Dynamical Stability of Slip-stacking Particles

TL;DR

This paper analyzes the stability of particles in slip-stacking at Fermilab, introducing universal phase space calculations and establishing beam quality requirements to optimize efficiency.

Contribution

It presents a universal method to calculate phase space for slip-stacking, perturbative solutions for stable trajectories, and links slip-stacking dynamics to classical systems.

Findings

Universal phase space area factors for beam parameters

Perturbative solutions for particle stability

Booster beam quality requirements for 97% efficiency

Abstract

We study the stability of particles in slip-stacking configuration, used to nearly double proton beam intensity at Fermilab. We introduce universal area factors to calculate the available phase space area for any set of beam parameters without individual simulation. We find perturbative solutions for stable particle trajectories. We establish Booster beam quality requirements to achieve 97\% slip-stacking efficiency. We show that slip-stacking dynamics directly correspond to the driven pendulum and to the system of two standing-wave traps moving with respect to each other.