  Recently, the study of integrable Hamiltonian systems has led to nonlinear
accelerator lattices with one or two transverse invariants and wide stable tune
spreads. These lattices may drastically improve the performance of
high-intensity machines, providing Landau damping to protect the beam from
instabilities, while preserving dynamic aperture. The Integrable Optics Test
Accelerator (IOTA) is being built at Fermilab to study these concepts with
150-MeV pencil electron beams (single-particle dynamics) and 2.5-MeV protons
(dynamics with self fields). One way to obtain a nonlinear integrable lattice
is by using the fields generated by a magnetically confined electron beam
(electron lens) overlapping with the circulating beam. The required parameters
are similar to the ones of existing devices. In addition, the electron lens
will be used in cooling mode to control the brightness of the proton beam and
to measure transverse profiles through recombination. More generally, it is of
great interest to investigate whether nonlinear integrable optics allows
electron coolers to exceed limitations set by both coherent or incoherent
instabilities excited by space charge.
