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.
Highlights
Improving proton beam power is a research priority at Fermilab and slip stacking will be a critical part of high-intensity operation at Fermilab for the foreseeable future [1,2,3]
Instead we propose to keep the main rf voltage constrained to 100 kV and only install a 20 kV harmonic rf cavity
After slip stacking in the Recycler, the two beams are transferred to the Main Injector where they are captured by a rf system operating at a single frequency
Summary
Improving proton beam power is a research priority at Fermilab and slip stacking will be a critical part of high-intensity operation at Fermilab for the foreseeable future [1,2,3]. 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]. Because it does not operate at precise multiple of any one rf cavity, but rather it operates at twice the average of the upper and lower frequency main rf cavities We refer to this modification of slip stacking as “harmonic slip stacking”. A simulation based on a realistic model of the beam finds a reduction in losses by a factor of 20 and a reduction in the final longitudinal emittance by 5% These results indicate a performance that would far exceed the slip stacking loss requirements of the Fermilab PIP-II upgrade. There is currently no 400 MHz rf cavity in the SPS [17,18], the results of this paper imply that such a cavity would improve the efficiency of slip stacking in the SPS and lower the final longitudinal emittance after slip stacking
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