Dispersion in the Presence of Strong Transverse Wakefields

To minimize emittance growth in a long linac, it is necessary to control the wakefields by correcting the beam orbit excursions. In addition, the particle energy is made to vary along the length of the bunch to introduce a damping, known as the BNS damping, to the beam break-up effect. In this paper, we use a two-particle model to examine the relative magnitudes of the various orbit and dispersion functions involved. The results are applied to calculate the effect of a closed orbit bump and a misaligned structure. It is shown that wake-induced dispersion is an important contribution to the beam dynamics in long linacs with strong wakefields like SLC. 1 WAKE INDUCED DISPERSION (TWO-PARTICLE MODEL) Consider a linac with uniform betatron focusing and no acceleration. Introduce an orbit kick at s = 0. The betatron equation of motion for a particle with relative energy error is x(s) + k 1 + x(s) = 1 + (s); (1)