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TY - UNPB AU - Williams, P.H. AU - Bailey, I.R. AU - Charles, T.K. AU - Perez-Segurana, G. ED - Meseck, Atoosa ED - McAteer, Meghan ED - Schaa, Volker R.W. ED - V\xF6lker, Jens TI - Analytic Longitudinal Phase Space Solutions for Multipass Energy Recovery Linacs J2 - Proc. of ERL2019, Berlin, Germany, 15-20 September 2019 CY - Berlin, Germany T2 - ICFA Advanced Beam Dynamics Workshop on Energy Recovery Linacs T3 - 63 LA - english AB - The longitudinal solution space of an energy recovery linac is an under-constrained system. For applications where we wish to compress the bunches for delivery to, for example, a free-electron laser or an interaction point, and simultaneously ensure full recovery it is useful to be able to rapidly ascertain and assess the possible solutions. Moreover, when we consider multi-pass ERLS, we quickly conclude that a trial-and-error approach to deriving such solutions (through for example one-dimensional particle tracking) is impractical. Here we extend an analytic recurrence method of deriving phase space solutions in multistage compression schemes, due to Zagorodnov & Dohlus, to multi-pass energy recovery linac systems. We use this method to categorise classes of solutions, and explore the implications of the energy recovery condition. PB - JACoW Publishing CP - Geneva, Switzerland ER -