Simulations of octupole compensation of head-tail instability at the Tevatron

The proton lifetime in the Tevatron depends sensitively on chromaticities. Too low chromaticities can make the beam unstable due to the weak head-tail instability. One way to compensate this effect is to introduce octupoles to create a larger amplitude dependent betatron tune spread. However, the use of octupoles will also introduce additional side effects such as second order chromaticity, differential tune shifts and chromaticities on both proton and anti-proton helices. The non-linear effects may also reduce the dynamic aperture. We report on a simulation study to find the best combinations of polarities and strengths of the octupoles.