Hybrid Fourier–Vlasov simulation in non-inertial reference frames

We present some useful extensions of the spectral Fourier–Vlasov algorithm for simulations of interactions of collisionless plasmas with ion beams. For many practical applications the relative drifts of various particle populations require high resolution of particle distribution functions (PDFs) or the use of large phase space domain, which makes the simulations extremely memory- and time-consuming. We propose using non-inertial reference frames moving in the velocity dimensions for the beam particle distribution functions. As a result, it is possible to simulate plasma–beam interactions at a much lower resolution. This method is particularly suitable for simulations of fast particle beams and plasmas with heavy ion species or cold particle populations. In addition, for simulations of strongly nonlinear instabilities which cause strong plasma heating, the adaptive mesh refinement and phase space reduction are proposed. Contrary to the Vlasov simulation in the real velocity space, plasma heating in the Fourier-inverted space leads to the PDF profile shrinking. Thus, instead of having to extrapolate the PDF into the regions where it was previously undefined, in the Fourier-space, it is sufficient to interpolate the pre-existing solution. ► A new method for simulation of ion beams is proposed, which deals with fast drifts and strong heating. ► The use of a non-inertial reference frame simplifies the solutions and allows to use lower resolution. ► Adaptive mesh refinement in Fourier space helps avoid the extrapolation of the energetic tails.