Scaling for faster macroparticle simulation in longitudinal multiparticle dynamics

J Maclachlan ,Zaira Nazario

doi:10.1103/physrevstab.3.114401

Abstract

Macroparticle tracking is a direct and attractive approach to following the evolution of a longitudinal phase space distribution. When the particles interact through short-range wake fields or when the interparticle force is included, calculations of this kind require a large number of macroparticles. However, it is possible to reduce both the number of macroparticles required and the number of tracking steps per unit simulated time by employing a simple scaling. It is demonstrated that the Vlasov equation is unchanged by introduction of the scaled quantities. It is further shown that under rather general conditions the speed of calculation improves with the fourth power of the scaling constant. Two examples comparing scaled and original cases illustrate the effectiveness of the approach. Limitations to the amount of rescaling are discussed.

Highlights

Multiparticle tracking programs have a long history and established utility for modeling the evolution of the longitudinal phase space distributions for particles in accelerators as the particles respond to the rf in acceleration or bunch manipulation
The macroparticle distribution can be used to approximate the evolution of the beam current distribution or Fourier spectrum throughout the process being modeled
Passing from single particle dynamics to multiparticle dynamics by calculating the beam current every time step and including the contribution of the fields induced by it to the single particle motion is a direct extension of the technique which makes a wide range of interesting problems accessible

Summary

INTRODUCTION

Multiparticle tracking programs have a long history and established utility for modeling the evolution of the longitudinal phase space distributions for particles in accelerators as the particles respond to the rf in acceleration or bunch manipulation. The question of the number of macroparticles needed or the relevant bandwidth for quantities calculated in frequency domain requires careful attention, and it is very easy to generate spectacular spurious instabilities by excessive time steps or an insufficient number of macroparticles. This issue is the source and focus of what follows; recent studies of high brightness injectors and the so-called factory accelerators have given it currency. It will be shown that modeling which might appear to require order 106 macroparticles and days of time on a fast computer can be scaled to the desktop and normal patience

SCALING CONCEPT

FORMAL ANALYSIS

COMPARISON OF SCALED AND UNSCALED TRACKING

UTILITY