Linear beam-beam tune shift estimates for the Tevatron collider

The Tevatron lattice has regions of nonzero dispersion which influence the beam size at the crossings locations. During six-on-six collider operation, each pbar bunch sees 12 crossings per revolution, producing large tune shifts. Estimates of linear beam-beam tune shift are given for various Tevatron lattices. These estimates are compared with those using the round beam approximation (RBA). Comparison between predictions and measured pbar tunes is made. For the Tevatron lattices studied (using typical beam emittances) the RBA always overpredicts the linear calculation. SYNCH calculations using nonlinear lenses due to the beam-beam interaction agree with the linear calculations. The dynamic beta effect is small for the injection cogged fixed target lattice. The results of the cogging experiment seem to agree in sign and order of magnitude with the predictions of the linear tune shift calculations.<>