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WEPSB021 |
McMillan Map and Its Application for Accelerator Physics | |
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McMillan map is an important discrete time model of 1D transverse nonlinear accelerator lattice. We will discuss a full analytical theory based on parametrization of individual canonical biquadratic curves*. Using the normal forms provided in* we were able to generalize this result to entire phase-plane of finite trajectories and calculate mechanical action-angle coordinates. In addition we will present an alternative way of analytical extraction of phase-advance variable out of map's invariant of motion (Danilov Theorem). The connection of these results with possible 2D generalizations, axially symetric and 2D-magnetostatic McMillan lenses, is presented.
Iatrou, A., & Roberts, J. A. (2002). Integrable mappings of the plane preserving biquadratic invariant curves II. Nonlinearity, 15(2), 459. |
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