Abstract
The U.S. electron ion collider will utilize high current electron and ion storage rings with many bunches and large rf systems. Because of the dissimilarity of the two rings, the rf transients created by gaps or variations in the current distributions will be very different in the two rings. These transients cause a shift in the synchronous phase of the beams as a function of rf bucket position, can impact the luminosity through shifts in longitudinal position of the IP, will affect the performance of the rf and LLRF control loops, and may require significant rf power overhead to control. A machine design that uses superconducting crab cavities will also have sensitivity to gap transients and synchronous phase variations along the bunch train with variations in crab cavity voltage seen by each bunch, since the high $Q$ of the crab cavities precludes modulating them to compensate for the time of arrival shifts caused by the gap transients in the main rf systems. All these effects make the problem of managing gap transients crucial to the operation of the EIC. This work presents methods to study the dynamics of the rf and LLRF systems for these heavily beam loaded facilities. An illustrative machine design example is presented and used to investigate the expected magnitudes of the rf gap transients, and exploration of various possible remedies to match the gap transients in the two dissimilar EIC rings. In addition to the study of the power required and gap transients, this work also estimates longitudinal coupled-bunch instabilities due to the baseline cavity fundamental impedance. The work is motivated to emphasize the importance of tools and methods to estimate these effects as part of the early design phase of the Electron-Ion Collider or any high current storage ring design.
Highlights
The U.S electron ion collider will utilize high current electron and ion storage rings with many bunches and large rf systems
A machine design that uses superconducting crab cavities will have sensitivity to gap transients and synchronous phase variations along the bunch train with variations in crab cavity voltage seen by each bunch, since the high Q of the crab cavities precludes modulating them to compensate for the time of arrival shifts caused by the gap transients in the main rf systems
This loop is a periodic structure that implements gain at multiples of the revolution frequency, acting to reduce the impedance seen by the beam near the revolution frequency sidebands around the rf fundamental
Summary
The design and operation of heavily beam loaded circular accelerators requires care in the design and set up of the rf accelerating systems, and often requires complex LLRF systems to manage the stability of the beam as well of the rf system itself [1,2,3]. To evaluate possible gap transient effects, and the impact of LLRF and rf system design choices and technical characteristics, we use a time-domain simulation that has block models representing the rf cavities, rf power stages, the essential LLRF system loops, and a dynamic description of the bunches (determined by the ring lattice momentum compaction, the effective rf cavity voltage as sampled by the bunch and the equations of synchrotron motion). As this is a time domain simulation, it is possible to include nonlinear behavior of a power stage, to include harmonic cavities, to implement limiters or saturating elements in the LLRF systems, or to include other system elements that might be in a practical system.
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