Landau Damping of the Weak Head-Tail Instability at Tevatron

Two-step improvement of transverse beam stability has been done at the Tevatron. First, shielding of the laminated Lambertson magnets significantly reduced the transverse impedance. Second, Landau damping induced by the octupoles allowed machine operation with zero chromaticity at injection. That has resulted in a dynamic aperture increase and weakening of long-range beam-beam effects due to smaller chromatic tune modulation. At collisions, the coherent tunes and incoherent tune continuum are separated due to the head-on collisions. That leads to Landau damping loss at small chromaticities. Predictions of the analytical Landau damping model are compared with experiments.