Speaker
Description
Many accelerator tracking codes include interactions, models, and coordinate transformations that make it difficult to evaluate symplecticity analytically. The stability of long term tracking depends on preservation of Hamiltonian structure, making numerical verification of symplecticity important. We present a symplectic verification method based on truncated power series (TPS) propagation through polymorphic tracking codes. Initial phase-space coordinates are represented as TPS variables and passed directly through the tracking routine. The first-order TPS coefficients give the Jacobian matrix while higher-order coefficients retain the nonlinear structure of the map. Since each Jacobian element is itself a TPS, the symplectic condition $J^T S J = S$ can be evaluated order-by-order, enabling verification of symplecticity up to the truncation order. We demonstrate the method on a weak-strong beam-beam simulation including hourglass and slingshot effects. These effects complicate direct analytic derivation of the full six-dimensional map, while TPS propagation verifies symplecticity directly through tracking.
Funding Agency
Department of Energy funding from grant DE-SC0025351
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