A perturbative framework builds approximate invariants for nonlinear symplectic maps as a direct nonlinear extension of Courant-Snyder theory, demonstrated on operational accelerator configurations.
Theory of the alternating-gradient synchrotron,
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The symmetric McMillan map with mixed nonlinearity reduces to two key parameters and yields exact action-angle variables with closed-form rotation number and nonlinear tune shift.
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Geometry of Almost-Conserved Quantities in Symplectic Maps. Part III: Approximate Invariants in Nonlinear Accelerator Systems
A perturbative framework builds approximate invariants for nonlinear symplectic maps as a direct nonlinear extension of Courant-Snyder theory, demonstrated on operational accelerator configurations.
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Dynamics of McMillan mappings III. Symmetric map with mixed nonlinearity
The symmetric McMillan map with mixed nonlinearity reduces to two key parameters and yields exact action-angle variables with closed-form rotation number and nonlinear tune shift.