Crab Cavity Low-Level RF Design Simulation Tools for the Electron-Ion Collider

The Electron-Ion Collider (EIC) requires crab cavities to compensate for a 25 mrad crossing angle and achieve maximum luminosity. The crab cavity Low-Level Radio Frequency (LLRF) system will need to regulate the crabbing/uncrabbing voltages and reduce the transverse impedance presented to the beam, while maintaining low levels of injecting noise to avoid transverse emittance growth and luminosity reduction. In this work, we present simulation tools and analytical formalisms that estimate the beam performance (transverse position offset, jitter, emittance growth, and stability) and transmitter power, as a function of LLRF architectures and parameters. These results will be used to determine the EIC crab cavity LLRF design.