Constraints on the magnetic field evolution in tokamak power plants

Abstract

Forty-five years ago a coordinate system was shown to exist that gave simple but exact expressions whenever and wherever a toroidal plasma equilibrium $\vec{\nabla}p=\vec{j}\times\vec{B}$ exists. These coordinates, now called Boozer coordinates, which revolutionized the stellarator program, are also applicable to tokamaks. Here expressions for Faraday's Law, the safety factor, and the internal inductance are derived. Their constraints should be useful in the design of tokamak power plants and for the thoughtful allocation of resources to minimize the time and the cost to the achievement of practical fusion power. Simple explanations are obtained for (1) why disruptions in tokamaks are so common, (2) why current-profile control though difficult may be required, especially during plasma shutdowns, and (3) why only pulsed tokamaks seem possible. Lack of familiarity with Boozer coordinates can make simple but exact expressions appear naive. Complicated derivations with dubious assumptions have been interpreted as ``more rigorous.''