Next-generation high-power lasers that can be focused to intensities exceeding 10^23 W/cm^2 are enabling new physics and applications. The physics of how these lasers interact with matter is highly nonlinear, relativistic, and can involve lowest-orde
r quantum effects. The current tool of choice for modeling these interactions is the particle-in-cell (PIC) method. In strong fields, the motion of charged particles and their spin is affected by radiation reaction. Standard PIC codes usually use Boris or its variants to advance the particles, which requires very small time steps in the strong-field regime to obtain accurate results. In addition, some problems require tracking the spin of particles, which creates a 9D particle phase space (x, u, s). Therefore, numerical algorithms that enable high-fidelity modeling of the 9D phase space in the strong-field regime are desired. We present a new 9D phase space particle pusher based on analytical solutions to the position, momentum and spin advance from the Lorentz force, together with the semi-classical form of RR in the Landau-Lifshitz equation and spin evolution given by the Bargmann-Michel-Telegdi equation. These analytical solutions are obtained by assuming a locally uniform and constant electromagnetic field during a time step. The solutions provide the 9D phase space advance in terms of a particles proper time, and a mapping is used to determine the proper time step for each particle from the simulation time step. Due to the analytical integration, the constraint on the time step needed to resolve trajectories in ultra-high fields can be greatly reduced. We present single-particle simulations and full PIC simulations to show that the proposed particle pusher can greatly improve the accuracy of particle trajectories in 9D phase space for given laser fields. A discussion on the numerical efficiency of the proposed pusher is also provided.
The 3D quasi-static particle-in-cell (PIC) algorithm is a very efficient method for modeling short-pulse laser or relativistic charged particle beam-plasma interactions. In this algorithm, the plasma response to a non-evolving laser or particle beam
is calculated using Maxwells equations based on the quasi-static approximate equations that exclude radiation. The plasma fields are then used to advance the laser or beam forward using a large time step. The algorithm is many orders of magnitude faster than a 3D fully explicit relativistic electromagnetic PIC algorithm. It has been shown to be capable to accurately model the evolution of lasers and particle beams in a variety of scenarios. At the same time, an algorithm in which the fields, currents and Maxwell equations are decomposed into azimuthal harmonics has been shown to reduce the complexity of a 3D explicit PIC algorithm to that of a 2D algorithm when the expansion is truncated while maintaining accuracy for problems with near azimuthal symmetry. This hybrid algorithm uses a PIC description in r-z and a gridless description in $phi$. We describe a novel method that combines the quasi-static and hybrid PIC methods. This algorithm expands the fields, charge and current density into azimuthal harmonics. A set of the quasi-static field equations are derived for each harmonic. The complex amplitudes of the fields are then solved using the finite difference method. The beam and plasma particles are advanced in Cartesian coordinates using the total fields. Details on how this algorithm was implemented using a similar workflow to an existing quasi-static code, QuickPIC, are presented. The new code is called QPAD for QuickPIC with Azimuthal Decomposition. Benchmarks and comparisons between a fully 3D explicit PIC code, a full 3D quasi-static code, and the new quasi-static PIC code with azimuthal decomposition are also presented.
When using an electromagnetic particle-in-cell (EM-PIC) code to simulate a relativistically drifting plasma, a violent numerical instability known as the numerical Cerenkov instability (NCI) occurs. The NCI is due to the unphysical coupling of electr
omagnetic waves on a grid to wave-particle resonances, including aliased resonances, i.e., $omega + 2pimu/Delta t=(k_1+ 2pi u_1/Delta x_1)v_0$, where $mu$ and $ u_1$ refer to the time and space aliases and the plasma is drifting relativistically at velocity $v_0$ in the $hat{1}$-direction. Recent studies have shown that an EM-PIC code which uses a spectral field solver and a low pass filter can eliminate the fastest growing modes of the NCI. Based on these studies a new spectral PIC code for studying laser wakefield acceleration (LWFA) in the Lorentz boosted frame was developed. However, we show that for parameters of relevance for LWFA simulations in the boosted frame, a relativistically drifting plasma is susceptible to a host of additional unstable modes with lower growth rates, and that these modes appear when the fastest growing unstable modes are filtered out. We show that these modes are most easily identified as the coupling between modes which are purely transverse (EM) and purely longitudinal (Langmuir) in the rest frame of the plasma for specific time and space aliases. We rewrite the dispersion relation of the drifting plasma for a general field solver and obtain analytic expressions for the location and growth rate for each unstable mode, i.e, for each time and space aliased resonances. We show for the spectral solver that when the fastest growing mode is eliminated a new mode at the fundamental resonance ($mu= u_1=0$) can be seen. (Please check the whole abstract in the paper).
