Isochronous machines with sector magnet fields and conditions for similarity of the orbits

Circular machines with a fixed field and an alternating gradient (FFAG) have been proposed for the ionization cooling, the phase rotation and the acceleration of the muons of a neutrino factory. Using a circular machine instead of a linear arrangement reduces the number of accelerating structures and the number of ionization units. A magnetic field fixed in time is necessary for rapid accleration of particles with a short lifetime and the large acceptance in energy of the FFAG is well adapted to the production of muons resulting from interaction of a proton beam on a target. Both the focusing and the synchronism of the acceleration with the revolution frequency are considered in this study.