KEK-Report-2004-7

Abstract

An advanced analytic approach has been developed in order to estimate the beam-beam tune shift with an amplitude, even if particles have an unbalanced emittance, which means zero emittance in the horizontal direction and an extremely large emittance in the vertical, or its inverse. The developed approach has been qualitatively and quantitatively proved to be a useful tool to estimate the beam-beam tune shift. As an example, the relation between the beam-beam tune shift with the amplitude and the crossing geometry in a super-bunch hadron collider has been examined. The depressed tune shift and the pushed-up tune shift induced by the long-range interaction strongly depend on the emittance of particles, so that particles with zero emittance or unbalanced emittance illustrate the characteristic beam-beam tune shift on the tune diagram by combinating the crossing geometry.