Limits on the field of ohmic heating solenoids, applied to a Tokamak TNS

If the ohmic heating solenoid for the TNS or other large Tokamak is an ungraded cryostable superconducting solenoid, with NbTi at 4.2 K as the superconductor, then the smallest outer diameter is not achieved at the highest attainable field. There is a lower optimum field which minimizes the outer diameter for a given volt-second requirement. At higher fields the mean diameter decreases; but the high fields require more superconductor, more copper stabilizer, more stainless steel for support, and more liquid helium coolant. For the GA-ANL design for TNS, the optimum field is 7.55 T and the minimum outside diameter for the solenoid is 2.15 m. If, on the other hand, the solenoid is graded, with more NbTi, copper, and stainless steel on the inner turns where the field is higher, then the volt-seconds can always be increased, for a given outer diameter, by adding more turns at a higher field inside until either the critical field is reached or the solenoid bore is filled.