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Next-generation high-power lasers that can be focused to intensitiesexceeding 10^23 W/cm^2 are enabling new physics and applications. The physicsof how these lasers interact with matter is highly nonlinear, relativistic, andcan involve lowest-order quantum effects. The current tool of choice formodeling these interactions is the particle-in-cell (PIC) method. In strongfields, the motion of charged particles and their spin is affected by radiationreaction. Standard PIC codes usually use Boris or its variants to advance theparticles, which requires very small time steps in the strong-field regime toobtain accurate results. In addition, some problems require tracking the spinof particles, which creates a 9D particle phase space (x, u, s). Therefore,numerical algorithms that enable high-fidelity modeling of the 9D phase spacein the strong-field regime are desired. We present a new 9D phase spaceparticle pusher based on analytical solutions to the position, momentum andspin advance from the Lorentz force, together with the semi-classical form ofRR in the Landau-Lifshitz equation and spin evolution given by theBargmann-Michel-Telegdi equation. These analytical solutions are obtained byassuming a locally uniform and constant electromagnetic field during a timestep. The solutions provide the 9D phase space advance in terms of a particle'sproper time, and a mapping is used to determine the proper time step for eachparticle from the simulation time step. Due to the analytical integration, theconstraint on the time step needed to resolve trajectories in ultra-high fieldscan be greatly reduced. We present single-particle simulations and full PICsimulations to show that the proposed particle pusher can greatly improve theaccuracy of particle trajectories in 9D phase space for given laser fields. Adiscussion on the numerical efficiency of the proposed pusher is also provided.

Accurately simulating nine-dimensional phase space of relativistic particles in strong fields