Preserving high multibunch luminosity in linear colliders

An analytic theory of cumulative multibunch beam breakup in linear colliders is developed. Included is a linear variation of transverse focusing across the bunch train as might be applied, e.g., by chirping the radio frequency power sources or by using radio frequency quadrupole magnets. The focusing variation saturates the exponential growth of the beam breakup and establishes an algebraic decay of the transverse bunch displacement versus bunch number. A closed-form expression for the transverse bunch displacement is developed. It is used to quantify the total normalized emittance and thereby isolate the region of parameter space corresponding to high multibunch luminosity.