Experimental demonstration of beam-beam compensation by Tevatron electron lenses and prospects for the LHC

Electromagnetic long-range and head-on interactions of high intensity proton and antiproton beams are significant sources of beam loss and lifetime limitations in the Tevatron Collider Run II (2001-present). We present observations of the beam-beam phenomena in the Tevatron and results of relevant beam studies. We analyze the data and various methods employed in high energy physics (HEP) operation, predict the performance for planned luminosity upgrades and discuss ways to improve it.