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

• Published in: Journal of computational physics Vol. 230; no. 15; pp. 5908 - 5929
• Main Authors: Vay, J.-L., Geddes, C.G.R., Cormier-Michel, E., Grote, D.P.
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Inc 01.07.2011; Elsevier
• Subjects: 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; ACCELERATION; ACCELERATORS; ALGORITHMS; Boosted frame; Computational techniques; Computer simulation; Damping; DIGITAL FILTERS; ENERGY RANGE; Exact sciences and technology; Filtering; Frames; GEV RANGE; GEV RANGE 01-10; INSTABILITY; Laser wakefield acceleration; LASERS; LINEAR ACCELERATORS; MATHEMATICAL LOGIC; MATHEMATICAL METHODS AND COMPUTING; Mathematical methods in physics; Mathematical models; Numerical instability; Particle-in-cell; Physics; PLASMA; PLASMA GUNS; PLASMA SIMULATION; RELATIVITY THEORY; SIMULATION; Special relativity; Stability; WAKEFIELD ACCELERATORS; Plasma simulation; Numerical instability; Boosted frame; Laser wakefield acceleration; Special relativity; Particle-in-cell; Damping; Plasma; Numerical method; Calculation methods; Algorithms; Referential; Particle code; Instability; Modelling; Calculation
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1016/j.jcp.2011.04.003

Modeling of laser-plasma wakefield accelerators in an optimal frame of reference [1] has been shown to produce orders of magnitude speed-up of calculations from first principles. Obtaining these speedups required mitigation of a high-frequency instability that otherwise limits effectiveness. In this paper, methods are presented which mitigated the observed instability, including an electromagnetic solver with tunable coefficients, its extension to accommodate Perfectly Matched Layers and Friedman’s damping algorithms, as well as an efficient large bandwidth digital filter. It is observed that choosing the frame of the wake as the frame of reference allows for higher levels of filtering or damping than is possible in other frames for the same accuracy. Detailed testing also revealed the existence of a singular time step at which the instability level is minimized, independently of numerical dispersion. A combination of the techniques presented in this paper prove to be very efficient at controlling the instability, allowing for efficient direct modeling of 10 GeV class laser plasma accelerator stages. The methods developed in this paper may have broader application, to other Lorentz-boosted simulations and Particle-In-Cell simulations in general.