Scaling and Modeling Studies of High-bootstrap Fraction Tokamaks

A theoretical framework is developed to generate tokamak equilibrium configurations for which, on one hand, the current results entirely from the bootstrap current source driven by the pressure gradient while, on the other hand, the pressure gradient is determined from the thermal conduction equation with a thermal diffusivity constructed to have properties observed in confinement experiments: gyroBohm confinement, gradients only with respect to the poloidal flux, global confinement depending only on plasma current and independent of toroidal field, a critical temperature gradient, and an overall confinement improvement with negative shear. The nondimensional method used yields eigenvalues composed of a collection of physics quantities, resulting in scaling relations among physics variables. It is found that the the plasma temperature scales as T∝ P2/3ε-1/3 , while Ip∝ n1/2 P1/3 a ε1/12. The system has a solvability criterion which does not permit solutions when the confinement improves rapidly with increasing negative shear. A simplified 1-D model captures the essential physics of the coupling between bootstrap currrent generation and thermal conduction.