Circumference Correction Chicanes for Damping Rings

Abstract

Several low-emittance damping rings are presently being designed to meet the requirements of future linear colliders. These rings tend to have relatively large circumferences {approx}300 m so that they can damp many trains of bunches at the same time. With the large circumference, the ring path length may become quite sensitive to thermal and ground motion effects. In addition, most of the rings include damping wigglers whose path length varies with their strength. In e{sup -}/e{sup +} storage rings, the beam revolution time is determined by the rf frequency. Thus, to restore the proper revolution time, a change in the nominal path length will cause a change in both the beam energy and the closed orbit. The change in energy is given by: dE/E{sub 0} = - 1/{alpha}{sub p} {Delta}C/C{sub 0}, where {alpha}{sub p} is the momentum compaction and C{sub 0} is the nominal ring circumference. The change in the closed orbit is simply given by the energy change and the dispersion function. This change in orbit and energy can decrease the dynamic acceptance of the ring and make it difficult to preserve the ultra-small damped emittances. Because damping rings need strong focusing to attain the small beam emittances and thus tend to have very small values of momentum compaction, they can be very sensitive to changes in their circumference. For example, to limit the energy fluctuations in the NLC damping rings to 10% of the beam equilibrium energy spread, the path length must be controlled to about 20 {micro}m. Circumference variations have been seen at most storage rings including LEP, the APS at Argonne, the SLAC damping rings, and the ATF damping ring test facility [1] at KEK. At the APS, typical path length variations are {approx}0.2 mm [2] and are correlated with seasonal, tidal, and diurnal fluctuations. The SLAC damping rings change by millimeters during approach to thermal equilibrium when the rings are started, but little variation is seen after equilibrium is reached. At the ATF, variations of up to {+-}3 mm over months have been observed [3]. The precise mechanisms responsible for these changes are not, at present, well understood. Another path length variation arises when the strength of the damping wigglers is changed. Assuming a sinusoidal wiggler field, the circumference change is {Delta}C {approx} 1/4 L{sub w}/{rho}{sub w}{sup 2}{kappa}{sub w}{sup 2}, where L{sub w} is the wiggler length, {rho}{sub w} is the peak wiggler bend radius, and {kappa}{sub w} is its wavenumber ({triple_bond} 2{pi}/{lambda}). At the ATF (and similarly for the NLC ring), the wigglers increase the circumference by {approx}2 mm at full strength. Although some of the variation in path length can probably be reduced by design, the inclusion of a circumference correction method in the design of future damping rings seems prudent. There are a few possible approaches: (1) physical displacement of the arc magnetic elements; (2) control of the orbit using steering correctors or, equivalently, variation of the arc bending magnets and quadrupoles (the later is necessary to keep tunes constant); and (3) additional elements dedicated to path length control. In this note, we describe the correction available by adding a simple 4-dipole chicane to a straight-section in a damping ring. A chicane has the advantage of being varied without significantly affecting ring optics or trajectory outside of the chicane. Thus, the path length can be varied during operation and the chicane can be used in a feedback system to stabilize the circumference. In the following, we describe the effects of the chicane on critical ring parameters, including the equilibrium emittance and momentum compaction.