Elimination of the numerical Cerenkov instability for spectral EM-PIC codes

Understand

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 electromagnetic waves on a grid to wave-particle resonances, including aliased resonances, i.e., $\omega + 2\pi\mu/\Delta t=(k_1+ 2\pi\nu_1/\Delta x_1)v_0$, where $\mu$ and $\nu_1$ 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.