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An electron lens is planned for the Fermilab Integrable Optics TestAccelerator as a nonlinear element for integrable dynamics, as an electroncooler, and as an electron trap to study space-charge compensation in rings. Wepresent the main design principles and constraints for nonlinear integrableoptics. A magnetic configuration of the solenoids and of the toroidal sectionis laid out. Single-particle tracking is used to optimize the electron path.Electron beam dynamics at high intensity is calculated with a particle-in-cellcode to estimate current limits, profile distortions, and the effects on thecirculating beam. In the conclusions, we summarize the main findings and listdirections for further work.

Field calculations, single-particle tracking, and beam dynamics with  space charge in the electron lens for the Fermilab Integrable Optics Test  Accelerator