TUSCI1
MSU, East Lansing, Michigan, USA
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TUSCI1 |
The Fast Multipole Method in the Differential Algebra Framework for the Computation of 3D Space Charge Fields and Transfer Maps | |
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| A new algorithm which combines the classical multiple level fast multipole algorithm with differential algebraic tools for three dimensional electrostatic field calculation of N-body systems is presented. The whole charged domain is hierarchically decomposed into boxes of varying sizes according to the local charge density. Each box has a near region, where the interaction is calculated directly, and its a region, where the interaction is represented by expansions in multipoles at infinity. The total field is the summation of the near region field and the far region field. This algorithm can treat any arbitrary charge distribution with an efficiency of O(N). Differential algebra simplifies the math especially for non-point charge macro particles, and allows the calculation of high order field derivatives, which is essential to generate the transfer map. Examples of applying the methods in beam dynamics simulations are given. | ||
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Slides TUSCI1 [3.302 MB] | |