Modeling Laser Wakefield Accelerators in a Lorentz Boosted Frame

Abstract

Modeling of laser-plasma wakefield accelerators in an optimal frame of reference [1] is shown to produce orders of magnitude speed-up of calculations from first principles. Obtaining these speedups requires mitigation of a highfrequency instability that otherwise limits effectiveness in addition to solutions for handling data input and output in a relativistically boosted frame of reference. The observed high-frequency instability is mitigated using methods including an electromagnetic solver with tunable coefficients, its extension to accomodate Perfectly Matched Layers and Friedman's damping algorithms, as well as an efficient large bandwidth digital filter. It is shown that choosing the frame of the wake as the frame of reference allows for higher levels of filtering and damping than is possible in other frames for the same accuracy. Detailed testing also revealed serendipitously the existence of a singular time step at which the instability level is minimized, independently of numerical dispersion, thus indicating that the observed instability may not be due primarily to Numerical Cerenkov as has been conjectured. The techniques developed for Cerenkov mitigation prove nonetheless to be very efficient at controlling the instability. Using these techniques, agreement at the percentage level is demonstrated between simulations using different frames of reference, with speedups reaching two orders of magnitude for a 0.1 GeV class stages. The method then allows direct and efficient full-scale modeling of deeply depleted laser-plasma stages of 10 GeV-1 TeV for the first time, verifying the scaling of plasma accelerators to very high energies. Over 4, 5 and 6 orders of magnitude speedup is achieved for the modeling of 10 GeV, 100 GeV and 1 TeV class stages, respectively.

Numerical methods for instability mitigation in the modeling of laser wakefield accelerators in a Lorentz-boosted frame

“…Extensive testing confirmed, as was discussed elsewhere [25,34], that choosing the frame of the wake as the frame of reference allows for higher levels of filtering and damping than is possible in other frames with the same accuracy. It also revealed that there exists a singular time step for which the level of instability is minimal, independently of other numerical parameters, especially the numerical dispersion of the solver.…”

“…Comparing the timings with those of Fig. 13 (middle-left) from [25] shows that the smoothing and the damping added less than a factor of two of total runtime to the simulations. These results lead to several observations:…”

“…First, simulations with a boost c % c w require fewer time steps than simulations using a lower value of c. Thus, for a given value of the damping coefficient h, the integrated amount of damping will be lower for the simulations with c % c w . Second, as explained in [25,34], a large fraction of the short wavelength content that is present in the simulations in the laboratory frame is transformed into time oscillations in simulations in the wake frame. Hence, filtering short wavelengths has less effect on the physics when calculating in the wake frame than when calculating in the laboratory frame, 3. the computational cost of using even the most aggressive damping or smoothing is low, especially considering that the simulations presented here were using only two plasma macro-particles per cell.…”

“…In this paper, the effect of the instability, filtering or damping on the physical quantities of interest (laser, wake and accelerated beam evolutions), are captured by examination of the beam energy history, which was chosen since it integrates the other effects, as the beam energy is affected by the wake evolution which is itself affected by the laser evolution. Details of the convergence of the laser and wake evolutions, as well as of the beam transverse and longitudinal properties, are analyzed in [25] and in a paper to be published elsewhere.…”

“…Results are contrasted to a run at c ¼ 13 with little filtering and no damping (crosses in Figs. 9 and 10) that was in turn benchmarked against a run in the laboratory frame [25], and serves as the reference. None of these simulations were disrupted by short wavelength instability.…”