Head-on and long-range induced tunespread of about 0.025 in the Tevatron collider at Run II (together with the increased strength of the resonances) can significantly deteriorate the p lifetime and the collider luminosity. It was proposed to employ the so-called Tevatron Electron Lenses (TEL) to compress the beam-beam footprint and eliminate completely the bunch-to-bunch tunespread (PACMAN effect) for small amplitude particles. The first lens has been recently installed and tested [1]. This report presents results of analytical studies and tracking simulations of the linear beam-beam compensation (elimination of the bunch-to-bunch tune variation). Compression of the beam-beam footprint (nonlinear compensation) is discussed in [2].
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