  An electron lens is planned for the Fermilab Integrable Optics Test
Accelerator as a nonlinear element for integrable dynamics, as an electron
cooler, and as an electron trap to study space-charge compensation in rings. We
present the main design principles and constraints for nonlinear integrable
optics. A magnetic configuration of the solenoids and of the toroidal section
is laid out. Single-particle tracking is used to optimize the electron path.
Electron beam dynamics at high intensity is calculated with a particle-in-cell
code to estimate current limits, profile distortions, and the effects on the
circulating beam. In the conclusions, we summarize the main findings and list
directions for further work.
