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04_multigrd_space - 714 IEEE TRANSACTIONS ON MAGNETICS VOL...

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714 IEEE TRANSACTIONS ON MAGNETICS, VOL. 40, NO. 2, MARCH 2004 Multigrid Algorithms for the Fast Calculation of Space-Charge Effects in Accelerator Design Gisela Pöplau, Ursula van Rienen , Member, IEEE , Bas van der Geer, and Marieke de Loos Abstract— Numerical prediction of charged particle dynamics in accelerators is essential for the design and understanding of these machines. Methods to calculate the self-fields of the bunch, the so-called space-charge forces, become increasingly important as the demand for high-quality bunches increases. We report on our development of a new three-dimensional (3-D) space-charge rou- tine in the general particle tracer (GPT) code. It scales linearly with the number of particles in terms of CPU time, allowing over a mil- lion particles to be tracked on a normal PC. The model is based on a nonequidistant multigrid Poisson solver that has been constructed to solve the electrostatic fields in the rest frame of the bunch on meshes with large aspect ratio. Theoretical and numerical inves- tigations of the behavior of SOR relaxation and PCG method on nonequidistant grids emphasize the advantages of the multigrid al- gorithm with adaptive coarsening. Numerical investigations have been performed with a wide range of cylindrically shaped bunches (from very long to very short) occuring in recent applications. The application to the simulation of the TU/e DC/RF gun demonstrates the power of the new 3-D routine. Index Terms— Adaptive meshing, charged particle trajectories, electrostatics. I. I NTRODUCTION N OWADAYS, particle accelerators play an important role for scientific research as well as for medical and indus- trial applications. Demanding applications such as high-energy linear colliders and self-amplified spontaneous emission free electron lasers (SASE-FELs) require very high quality electron bunches, where any anomaly severely degrades the final perfor- mance. The calculation of space-charge forces is an important part of the simulation of the behavior of charged particles in these ma- chines. As the quality of the charged particle bunches increases, so do the requirements for the numerical space-charge calcula- tions. The requirements of new machines like the DESY-TTF [1] are for example so tight that effects like nonuniform emis- sion from the photo-cathode and noncylindrically symmetric fields caused by side-coupled cavities have a significant effect on the gain in the downstream undulator. Studying these ef- fects requires three-dimensional (3-D) calculations, with a pre- cision matching the quality of the bunch. This full 3-D treatment is particularly challenging because the bunches typically have varying shape during their path through the accelerator ranging Manuscript received July 1, 2003. This work was supported by DESY, Ham- burg, Germany.
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