Emittance growth, tune shift, and the bunched-beam, bunched-beam interaction

While it is understood that the main limitation of beam lifetime in the Relativistic Heavy Ion Collider (RHIC) at Brookhaven is the emittance growth due to intra-beam scattering, it is important to evaluate and understand both the emittance growth and nature of the tune shift due to multiple beam-beam crossings of the bunched-beams of heavy ions. We note within RHIC, fully stripped 197Au ions (charge 79e+) will survive up to ten hours in the collider, with six beam crossings per revolution. With this motivation, we have developed a fully relativistic theory of both the averaged emittance growth and the averaged tune shift for the bunched-beam, bunched-beam interaction that is based on a convolution integral over the densities of the two interpenetrating bunches. In order to calculate this integral, we choose to work in a frame where one bunch of the collider is stationary, and the other is highly relativistic. This frame has the additional advantage that the microscopic heavy ion interaction becomes perpendicular in nature. In this frame the convolution integral acquires many simplifying and physically interesting features. 8 refs