Study and optimal correction of a systematic skew quadrupole field in the Tevatron

Increasing demands for luminosity in existing and future colliders have made lattice design and error tolerance and correction critical to achieving performance goals. The current state of the Tevatron collider is an example, with a strong skew quadrupole error present in the operational lattice. This work studies the high-order performance of the Tevatron and the strong nonlinear behavior introduced when a significant skew quadrupole error is combined with conventional sextupole correction, a behavior still clearly evident after optimal tuning of available skew quadrupole circuits. An optimization study is performed using different skew quadrupole families, and, importantly, local and global correction of the linear skew terms in maps generated by the code COSY INFINITY [M. Berz, COSY INFINITY version 8.1 user's guide and reference manual, Department of Physics and Astronomy MSUHEP-20704, Michigan State University (2002). URL http://cosy.pa.msu.edu/cosymanu/index.html]. Two correction schemes with one family locally correcting each arc and eight independent correctors in the straight sections for global correction are proposed and shown to dramatically improve linearity and performance of the baseline Tevatron lattice.