Simulation of the ESR injection system

In order to improve the acceptance of the ESR beam injection system the influence of the fringe field of the main dipole magnet on the ion optics has to be analysed. Therefore, we perform a 3D MAFIA simulation of the dipole magnet and calculate the injection line which enters the radial fringe field in a tangential way. Starting from the given ESR beta function we trace the beam ellipse backwards in order to obtain the phase space requirements near the exit plane of the inflector magnet. Simulated phase space “monitors” defined at the start and the end of the curved reference trajectory give insight in the change of the beam emittance ellipse and indicate if aperture limitations may lead to beam losses. We obtain the second-order mapping of the phase space ellipse by calculating the first- and second-order field coefficients along the curved reference trajectory and solving the differential equations corresponding to each matrix element numerically. After an introduction into the field calculation method and the principles used to get the field index and second-order field coefficients, we will discuss our results and compare them with calculations based on measured field data (Spiller et al., GSI Scientific Report, 1996, p. 165).