The role of noise in PIC and Vlasov simulations of the Buneman instability

Abstract

The effects of noise in particle-in-cell (PIC) and Vlasov simulations of the Buneman instability in unmagnetized plasmas are studied. It is found that, in the regime of low drift velocity, the linear stage of the instability in PIC simulations differs significantly from the theoretical predictions, whereas in the Vlasov simulations it does not. A series of highly resolved PIC simulations with increasingly large numbers of macroparticles per cell is performed using a number of different PIC codes. All the simulations predict highly similar growth rates that are several times larger than those calculated from the linear theory. As a result, we find that the true convergence of the PIC simulations in the linear regime is elusive to achieve in practice and can easily be misidentified. The discrepancy between the theoretical and the observed growth rates is attributed to the initial noise inherently present in PIC simulations, but not in Vlasov simulations, that causes particle trapping even though the fraction of trapped particles is low. We show analytically that even weak distortions of the electron velocity distribution function (such as flattening due to particle trapping) result in significant modifications of the growth rates. It is also found that the common quiet-start method for PIC simulations leads to more accurate growth rates but only if the maximum growth rate mode is perturbed initially. We demonstrate that the quiet-start method does not completely remedy the noise problem because the simulations generally exhibit inconsistencies with the linear theory.

Effects of multi-dimensionality and energy exchange on electrostatic current-driven plasma instabilities and turbulence

“…We leverage this superiority of the DK method to gain more precise insights into instability development and transition to turbulence. The DK method has been shown to yield more accurate linear instability growth rates than the particle-in-cell method due to the statistical noise inherent in the latter, which is seen to vary with the number of particles per cell and the wavenumber of interest (Dieckmann et al 2004b;Tavassoli et al 2021). We verify these growth rates in § 3.1 and also demonstrate the utility of the large dynamic range of direct kinetic solvers in resolving turbulence structures in § 3.2.…”

“…2004 b ; Tavassoli et al. 2021). We verify these growth rates in § 3.1 and also demonstrate the utility of the large dynamic range of direct kinetic solvers in resolving turbulence structures in § 3.2.…”

A two-dimensional numerical study of ion-acoustic turbulence

“…Indeed, even with today's computational resources, simulating resonant kinetic instabilities with the PIC method can be challenging (see, e.g., Tavassoli et al. (2021) for an example concerning the Buneman instability).…”