1 Brief Description of BBC and TEL
In the Tevatron, the antiproton bunches suffer a tuneshift due to their interactions with the more intense proton bunches. In multibunch operation, the tuneshifts vary from antiproton bunch to antiproton bunch, leading to an effective spread in tune. An electron lens, consisting of a short, low energy, electron beam colliding with antiprotons, can induce a tuneshift on the antiproton bunches, which has the opposite sign to that, which they experience, from the protons. With appropriate choice of parameters two such lenses could provide effective beam-beam tuneshift compensation. An R&D program has resulted in the construction and, recently, the successful testing of a single such device. If results continue to be positive the use of such devices could lead to a longer luminosity lifetime in the Tevatron and hence to a large integrated luminosity. Another potential luminosity improvement may come from compensation of non-linear tune spread within each antiproton bunch (footprint compression) by using electron beams with Gaussian profiles [2].