Propagation of numerical noise in particle-in-cell tracking

TL;DR

This paper models the numerical noise in particle-in-cell algorithms used for beam tracking, analyzing its impact on particle dynamics over long simulations and proposing mitigation strategies.

Contribution

It introduces a new model for PIC-induced numerical noise, deriving a scaling law for artificial emittance growth and discussing mitigation methods.

Findings

Derived a scaling law for emittance growth due to noise

Analyzed effects of correlated and decorrelated numerical noise

Proposed strategies to mitigate numerical noise impact

Abstract

Particle-in-cell (PIC) is the most used algorithm to perform self-consistent tracking of intense charged particle beams. It is based on depositing macro-particles on a grid, and subsequently solving on it the Poisson equation. It is well known that PIC algorithms occupy intrinsic limitations as they introduce numerical noise. Although not significant for short-term tracking, this becomes important in simulations for circular machines over millions of turns as it may induce artificial diffusion of the beam. In this work, we present a modeling of numerical noise induced by PIC algorithms, and discuss its influence on particle dynamics. The combined effect of particle tracking and noise created by PIC algorithms leads to correlated or decorrelated numerical noise. For decorrelated numerical noise we derive a scaling law for the simulation parameters, allowing an estimate of artificial emittance growth. Lastly, the effect of correlated numerical noise is discussed, and a mitigation strategy is proposed.