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Nonlinear δf Method for Beam-Beam Simulation

2000/10/23 by Yunhai Cai, Cai, Yunhai, Alexander W. Chao +5
Engineering · Physics and Astronomy · #Accelerator Physics (physics.acc-ph) #Computational Physics (physics.comp-ph) #Electromagnetic Simulation and Numerical Methods #FOS: Physical sciences #Particle Accelerators and Free-Electron Lasers #Particle accelerators and beam dynamics #physics.acc-ph #physics.comp-ph

paper · pdf · doi:10.48550/arxiv.physics/0010055

14 pages

arxiv created 2000/10/23 · openalex publication_date 2000/10/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We have developed an efficacious algorithm for simulation of the beam-beam interaction in synchrotron colliders based on the nonlinear δf method, where δf is the much smaller deviation of the beam distribution from the slowly evolving main distribution f0. In the presence of damping and quantum fluctuations of synchrotron radiation it has been shown that the slowly evolving part of the distribution function satisfies a Fokker-Planck equation. Its solution has been obtained in terms of a beam envelope function and an amplitude of the distribution, which satisfy a coupled system of ordinary differential equations. A numerical algorithm suited for direct code implementation of the evolving distributions for both δf and f0 has been developed. Explicit expressions for the dynamical weights of macro-particles for δf as well as an expression for the slowly changing f0 have been obtained.

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