  Electron cooling as a method of creating intense ion beams has a practical
upper limit when it comes to the peak phase space density of ion beams which
can be achieved in practice. We describe a new experiment to study electron
cooling of 2.5 MeV protons at the intensity limit using the Integrable Optics
Test Accelerator (IOTA), which is a storage ring dedicated to beam physics
research at Fermilab. This system will enable the study of magnetized electron
cooling of a proton beam with transverse incoherent tune shifts approaching
-0.5 due to the presence of intense space-charge forces. We present an overview
of the hardware design, simulations and specific experiments planned for this
project.
