Speaker
Description
The equilibrium longitudinal beam distribution in electron storage rings is can be obtained by numerically solving the Fokker–Planck equation, which includes the RF potential, collective wake fields, synchrotron-radiation damping, and quantum excitation. Traditional auto-differentiation–based solvers treat stochastic effects as post-processing corrections, rather than incorporating them directly into the calculation of the equilibrium distribution.
In this work, we present a stochastic auto-differentiation framework that overcomes this limitation by solving the Fokker–Planck equation associated with longitudinal beam dynamics. Automatic differentiation is propagated through the complete stochastic system, treating quantum fluctuations and radiation damping as intrinsic components of the self-consistent differentiable solution. This approach fills a critical need of finding parameter dependance in the computation of the Haissinski distributions and longitudinal dynamics optimization by consistently incorporating stochasticity throughout the numerical procedure.
Funding Agency
This work is supported by DOE Office of Science, Office of High Energy Physics with award number DE-SC0024170.
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