Applications of Caustic Methods to Longitudinal Phase Space Manipulation

Longitudinal phase space management is a key feature of recirculating machines. Careful consideration of the longitudinal matching is required not only in order to ensure a high peak current, low energy spread bunch is delivered to the FEL but also to support the deceleration and energy recovery of the spent beam. In a similar manner, longitudinal phase space manipulation can be utilised for pulse shaping in bunch compression, to minimise the influence of CSR-induced emittance growth. In this paper, we present a method for longitudinal phase space matching based upon the avoidance of electron trajectory caustics. Through considering the conditions under which caustics will form, we generate exclusion plots identifying the viable parameter space at numerous positions through beam acceleration and energy recovery. The result is a method for selecting the linear momentum compaction and the higher-order momentum compaction to satisfy the non-caustic condition whilst achieving the bunch compression or lengthening as required.