Bunching for shorter damping rings for the ILC

A variant rearrangement of the bunch trains for the ILC that enables much shorter damping rings is presented. In a particular example the {approx}2280 bunches are regrouped into {approx}450 subtrains of five adjacent bunches. These subtrains are extracted from the damping rings at {approx}2.2 {micro}s intervals, obtaining the 1ms macrobunch length of the baseline TESLA collider scenario. If the baseline damping rf frequency is 325 MHz and the kicker rise and fall times are {approx}20 ns, a ring circumference of {approx}4.5km is required. Variations of the scheme could easily reduce the circumference to {approx}3km, and faster kickers could reduce it even further.