Enhanced Dynamical Stability with Harmonic Slip-stacking

TL;DR

This paper introduces a harmonic RF cavity configuration that enhances slip-stacking stability and efficiency at Fermilab, reducing particle loss and longitudinal emittance in proton beam accumulation.

Contribution

It proposes a novel harmonic RF cavity setup that cancels resonances between main RF cavities, improving slip-stacking performance and providing a method to calculate phase space area without simulations.

Findings

Harmonic RF cavity cancels resonance effects between main RFs.

The setup reduces particle loss during slip-stacking.

It decreases the final longitudinal emittance.

Abstract

We develop a configuration of radio-frequency (rf) cavities to dramatically improve the performance of slip-stacking. Slip-stacking is an accumulation technique used at Fermilab to nearly double proton intensity by maintaining two beams of different momenta in the same storage ring. The two particle beams are longitudinally focused in the Recycler by two 53 MHz 100 kV rf cavities with a small frequency difference between them. We propose an additional 106 MHz 20 kV rf cavity with a frequency at the double the average of the upper and lower main rf frequencies. We show the harmonic rf cavity cancels out the resonances generated between the two main rf cavities and we derive the relationship between the harmonic rf voltage and the main rf voltage. We find the area factors that can be used to calculate the available phase space area for any set of beam parameters without individual simulation. We establish Booster beam quality requirements to achieve 99\% slip-stacking efficiency. We measure the longitudinal distribution of the Booster beam and use it to generate a realistic beam model for slip-stacking simulation. We demonstrate that the harmonic rf cavity can not only reduce particle loss during slip-stacking, but also reduce the final longitudinal emittance.