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The McMillan system is a novel method to increase the tune spread of a beamwithout decreasing its dynamic aperture due to the systems integrability. Whilethe ideal system is based on an infinitely thin kick, the physical designrequires a thick electron lens, including a solenoid. Particle transportthrough the lens is difficult to simulate due to the nature of the force on thecirculating beam. This paper demonstrates accurate simulation of a thickMcMillan lens in a solenoid using symplectic integrators derived from Yoshidasmethod.

Symplectic Particle Tracking in a Thick Nonlinear McMillan Lens for the Fermilab Integrable Optics Test Accelerator (IOTA)