Optimizing VLHC single-particle performance

Since the sine qua non of building the Very Large Hadron Collider (VLHC) is the ability to bend 50 TeV particles in a circle stably and cheaply, we concentrate on the “arcs” of the VLHC, excluding all other problems. Considering only single-particle stability, the arcs are analyzsed using scaling considerations to choose the guide field B that minimizes cost. The extent to which the arcs can act as “achromatic optical fibers” for the beams is studied, in hopes of reducing the need for correction elements and spool pieces. Prescriptions are given to ameliorate the effects of resonance by choosing the best tunes and other parameters. For the (admittedly uncertain) parameters adopted in the paper the optimal value for B seems to be about 3 T, if NbTi superconductor is used. Possible cost savings through the use of iron at low field or superconductor other than NbTi at high field are not analyzsed.