6-D ELEMENT-BY-ELEMENT PARTICLE TRACKING WITH CRAB CAVITY PHASE NOISE AND WEAK-STRONG BEAM-BEAM INTERACTION FOR THE HADRON STORAGE RING OF THE ELECTRON-ION COLLIDER
The Electron Ion Collider (EIC) presently under construction at Brookhaven National Laboratory will collide polarized high energy electron beams with hadron beams with luminosities up to 10^34 cm?^2 s^?1 in center mass energy range of 20-140 GeV. Crab cavities are used to compensate the geometric luminosity due to a large crossing angle 25 mrad in the EIC. It was found that the phase noise in crab cavities will generate a significant emittance growth for the hadron beams. The phase noise tolerance from the analytical calculation is very small for the Hadron Storage Ring (HSR) of the EIC. In this article, we present our preliminary numerical simulation results with a 6-d symplectic particle tracking to determine the proton emittance growth rate with crab cavity phase noise and beam-beam interaction for the HSR.