  At the Fermilab Tevatron collider, we studied the feasibility of suppressing
the antiproton head-on beam-beam tune spread using a magnetically confined
5-keV electron beam with Gaussian transverse profile overlapping with the
circulating beam. When electron cooling of antiprotons was applied in regular
Tevatron operations, the nonlinear head-on beam-beam effect on antiprotons was
small. Therefore, we first focused on the operational aspects, such as beam
alignment and stability, and on fundamental observations of tune shifts, tune
spreads, lifetimes, and emittances. We also attempted two special collider
stores with only 3 proton bunches colliding with 3 antiproton bunches, to
suppress long-range forces and enhance head-on effects. We present here the
results of this study and a comparison between numerical simulations and
observations. These results contributed to the application of this compensation
concept to RHIC at Brookhaven.
