to distinct F-D Vlasov equations on phase-space. The standard structure breaks continuous time invariants, but the second admits unconditionally stable Crank-Nicolson implementation with operator splitting, and the third, RK4. Both models conserve particle number and momentum, and one each of energy or enstrophy. We apply these to study laser-driven trapping and acceleration.