Feasibility of electron cooling and luminosity potentials of colliders

Luminosity upgrades of colliders with hadron beams tend to require decreased and maintained beam emittances using a suitable cooling technique. The breakthroughs of recent years: realization of beam energy recovery in superconducting linear accelerators; flat to round beam transformations; and new beam transport concepts (discontinuous solenoid, circulator rings, hollow beams, dispersive cooling); have promoted the feasibility of efficient electron cooling of intense high energy hadron beams. Electron cooling, in cooperation with strong SRF fields in storage rings, will allow one to obtain very short hadron bunches, as result of which the luminosity can be raised by making a low beta-star. Short bunches also would make feasible crab crossing, that allows one to remove the parasitic beam-beam interactions and maximize the collision rate. Cooling also results in flatness of uncoupled beam equilibrium; this can be used to diminish the IBS impact on luminosity