RF focusing effects and multi-bunch beam breakup in superconducting linear colliders

A high gradient standing wave linear accelerator provides axisymmetric transverse focusing due to the presence of strong alternating gradient transverse electromagnetic fields arising from the backward RF wave. This effect is second order in both the field amplitude and in γ^-1, so it is of importance only for high gradient, relatively low energy beams, The purpose of the present analysis is to examine the effect of this focusing on multi-bunch beam breakup in a superconducting linear collider, which has both a high accelerating gradient and long bunch train. As an interesting test case, we discuss the beam-breakup problem in the TESLA test bed at DESY