Preserving high multibunch luminosity in linear colliders

An analytic theory of cumulative multibunch beam breakup in linear collider s is developed. Included is a linear variation of transverse focusing acros s the bunch train as might br applied, e.g., by chirping the radio frequenc y power sources or by using radio frequency quadrupole magnets. The focusin g variation saturates the exponential growth sf the beam breakup and establ ishes an algebraic decay of the transverse bunch displacement versus bunch number. A closed-form expression for the transverse bunch displacement is d eveloped. It is used to quantify the total normalized emittance and thereby isolate the region of parameter space corresponding to high multibunch lum inosity.