Beam-beam phenomena in the Tevatron T. Sen FNAL 1 Introduction Protons and anti-protons in the Tevatron circulate on separated helical orbits within the same beam pipe and collide at two experimental detectors CDF and D0. Electrostatic separators placed at several locations create these helical orbits. In Run I there were six bunches per beam. In Run II, which started in April 2001, each beam has three trains of twelve bunches. Consequently there are six times as many long-range beam-beam interactions as in Run I. It was anticipated and observed that these long-range beam-beam interactions would have a more serious impact on beam lifetime and losses. Table 1 contains a brief list of the important parameters. After a slow start partly due to the impact of the long-range interactions, the luminosity in Run II has been steadily increasing over time. Figure 1 shows the luminosity evolution over the past few years. In 2004, the Tevatron surpassed the luminosity goals set for the 1st stage of Run II. The record until now was set on July 16, 2004 when the average initial luminosity exceeded 10 32 cm −2 sec −1 . Several improvements in the injectors and the Tevatron made this possible, see Reference [1] for more details. A collider fill starts with coalesced proton bunches from the Main Injector loaded one bunch at a time onto the central orbit in the Tevatron. The electrostatic separators are powered after all 36 proton bunches are loaded and the protons are moved to their helical orbit. Anti-protons are loaded four bunches at a time into one of three abort gaps onto the anti-proton helical orbit. The anti-proton bunches are moved longitudinally relative to the proton bunches (“cogged”) to make room for the next four bunches in the abort gap. After each train is full the two beams are accelerated to top energy. A final cogging is done at the end of the acceleration. The optics is changed to lower the beta functions at the IPs from 1.6m to 0.35m. After the final step of this beta squeeze, the transverse separations at the IPs are reduced to zero with the use of the appropriate separators around the IPs. Collimators are moved in to reduce the beam halo and background in the detectors and a store begins. The configuration of beam-beam interactions is different at injection and collision. Each bunch experiences 72 long-range interactions at injection but at collision there are 70 long-range interactions and two head-on collisions per bunch. In total there are 138 locations around the ring where beam-beam interactions occur. The sequence of 72 interactions out of the 138 interactions is different for each bunch, hence the effects are different from bunch to bunch. The locations of these interactions and the beam separations change from injection to collision. The left plot in Figure 2 shows the separations at all 138 interaction points in the ring after the 2nd cogging at injection. Parameter Injection Collision (p/ p) (p/ p) Circumference [m] 6283.187 Number of bunches 36 Bunch spacing [nsec] 396 Energy [GeV] 150 980 Beta ∗ at IP [m] 1.6 0.35 Normalized transverse emittance (95 %)[πmm-mrad] 20/15 Bunch intensity (×10 11 ) 2.5/0.36 Bunch length [cm] 80 48 Beam-beam parameter 0.0018/0.0092 Table 1: Selected beam parameters in the Tevatron 1