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.
Highlights
It is well known that in operational scenarios requiring long-term storage, sources of noise in the machine can lead to detrimental effects on the beam
A similar concern has been raised for numerical noise in self-consistent simulation of high intensity beams
We start with an analysis of the noise due to the PIC algorithm, and discuss how it propagates via the beam dynamics integration
Summary
It is well known that in operational scenarios requiring long-term storage, sources of noise in the machine can lead to detrimental effects on the beam. The study of space charge effects via self-consistent simulations has become important with the advent of new projects, like the future SIS100 synchrotron of the FAIR project [7], and the LIU project [8] for the CERN accelerator complex In these projects some scenarios require the storage of a high intensity bunched beam for seconds. There, the space charge is computed assuming the beam remains frozen, allowing an analytic description of the space charge force We start with an analysis of the noise due to the PIC algorithm, and discuss how it propagates via the beam dynamics integration Following this approach, the dependence of rms-emittance growth on simulation parameters is derived. In Appendix C, we discuss the impact of the strength of space charge forces on the excitation of stochastic resonances
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