Linear beam-beam tune shift calculations for the Tevatron Collider
Abstract
A realistic estimate of the linear beam-beam tune shift is necessary for the selection of an optimum working point in the tune diagram. Estimates of the beam-beam tune shift using the ''Round Beam Approximation'' (RBA) have over estimated the tune shift for the Tevatron. For a hadron machine with unequal lattice functions and beam sizes, an explicit calculation using the beam size at the crossings is required. Calculations for various Tevatron lattices used in Collider operation are presented. Comparisons between the RBA and the explicit calculation, for elliptical beams, are presented. This paper discusses the calculation of the linear tune shift using the program SYNCH. Selection of a working point is discussed. The magnitude of the tune shift is influenced by the choice of crossing points in the lattice as determined by the pbar ''cogging effects''. Also discussed is current cogging procedures and presents results of calculations for tune shifts at various crossing points in the lattice. Finally, a comparison of early pbar tune measurements with the present linear tune shift calculations is presented. 17 refs., 13 figs., 3 tabs.
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