Damping of coupled bunch instabilities by rf frequency modulation

Abstract

In many high-energy synchrotrons and storage rings operating with bunched beams, instabilities occur due to coupling from bunch to bunch by wake fields in the surrounding vacuum chamber structures. The most direct cure is to reduce the strength of the wake fields by changing the structures which cause the strongest wakes, e.g. damping of higher modes (HOMs) in rf and/or incidental cavities, such as kicker tanks, or sleeving (shielding) of unavoidable cross section variations such as bellows or pumping T’s. A time honored method is to simply change the temperature of the cooling water which may change the frequency of the resonant modes in a cavity sufficiently to avoid coupling to an unstable beam mode of oscillation. However, in many instances these methods are insufficient and other measures have to be used, such as feedback systems. However, for machines with a large number of bunches such systems usually need to have a rather broad bandwidth and also require costly space around the machine circumference. It is often simpler to rely on reducing the coupling between bunches by other means. One method is to vary the distance between bunches e.g. introducing gaps of different lengths by leaving out a certain number of bunches from the regularly spaced “buckets” formed by the rf voltage. However, uneven spacing may have disadvantages in particular for colliders where the bunches should meet the opposing beam at the fixed locations of detectors. Therefore it is often preferable to reduce coupling by varying the natural oscillation frequencies of the bunches.