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The CBETA energy recovery linac uses a single fixed field alternating gradient (FFAG) beam line to return the beam for electron beams with four energies, ranging from 42 MeV to 150 MeV. To keep the beam line compact, the ends of the return line have a small radius of curvature, but the central part of the return line is straight. These are connected by transition lines that adiabatically change from one to the other. We first describe the design or the arc cell. We then describe how a straight cell is created to be a good match to this arc cell. We then describe the design of the transition line between them. The design process makes use of field maps for the desired magnets. Because we switch magnet types as we move from the arc, through the transition, and into the straight, there are discrete jumps in the fields that degrade the adiabaticity of the transition, and we describe corrections to manage that. 1. The Basic Parameters CBETA is an energy recovery linac that will make 4 accelerating passes through the linac, and return the beam to the linac using a single fixed field alternating gradient (FFAG) return line. At the ends of the linac are 4 spreader/combiner lines, each of which transports a single energy from the linac to the FFAG line or from the FFAG line back to the linac. The FFAG return line has arcs at it ends with a relatively small bending radius to keep the machine compact. Completing the return to the linac requires a section that is straight or with larger radius of curvature to connect the two arcs. We use an adiabatic transition section connecting each arc to a straight between them. Table 1 describes the basic requirements for the FFAG line design. The energies correspond to a four-pass energy recovery linac with a 6 MeV injection energy. The minimum drift lenghts result from allowing space for various devices (the short drift allows for a button beam position monitor (BPM), the long drift will allow for a wide variety of devices) and any overhang of magnet hardware. The radius of curvature is a result of a space limitation. The magnet lengths and maximum energy are parameters related to an earlier design using an iron-dominated magnet design, but are reasonable choices that were kept for efficiency in the design process. Each arc has 16 cells, giving 80 degrees of bend. The transition will be designed with a symmetry such that the Email address: jsberg@bnl.gov (J. Scott Berg) 1This manuscript has been authored by employees of Brookhaven Science Associates, LLC under Contract No. DE-SC0012704 with the U.S. Department of Energy. The United States Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes. Table 1: Basic parameters for the FFAG return line. Total energy, pass 1 (MeV) 42 Total energy, pass 2 (MeV) 78 Total energy, pass 3 (MeV) 114 Total energy, pass 4 (MeV) 150 Focusing quadrupole length (mm) 133 Defocusing magnet length (mm) 122 Minimum short drift length (mm) 66 Minimum long drift length (mm) 123 Arc radius of curvature, approximate (m) 5.1 Arc cell bend angle (deg.) 5 Cells per arc 16 Cells per transition section 24 average bend per cell is half the arc cell bend angle. Thus each transition section supplies 60 degrees of bend. Thus each spreader/combiner supplies the remaining 40 degrees of bend for half the machine. Every focusing quadrupole will have a horizontal corrector (vertical dipole field), while every defocusing magnet will have a vertical corrector.

The FFAG return loop for the CBETA Energy Recovery Linac