Free space charge dominated instabilities and resonances in synchrotrons

A Multiple Loop Square Well Model has been developed to simulate coherent motion in synchrotron machines, while including space charge and wakefields. The model builds upon previous single-well work by Blaskiewicz and Burov to allow the approximation of arbitrary potentials via the superposition of multiple square wells. Model predictions and experimental observations are discussed. In particular the model predicts TMCI thresholds at large space charge tune shifts that are not present in similar models. At the same time, a more realistic solution for convective motion and chromatic effects is arrived at due to the the more complex longitudinal dynamics.