Speaker
Description
Accurate modeling of insertion devices is critical for next-generation light sources and colliders, yet traditional tracking schemes often rely on paraxial approximations or Taylor expansions that break down at large angles or low energies. We present a high-performance framework for exact symplectic tracking of arbitrary Hamiltonians using implicit integration schemes. By employing SIMD-vectorized Newton solvers and automatic differentiation within Julia, we solve the implicit equations of motion to machine precision, computing the exact gradients and Hessians of the Hamiltonian on the fly. As a demonstration of this framework’s utility, we simulate the exact relativistic motion of particles through a wiggler field described by an exact hyperbolic and sinusoidal vector potential without invoking the paraxial approximation. We highlight the divergence between this exact solution and standard drift-kick-drift methods in the non-paraxial regime. This approach provides a generalizable, highly efficient pathway for simulating arbitrary electromagnetic fields where the vector potential is known analytically, ensuring full symplectic preservation without manual derivation of transfer maps.
Funding Agency
This work was funded by U.S. DOE grant DE-SC0025351
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