Non scaling FFAG machines have until recently been considered as an alternative.
Because non-scaling FFAG accelerators have otherwise very desirable features, it is important to investigate analytically and numerically some of the peculiarities of the beam dynamics, the new type of fast acceleration regime (so-called serpentine acceleration) and the effects of crossing of linear as well as nonlinear resonances.
An example of the theory developed here is presented for the parameters of the Electron Machine with Many Applications (EMMA) , a prototype electron non-scaling FFAG to be hosted at Daresbury Laboratory.
Firstly, we review some generalities and first principles of the Hamiltonian formalism [8-10] suitably modified to cover the case of a nonscaling FFAG lattice.
The accelerating field in AVF cyclotrons and FFAG machines can be represented by a scalar potential [phi] (the corresponding vector potential A = 0).
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.