Quasi-isochronous buckets in storage rings

In order to maintain a reasonable r.f. system, it may be necessary for a collider with ultra-short bunches to operate with a small slippage factor, for example, η < 1 × 10−6 for all the particles in the bunches. The buckets dominated by the zeroth order, first order, or second order of η are examined, and the required r.f. voltages are computed. The problem of microwave instability is addressed. The reliability of computing higher-order momentum-compaction factor using lattice codes is examined.