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- W2554181264 abstract "Simulation of high intensity accelerators leads to the calculation of space charge forces between macroparticles in the presence of acceleration chamber walls. To calculate space-charge forces, one solves the Poisson's equation in 3-D. For an accelerator with long bunches, the 3-D problem is usually reduced to 2-D, because the transverse motion can be decoupled from the longitudinal due to very different characteristic times. The simulation of large macroparticle ensembles requires rapid evaluations of space-charge forces. Fast field solvers are usually based on Fourier-transform methods (FFT), but they are not applicable for arbitrary geometries of walls. For arbitrary walls, the solution for Poisson's equation can be derived using a Green function, which is numerically calculated on discrete mesh points. For simple wall geometries, e.g., circle and ellipse, it can be expressed analytically. Usually, such technique results in slow solvers. We discuss here a method, which combines a Green function technique and a FFT solver. In the first step, the Green function technique is used for arbitrary walls to calculate potentials on an intermediate rectangular boundary, which includes all macroparticles. In the second step, a FFT solver calculates potentials inside this rectangular domain with given potentials on its boundary. Preliminary numerical results will be reported." @default.
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- W2554181264 date "2002-01-01" @default.
- W2554181264 modified "2023-09-26" @default.
- W2554181264 title "A METHOD FOR NUMERICAL SOLUTION 2-D POISSON'S EQUATION WITH IMAGE FIELDS" @default.
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