Beam stability issues of the VLHC rings

Beam stability issues of the VLHC rings in Phase 1 and Phase 2 are reviewed. For accelerator rings of circumference 232 km and beam pipe radius of the order of 1 cm, the impedance of the vacuum chamber is dominated by the resistive wall. The most dangerous instabilities are the single-bunch transverse mode coupling instability and the transverse coupled bunch instability driven by the resistive wall at sub-revolution frequency. Scaling is studied concerning the thresholds of these instabilities and the dominance of the resistive wall impedance as the size of the accelerator increases