Beam Dynamics Studies in Recirculating Machines

The LHeC and the CLIC Drive Beam share not only the high-current beams that make them prone to show instabilities, but also unconventional lattice topologies and operational schemes in which the time sequence of the bunches varies along the machine. In order to asses the feasibility of these projects, realistic simulations taking into account the most worrisome effects and their interplays, are crucial. These include linear and non-linear optics with time dependent elements, incoherent and coherent synchrotron radiation, short and long-range wakefields, beam-beam effect and ion cloud. In order to investigate multi-bunch effects in recirculating machines, a new version of the tracking code PLACET has been developed from scratch. PLACET2, already integrates most of the effects mentioned before and can easily receive additional physics. Its innovative design allows to describe complex lattices and track one or more bunches accordingly to the machine operation, reproducing the bunch train splitting and recombination to and from multiple beamlines. After some initial testing, PLACET2 has been applied to the LHeC Energy Recovery Linac design in order to complete the first end-to-end tracking simulation. The transport of the beam to the dump has been verified in presence of incoherent synchrotron radiation, wakefields and beam-beam effect. Unexpected high radiation losses have been found in specific sections of the lattice, solutions have been proposed to improve both the machine performance and the beam quality. These include a new design of the spreading sections and return arcs based on combined function magnets. The detector bypass, that was originally missing, have now been designed and integrated in the lattice. Tracking simulations have also been performed for PERLE, which have been developed to validate on a smaller scale the technology and the operation of the LHeC. Its performances have been assessed and the design has been consolidated and improved. The work at CTF3 focused on the Combiner Ring. Its length plays a crucial role in the phase structure of the combined beam and must be carefully tuned. The control of the ring length by means of optics scaling, has been measured on the machine and reproduced with the PLACET2 model. Moreover the code has been used to verify a multi-bunch instability that appeared during the commissioning of the ring.