The influence of accelerator physics on the magnet design of a very large hadron collider

We present a study of the influence of accelerator physics on the design of magnets for very high energy hadron colliders. The limiting specifications of a particular VLHC model are estimated, and their effect on the design of the accelerator magnets is determined using simulations and scaling laws for magnet aperture, field quality, cryogenic and vacuum properties and cost. We show that there is a maximum useful field due to synchrotron radiation power and cost, and a minimum useful aperture due to synchrotron radiation and beam-stability.