The low beta triplet in the Tevatron is instrumented such that it is possible to move the horizontal and/or the vertical beta star in the longitudinal direction. This control over beta star allows us to minimize the longitudinal separation of horizontal and vertical beta star at each interaction region independently, thus maximizing the luminosity. Results of varying the longitudinal separation of horizontal and vertical beta star are shown and the sensitivity of the luminosity on this parameter is discussed.

The primary goal of the interaction region (IR) is to de- magnify the transverse beam dimension to a small spot size at the interaction point (IP) to reach the required luminosity. With an experimental drift space of m and a quadrupole focus- ing strength of 360 T/m at the triplets, a of 0.1 m can be achieved at a beam energy of 50 TeV. Only two families of sex- tupoles are needed to globally correct the chromaticity. Since the momentum spread of the beam is small ( ), a relatively large (about 20) linear chromaticity can be tolerated so that higher-order chromatic aberration produced by the low- optics is negligible. With a crossing angle of 70 r and a beam separation of 5 , the required minimum aperture of the triplet magnets is about 3 cm. The luminosity reduction resulted from such a crossing angle is about 13%. Crab crossing can be used to further reduce to below 0.05 m. At the same time, luminosity degradation caused by the angle crossing is eliminated. With crab cavities positioned near the triplet operating at a voltage of a few MV, the required voltage of the 379 MHz storage rf system can be reduced from the nominal 100 MV to below 10 MV. The requirements on the accuracy of the positioning of the crab cavities and the oper- ating voltage are both moderate. More than two families of sextupoles are needed for global chromatic compensation only when approaches 0.05 m and below.

During collider studies it was observed that with bunch intensities of >60*10/sup 9/ particles per bunch in the Tevatron, the beam would go unstable if the machine ran close to the coupling resonance. Simple head-tail stability only requires the horizontal and vertical chromaticities to be positive. Since the beam went unstable even when this condition was met, a set of experiments were performed which showed that if there is significant linear coupling the head-tail stability criterion is modified. A formalism for calculating head-tail stability is presented. The predictions of the formalism are compared to data taken with the Tevatron.<>

The Tevatron low- beta lattice that allows operation of two independent low- beta insertions is described. The measurement of the beta functions at various locations near the interaction region of the B0 and comparisons to theoretical calculations are reported.< >

The upgraded Tevatron collider has two new matched low beta insertions and operates with electrostatic separators to have different orbits for the proton and pbar beams. A general-purpose application program has been developed which allows the operator to control approximately 200 function generators and associated timers to commission, tune, and operate the machine. The program and relevant aspects of the Fermilab controls environment are discussed.<>

The Tevatron is running very close to the beam-beam limit. Therefore, in order to increase the luminosity, the proton and antiproton beams must be separated to eliminate unwanted beam crossings. To achieve this beam-beam separation, the proton and antiproton beams must travel on separate helical orbits, except at the collision areas. Particles moving on helical orbits in the Tevatron have both their tune and coupling changed with no measurable change in their chromaticity or lifetime. The tune and coupling changes are due to b/sub 2/ multipole errors in the main bending magnets. The size of the changes depends on the phase of the helical orbit relative to the distribution of b/sub 2/ errors around the ring. For the upgraded Tevatron with separated orbits, the protons and antiprotons live on different helical orbits. Therefore, the antiprotons are tune-shifted relative to the protons by approximately 0.01 in both the horizontal and vertical planes, and they experience a different skew quadrupole field (Q/sub s/) of approximately 0.2*10/sup -2/ m/sup -1/. >