METHODS FOR ADDRESSING THE PROBLEM OF THE DEPENDENCE OF THE TIME OF FLIGHT ON TRANSVERSE AMPLITUTE IN LINEAR NON-SCALING FFAGs

Because the time of flight in a linear non-scaling FFAG depends on the transverse amplitude, motion in the longitudinal plane will be different for different transverse particle amplitudes. This effect, if not considered, will lead the failure of a substantial portion of the beam to be accelerated. I will first briefly review this effect. Then I will outline some techniques for addressing the problems created by the effect. In particular, I will discuss partially correcting the chromaticity and increasing the energy gain per cell. I will discuss potential problems with another technique, namely the introduction of higher harmonic cavities.