Modeling of laser wakefield acceleration in Lorentz boosted frame using EM-PIC code with spectral solver

Abstract

Simulating laser wakefield acceleration (LWFA) in a Lorentz boosted frame in which the plasma drifts towards the laser with v b can speedup the simulation by factors of γ2 ) −1 . In these simulations the relativistic drifting plasma inevitably induces a high frequency numerical instability that contaminates the interested physics. Various approaches have been proposed to mitigate this instability. One approach is to solve Maxwell equations in Fourier space (a spectral solver) as this has been shown to suppress the fastest growing modes of this instability in simple test problems using a simple low pass or "ring" or "shell" like filters in Fourier space. We describe the development of a fully parallelized, multi-dimensional, particle-in-cell code that uses a spectral solver to solve Maxwell's equations and that includes the ability to launch a laser using a moving antenna. This new EM-PIC code is called UPIC-EMMA and it is based on the components of the UCLA PIC framework (UPIC). We show that by using UPIC-EMMA, LWFA simulations in the boosted frames with arbitrary γ b can be conducted without the presence of the numerical instability. We also compare the results of a few LWFA cases for several values of γ b , including lab frame simulations using OSIRIS, a EM-PIC code with a finite difference time domain (FDTD) Maxwell solver. These comparisons include cases in both linear and nonlinear regimes. We also investigate some issues associated with numerical dispersion in lab and boosted frame simulations and between FDTD and spectral solvers.

Summary report of working group 2: Computations for accelerator physics

“…It was shown that the instability associated with the (0,0) mode could be eliminated by filtering or could be mitigated by reducing the time step (see Fig. 1-right), in agreement with [4]. A systematic study of NCI modes was given and a localized patch scheme was proposed to reduce the instability by filtering out only a predetermined portion of the field in k-space.…”

“…Recognizing that the Particle-In-Cell (PIC) method has been established as a credible tool for the modeling of advanced accelerators, it is noted that the field of advanced accelerator concepts has been actively stimulating new research in PIC methodology. Thanks to recent work, the analysis of numerical stability of the PIC methods is now well in hand, has been thoroughly validated by PIC simulations and encompasses many algorithms: finite-difference time-domain (FDTD) [1,2], pseudo-spectral time-domain (PSTD) [3,4], pseudo-spectral analytic time-domain (PSATD) [3] (see Fig. 1-left), and pseudo-spectral arbitrary order time-domain (PSAOTD) [5], with sub-cycling [6].…”

“…Yu presented results of the analysis and mitigation of numerical Cherenkov instability with the PSTD algorithm [4]. The equations of the NCI were recast in a form that made the spurious coupling of the Langmuir and electromagnetic mode more apparent.…”

Enabling Lorentz boosted frame particle-in-cell simulations of laser wakefield acceleration in quasi-3D geometry

“…Within these schemes, Gauss' Law is satisfied by either directly solving it (as is the case in UPIC [24,25,26]), or by using a current that satisfies the continuity equation through a correction (compensation) to match the current deposition scheme with the Maxwell solver (as is the case in here and in [18]). In the approaches which aim to eliminate the NCI [18,19] (rather than reducing its growth rate for any time step size to that for an optimum time step [15]), the use of an FFT is inevitable (at least in one direction) since it is very challenging to design a current deposition scheme in real space to match the EM dispersion of a modified Maxwell solver for an arbitrary order finite difference scheme.…”

“…Currently, UPIC-EMMA boosted frame simulations in Cartesian 2D/3D geometry uses a stationary window [ Fig. 1 (d)] [19].…”