Suppressing numerical cherenkov stabilities in FDTD PIC codes

Abstract

Typically, the most serious numerical instability in PIC simulations of relativistic particle beams is the numerical Cherenkov instability, arising from coupling between electromagnetic and nonphysical beam modes. <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> In recent papers we derived and solved electromagnetic dispersion relations for this instability in both finite difference time-domain (FDTD) and pseudo-spectral time-domain (PSTD) algorithms and successfully compared results with those of the Warp simulation code. <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2,3,4</sup> Our PSTD analysis, focused on Haber's Pseudo-Spectral Analytical Time-Domain algorithm, provided several methods for suppressing the numerical Cherenkov instability. This was done by a combination of digital filtering at large wave-numbers and improved numerical balancing of transverse fields at smaller wave-numbers. Doing so is mechanically straightforward for PSTD algorithms, because currents and fields are known in Fourier space and readily can be rescaled by the desired k-dependent factors. In this talk we carry over such methods to FDTD algorithms without resorting to Fourier transforms. Digital filtering is achieved with the usual bilinear smoothing, and improved numerical balancing of transverse fields is accomplished using a similar process but with coefficients based on rational interpolation functions approximating the desired k-dependent factors. Results are very encouraging.