Collisional effects on the numerical recurrence in Vlasov-Poisson simulations

TL;DR

This paper investigates how artificial collisions affect the recurrence phenomenon in Vlasov-Poisson simulations, revealing that such collisionality does not effectively prevent recurrence and can alter physical system evolution.

Contribution

It provides a detailed analysis of collisional effects on recurrence in Vlasov-Poisson systems using Fourier-Hermite decomposition and nonlinear simulations, highlighting limitations of artificial collisionality.

Findings

Artificial collisions do not prevent recurrence effectively.

Numerical effects can modify physical features even in nonlinear regimes.

Filamentation phenomena influence system evolution beyond low amplitude contexts.

Abstract

The initial state recurrence in numerical simulations of the Vlasov-Poisson system is a well-known phenomenon. Here we study the effect on recurrence of artificial collisions modeled through the Lenard-Bernstein operator [A. Lenard and I. B. Bernstein, Phys. Rev. 112, 1456-1459 (1958)]. By decomposing the linear Vlasov-Poisson system in the Fourier-Hermite space, the recurrence problem is investigated in the linear regime of the damping of a Langmuir wave and of the onset of the bump-on-tail instability. The analysis is then confirmed and extended to the nonlinear regime through a Eulerian collisional Vlasov-Poisson code. It is found that, despite being routinely used, an artificial collisionality is not a viable way of preventing recurrence in numerical simulations without compromising the kinetic nature of the solution. Moreover, it is shown how numerical effects associated to the generation of fine velocity scales, can modify the physical features of the system evolution even in nonlinear regime. This means that filamentation-like phenomena, usually associated with low amplitude fluctuations contexts, can play a role even in nonlinear regime.