Improved performance of tandem mirrors with thermal barriers

As originally conceived, tandem mirrors with thermal barriers are limited by MHD instabilities to values of central-cell ..beta.. that are significantly lower than those attainable in tandems without barriers. Much of the degradation in performance is due to the introduction of a new region of unfavorable field line curvature in the central cell. From a variational calculation that maximizes central cell fusion power subject to constraints on the vacuum field energy and allowable interchange instability drive, I derive an analytic expression for a central cell magnetic field strength profile for which the new instability drive is greatly reduced. As a result, central cell performance is enhanced to a point approaching that of tandem mirrors without barriers. Formulas showing how ..beta../sub c/ and fusion power scale with design parameters are also derived