Choice of Tevatron tune with matched low-. beta. insertions

Abstract

The Tevatron lattice, following closely the Main Ring lattice, is made up of approximately 90 FODO cells with six straight sections equally spaced. The straight sections are identical (neglecting the special high-..beta.. straight section used for resonant extraction) providing six-fold symmetry. Each straight section is comprised mainly of a pair of doublets, one at each end, in an antisymmetric configuration. The ..beta..-functions are matched to the building block cells but the dispersion function is not. The ..beta..-function matching implies that the structure is not sensitive to the tune of the sextant (i.e., structure resonances); however, the dispersion mismatch excites off-momentum dipole resonances and the dispersion structure of the ring is therefore sensitive to sextant tunes near an integer. The introduction of low-..beta.. insertions can be accomplished by replacing a standard insertion (expanded somewhat from the doublet pair straight section) with a low-..beta.. insertion. By matching the ends of the replacement units with respect to ..beta..-functions and dispersion function, the full lattice is made insensitive to linear structure resonances. Procedures are described here for introducing into the idealized Tevatron lattice considered here a single matched low-..beta.. insertion at BO, and two matched low-..beta.. insertions at BO and DO. The main consequencemore » is the need for a significant number of independently powered quadrupoles. Another conclusion is related to the choice of tune, where it is found that the arbitrary rule of maintaining a fixed tune for all configurations should be modified.« less