In the present paper we consider a FFAG lattice with polygonal structure.
Typical dependence of the horizontal and vertical betatron tunes on energy in the EMMA non-scaling FFAG is shown in Figures 1 and 2.
The process of acceleration in a non-scaling FFAG accelerator can be studied by solving Hamilton's equations of motion for the longitudinal degree of freedom.
The path length in a FFAG arc and therefore the time of flight [THETA] is often well approximated as a quadratic function of energy.
Based on the Hamiltonian formalism, the synchro-betatron approach for the description of the dynamics of particles in non-scaling FFAG machines has been developed.
The formulation thus developed has been applied to the electron FFAG machine EMMA.
Unlike the conventional synchronous acceleration, the acceleration process in FFAG accelerators is an asynchronous one in which the reference particle performs nonlinear oscillations around the crest of the RF waveform.