LAUSR

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.