Non-Linear Beam Dynamics in High Resolution Multi-Pass Time of Flight Mass Separator

A multi-pass time-of-flight mass separator (MTOF-MS) is under development by the University Radioactive Ion Beam (UNIRIB) collaboration. The MTOF consists of two coaxial electrostatic mirrors, focusing lenses and auxiliary injection, extraction and separation elements. The injected ions having almost the same energy but different masses undergo hundreds or thousands of reflections between the mirrors. In the course of this periodic motion, the ions of different masses and hence velocities are spatially separated in longitudinal direction. The periodic motion in the MTOF has been investigated with a recently developed ray tracing program utilizing the canonical integration technique. Results of the performed numerical simulations are discussed. The simulations displayed the nonlinear character of the ions’ behaviour both in transverse and longitudinal phase spaces. The ions’ transverse stability and longitudinal isochronicity were the matters of primary attention. It is shown in particular that at transverse tunes of around Q=0.75 the system can be adjusted to be isochronous up to at least the 3rd order of the time-of-flight (ToF) optical aberrations.