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For the GSI future project beam loss control of a high intensity bunched beam stored in SIS100 for 106 turns is an important issue. In a recent study (G. Franchetti et al., Phys. Rev. ST Accel. Beams 6, 124201 (2003)) an analytical space charge algorithm was proposed, which allowed noise-free calculations over a large number of turns. Here we present a generalization of this algorithm to arbitrary 3D dimensions and arbitrary distributions observing ellipsoidal symmetry. Applications to long-term tracking with space charge are presented
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