Simulation of the ESR injection system

In order to improve the acceptance of the ESR beam injection system the inf luence 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 m agnet and calculate the injection line which enters the radial fringe held 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 nea r the exit plane of the inflector magnet. Simulated phase space "monitors" defined at the start and the end of the curved reference trajectory eve ins ight in the change of the beam emittance ellipse and indicate if aperture l imitations may lead to beam losses. We obtain the second-order mapping of t he phase space ellipse by calculating the first- and second-order field coe fficients along the curved reference trajectory and solving the differentia l equations corresponding to each matrix element numerically. After an intr oduction into the field calculation method and the principles used to get t he field index and second-order field coefficients, we will discuss our res ults and compare them with calculations based on measured held data (Spille r et al., GSI Scientific Report, 1996, p. 165). (C) 1999 Elsevier Science B .V. All rights reserved.