Coupling in the Tevatron

The performance of the Fermilab Tevatron Collider at the commencement of collider run Ib (Jan. 1994) was far below expectations. The poor performance was found to be due to a rolled low-β quadrupole downstream of CDF. This rolled quadrupole coupled the horizontal and vertical motion of the Tevatron beams and significantly reduced the Tevatron luminosity. When the roll in the quadrupole was corrected the performance of the Tevatron improved dramatically. This note discusses the experimental data indicating the presence of coupling, and subsequent calculations which show how coupling can affect the luminosity