Evaluating High Order resonances using Resonant Normal Forms

Resonant normal forms allow to study various aspects of resonances up to high orders. We apply these techniques to evaluate resonances in four phase space variables. The input is truncated one-turn map derived from standard tracking codes. A code automatically finds fixed line locations in phase space resonances up to a desired order. The island widths and the island tunes of these resonances are calculated as well. As a check, it is shown to which extent results from first order perturbation theory can be reproduced and how well the predictions of resonant normal form agree with tracking simulations.