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.