THEORY OF CUMULATIVE BEAM-BREAKUPWITH BNS DAMPING

Analytic tools for the study ofmultibunch cumulative beam breakup (MBBU) in linear colliders (LCs) including BNS damping are developed. One approach is to consider cases for which exponential growth of MBBU is noticeable, al-though one generally wishes to avoid this regime in LCs to make operations easier. By developing scaling relations, one is able to see at once how to suppress it effectively. The formalism to studyMBBU including some interesting sub-tleties, such as BNS damping and misaligned accelerator components, is applied to both normal-conducting and su-perconducting linacs comprising LCs. 1 BEAM-BREAKUP EQUATION One of the limitations of future LCs is the MBBU of a long bunch train driven by the transverse wake potential in the cavities of the linacs, especially when the size of the cav-ities is small. Other factors, such as cavity misalignments and focusing quadrupole offsets, will also contribute to the emittance increase of the beam and can result in beam loss as well as reduction in collision luminosity. A spread in the focusing strength of the quadrupoles, or equivalently a spread in energy, along the bunch train can provide BNS damping [1] thatmay keep emittance growth under control. Consider a relativistic particle beam injected into a linac of length . At a distance s = σ into the linac, the trans-verse displacementx(σ, ζ) given beam energy γ(σ)E0 with E0 the rest energy satisfies the differential equation 1 γ(σ