Abstract-We present a design of a predictive control scheme for longitudinal beam dynamics in heavy ion synchrotrons. Specifically, we consider a linear-quadratic model predictive control (MPC) approach, whereby the quadratic program is solved via a fast gradient method. Furthermore, we investigate whether the fast gradient method allows for real-time feasible implementation of the proposed approach on a field programmable gate array (FPGA). Our results indicate that sampling rates in the order of 1MHz are achievable.Index Terms-model predictive control, heavy ion synchrotrons, longitudinal beam control, fast gradient method, field programmable gate array

In heavy-ion synchrotrons such as the SIS18 at Helmholtzzentrum für Schwerionenforschung, Helmholtz Centre for Heavy Ion Research (GSI), coherent oscillations of the particle bunches are damped by rf feedback systems to increase the stability and to improve the beam quality. In the longitudinal direction, important modes are the coherent longitudinal dipole and quadrupole oscillation. In this paper we present a new and rigorous approach to analyze the longitudinal feedback to damp these modes. The results are applied to the rf feedback loop at GSI that damps the quadrupole mode. The stability analysis is compared with simulations and is in good agreement with results of a beam experiment. Finally, we summarize practical implications for the operation of the feedback system regarding performance and stability.

The superconducting, heavy ion synchrotron SIS100 is the core of the new FAIR facility at GSI, Darmstadt, Germany. Its unique design is dedicated to the acceleration of intermediate charge state heavy ions. Several new technical approaches assure the stabilization of the vacuum dynamics and the minimization of charge related beam loss. Beside high intensity heavy ions, SIS100 will accelerate all ions from Protons to Uranium, and in spite of the fact that superconducting magnets are used, SIS100 shall be as flexible in ramping and cycling as a normal conducting synchrotron.

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