  Electron lenses are pulsed, magnetically confined electron beams whose
current-density profile is shaped to obtain the desired effect on the
circulating beam. Electron lenses were used in the Fermilab Tevatron collider
for bunch-by-bunch compensation of long-range beam-beam tune shifts, for
removal of uncaptured particles in the abort gap, for preliminary experiments
on head-on beam-beam compensation, and for the demonstration of halo scraping
with hollow electron beams. Electron lenses for beam-beam compensation are
being commissioned in the Relativistic Heavy Ion Collider (RHIC) at Brookhaven
National Laboratory (BNL). Hollow electron beam collimation and halo control
were studied as an option to complement the collimation system for the upgrades
of the Large Hadron Collider (LHC) at CERN; a conceptual design was recently
completed. Because of their electric charge and the absence of materials close
to the proton beam, electron lenses may also provide an alternative to wires
for long-range beam-beam compensation in LHC luminosity upgrade scenarios with
small crossing angles. At Fermilab, we are planning to install an electron lens
in the Integrable Optics Test Accelerator (IOTA, a 40-m ring for 150-MeV
electrons) as one of the proof-of-principle implementations of nonlinear
integrable optics to achieve large tune spreads and more stable beams without
loss of dynamic aperture.
