Intra-beam Scattering Scaling for Very Large Hadron Colliders

For Very Large Hadron Colliders (VLHC), flat hadron beams [2] with their vertical emittance much smaller than their horizontal emittance are proposed to maximize the design luminosity. Emittance growth caused by intra-beam scattering (IBS) is a concern on the realization of such flat-beam conditions. Based on existing IBS formalism on beams of Gaussian distribution, we analytically derive [6] the IBS growth rate and determine the IBS limit on the aspect ratio for a flat beam.