RLA design: RF optics

Opposite to the synchrotrons which work at fixed optics, the Recirculating Linear Accelerators work with a variable optics in the RF system. This is due to the increase of the particle energy at subsequent passages, which results in a decrease of the normalised quadrupole strengths. It is demonstrated in this note that this effect does not introduce any limitation in the total energy gain if FODO cells are used in the RF system. Consequently, a single recirculator could be designed to accelerate from 2GeV to 50GeV if there is no need of a first recirculator for any other reasons like bunch shaping or matching.