Speaker
Description
Finding the steady-state phase-space distribution function for a large ensemble of interacting particles is challenging when studying systems with complex Hamiltonian or weakly dissipative dynamics, such as accelerator beams. These densities characterize long-term behavior of the ensemble and are critical for assessing stability, confinement, and matched beam transport. Direct methods rely on expensive particle pushing and tracking and become especially costly when self-fields are present. We present a sparse transfer-operator method that constructs approximate invariant densities directly from a single ensemble push, replacing the long-time tracking step with a sparse-matrix iteration. We demonstrate the method in three relevant settings for beam dynamics: the Chirikov standard map (baseline), a Chirikov-like map with self-coupling (a space-charge-like analog), and a kick-tune map with a dynamic-aperture constraint. In all cases, second moments and emittance extracted from the converged invariant density agree with particle-tracking references. Convergence with grid resolution is shown by a systematic resolution-scaling study. The results suggest that this method is a practical tool for studying long term behavior where direct tracking is prohibitive. It integrates naturally with existing simulation codes.
| Working group | WG5 |
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