The steady-state collisional distribution function of a mirror-confined plasma which is known from Fokker-Planck calculations, implies a unique relationship between the plasma pressure and the magnetic field strength at any point within the plasma. Using this relationship it is possible to deduce the maximum β consistent with macroscopic stability in a mirror machine with given mirror ratio. This β limitation is found to impose a rather mild restriction upon reactor designs. For fields which satisfy this β limitation, the profile of the magnetic field along its axis is restricted but not fully determined, by the minimum-B requirement, and the remaining freedom can be used to optimize the magnet design by maximizing the ratio of the thermonuclear power produced to the cost of the magnetic field windings. It is found that even when the profile has been optimized in this way, the plasma density and pressure profiles are rather peaked towards the centre of the reactor, and the ratio of the thermonuclear power produced in such an optimized minimum-B reactor to the power which would be produced in a reactor of the same dimensions but with a square well profile (if it were stable) is approximately 1/4.
Wall stabilization of high-beta anisotropic plasmas in an axisymmetric mirror trap