Beam-beam studies for the Tevatron

In the first stage of Run II, the Tevatron will be operated with 36 bunches in each beam with bunch separations of 396 nanoseconds. The expected peak luminosity is L = 8.6 x 10{sup 31}cm{sup {minus}2}sec{sup {minus}1} with an average number of 2.3 interactions per bunch crossing. In the second stage of Run II, the goal is to increase the luminosity to about 1.5x10{sup 32} cm{sup {minus}2}sec{sup {minus}1}. If the bunch spacing were kept constant, the average number of interactions per bunch crossing would increase to about 4. This is thought to be unacceptably large and might saturate the efficiency of the detectors. This is the main reason for decreasing the bunch spacing at higher luminosities. One possibility is to reduce the bunch spacing to 132 nanoseconds which lowers the average number of interactions to an acceptable value of 1.4. This shorter bunch spacing though has several consequences on beam dynamics. Collisions between bunches will now occur every 19.78m. This is shorter than the distance of the nearest separators from the main IPs at B0 and D0. Consequently the beams will not be separated at the parasitic collisions nearest to the IPs if the geometry of the orbit is left unchanged. A sketch of this orbit is seen in the top part of Figure 1. This will lead to unacceptably large beam losses and background. Moving the separators closer to the detectors does not separate the beams sufficiently at the locations PC1L and PC1R. The phase advance from the first available position for the separators to these points is too small for the separator strengths that are available. One way to increase the transverse separation between the beams is to make the beams cross at an angle at the IPs. The optimum crossing angle depends upon a number of issues and requires a detailed investigation. The issues include a reduction in the luminosity, change in the beam-beam tune spreads, excitation of synchro-betatron resonances, orbit offset in IR quadrupoles which increases the nonlinear fields seen by the beams, required separation between the beams at the nearest parasitic collisions, the dispersion wave generated by the orbit offset, increase in the strength of the coupling etc. A crossing angle of {approximately}{+-}200{micro}rad in the 45 degree plane separates the beams by {approximately} 4{sigma} at the first parasitic collision. A sketch of the orbits with a crossing angle is shown in the bottom part of Figure 1