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|| /n, is 0.6 Ω, 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|| /n=0.3 Ω.