Transverse beam instability due to a broad-band impedance in very large hadron-collider ring

Abstract

The strong head-tail instability due to a broad-band impedance in the very large hadron-collider (VLHC) ring of 20 TeV is numerically, investigated. It is shown that the beam size increases significantly when the impedance, Z(parallel to)/n, is 0.6 Omega, which is the estimated impedance budget in the design. The beam instability is shown to be cured by introducing tune spreads, such as RF quadrupole, chromaticity and amplitude-dependent tune shift. It is shown that any of these tune spreads limits the growth of the beam size to less than 3%. It is shown that threshold impedance for the instability is estimated to be about Z(parallel to)/n = 0.3 Omega.