Transverse Periodic Beam Loading Effects in a Storage Ring

Uneven beam fill patterns in storage rings, such as gaps in the fill patterns, leads to periodic, or transient loading of the modes of the RF cavities. We show that an analogous effect can occur in the loading of a dipole cavity mode when the beam passes off the electrical center of the cavity mode. Although this effect is small, it results in a variation of the transverse offset of the beam along the bunch train. For ultralow emittance beams, such as optimized third generation light sources and damping rings, this effect results in a larger projected emittance of the beam compared with the single bunch emittance. The effect is particularly strong for the case when a strong dipole mode has been purposely added to the ring, such as a deflecting, or 'crab' cavity. We derive an approximate analytic solution for the variation of the beam-induced deflecting voltage along the bunch train.