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The beam-beam effects have been the dominating sources of beam loss and lifetime limitations in the Tevatron proton-antiproton collider [V. Shiltsev et al., Phys. Rev. ST Accel. Beams 8, 101001 (2005)]. Electron lenses were originally proposed for compensation of electromagnetic long-range and head-on beam-beam interactions of proton and antiproton beams [V. Shiltsev et al., Phys. Rev. ST Accel. Beams 2, 071001 (1999).]. Results of successful employment of two electron lenses built and installed in the Tevatron are reported by Shiltsev et al.

Applying the space-charge forces of a low-energy electron beam can lead to a significant improvement of the beam-particle lifetime limit arising from the beam-beam interaction in a highenergy collider [1]. In this article we present the results of various beam experiments with "electron lenses," novel instruments developed for the beam-beam compensation at the Tevatron, which collides 980-GeV proton and antiproton beams. We study the dependencies of the particle betatron tunes on the electron beam current, energy and position; we explore the effects of electron-beam imperfections and noises; and we quantify the improvements of the high-energy beam intensity and the collider luminosity lifetime obtained by the action of the Tevatron Electron Lenses.

One of the approaches to power distribution system of a superconducting proton linac that is under discussion at Fermilab requires development of a fast-action, megawatt-range phase shifter. Using two phase shifters with a waveguide hybrid junction can allow independent control of phase and amplitude of RF power at the input of each superconducting cavity of the linac. This promises significant saving in number of klystrons and modulators required for the accelerator. A prototype of a waveguide version of a phase shifter that uses Yttrium-Iron Garnet (YIG) blocks was developed and tested. This report presents design concept of the device and main results of simulation and proof-of-principle tests.