Preliminary performance estimates for a LEP proton collider

This analysis was stimulated by news from the United States where very large $p\bar{p}$ and $pp$ colliders are actively being studied at the moment. Indeed, a first look at the basic performance limitations of possible $p\bar{p}$ or $pp$ rings in the LEP tunnel seems overdue, however far off in the future a possible start of such a p-LEP project may yet be in time. What we shall discuss is, in fact, rather obvious, but such a discussion has, to the best of our knowledge, not been presented so far. We shall not address any detailed design questions but shall give basic equations and make a few plausible assumptions for the purpose of illustration. Thus, we shall assume throughout that the maximum energy per beam is $8 TeV$ (corresponding to a little over $9 T$ bending field in very advanced superconducting magnets) and that injection is at $0.4 TeV$. The ring circumference is, of course that of LEP, namely $26,659 m$. It should be clear from this requirement of "Ten Tesla Magnets" alone that such a project is not for the near future and that it should not be attempted be- fore the technology is ready.