Dynamical stability of slip-stacking particles

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.

Enhanced dynamical stability with harmonic slip stacking

“…At more moderate values of ω φ relative to ω s , the perturbation effect complicates the motion and reduces the stable phase-space area. This effect is quantified by the slip-stacking parameter α s [9,10,19,21,22] defined:…”

“…A perturbation analysis of the trajectory of slipstacking particles [10] shows that the influence of the second cavity creates a series of parametric resonances. The synchrotron tune-shift σ depends both on the synchrotron amplitude ρ and the slip-stacking parameter perturbation α −2 s .…”

“…Equation 1 is equivalent to the simple pendulum and Eq. 3 is equivalent to the driven pendulum [10], but there is no clear pendulum analogue for harmonic slip-stacking.…”

“…Loss studies indicate that single-particle dynamics associated with slip-stacking are a dominant source of particle loss [9]. Recent work in the single-particle longitudinal dynamics of slip-stacking [10] demonstrated that the slip-stacking loss rate could be significantly reduced by upgrading the Fermilab Booster cycle-rate from 15 Hz to 20 Hz. The 20 Hz Booster cycle-rate has subsequently been incorporated into the PIP-II proposal [11].…”

“…In this paper, we adopt and extend the tools for analyzing the dynamical stability of slip-stacking that were introduced in [10]. Our analysis finds that harmonic slipstacking can increase the stable phase-space area by 50% relative to conventional slip-stacking.…”