Instabilities driven by the fundamental crabbing mode

Abstract

The Electron Ion Collider (EIC) requires crab cavities to correct for crossing angle effects. These cavities produce a time varying horizontal kick that makes the collision head on in the center of mass frame of the bunches. This results in a luminosity that is very close to the the luminosity obtained without a crossing angle. Producing the kick requires a transverse RF field. This field requires a superconducting resonator and reasonable power levels require loaded quality factors of order a million. This results is a very large transverse impedance for the crabbing mode. The horizontal beta function is large and this, coupled with the large transverse impedance of the resonator can lead to strong instabilities. In the first section of the paper a simple model is used to describe the situation without feedback. There are large ranges of tune leading to strong instabilities in both the electron and hadron storage rings of the EIC. These estimates are confirmed with simulations. In the second section, RF feedback is used to reduce the apparent impedance of the crabbing mode. Simulating the actual feedback would require both a significant rewrite of the tracking code and a significant reduction in computational speed. Instead, the apparent impedance is fitted using one pole filters, which allows use of the existing simulation code. In the third section a transverse damping system is outlined.