Speaker
Description
The Complex Bend Achromat (CBA) lattice for the NSLS-II Upgrade (NSLS-IIU) achieves an ultralow emittance of 23 pm, but currently relies on hard-edge element models. Accurate dynamic aperture simulation requires symplectic transfer maps derived from realistic field models. The overlapping fringe fields and large sagitta in the CBA preclude standard fringe field map approximations and surface methods for generalized gradient expansions relying on infinite straight cylinders.
As a baseline, we use symplectic tracking, Gauss-Legendre 4 (GL4) integrator, with divergence-free interpolation of magnetic field, computed in Radia on a grid. We then investigate three approaches utilizing neural networks to learn the symplectic transfer maps in CBA: (1) training a HenonNet directly on the trajectories obtained by GL4 tracking; (2) formulating the equations of motion as a Partial Differential Equation (PDE) for the canonical transformation, describing evolution in phase-space, and solving it using a HenonNet ansatz; and (3) solving the Hamilton-Jacobi equation for a generating function, represented as a neural network, which implicitly encompasses trajectories in phase space.
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