Emittance-Imposed Alignment and Frequency Tolerances for the TESLA Collider

One option in building a future 500 GeV c.m. linear collider is to use superconducting 1.3 GHz 9-cell cavities. However, wakefields excited by the bunch train in the TESLA (TeV-Energy Super Conducting Linear Accelerator) collider can resonantly drive the beam into unstable operation such that a BBU (Beam Break Up) mode results or at the very least significant emittance dilution occurs. The largest kick factors (proportional to the transverse fields which kick the beam off axis) are found in the first three dipole bands and hence multi-bunch emittance growth is mainly determined from these bands. These higher order dipole modes are damped by carefully orientating special couplers placed at both ends of the cavities. We investigate the dilution in the emittance of a beam with a random misalignment of cavities down the complete main linac. The beneficial effects of frequency errors on ameliorating the beam dilution are discussed