Constraints on the magnetic field evolution in tokamak power plants

TL;DR

This paper explores the application of Boozer coordinates to tokamaks, deriving key expressions and constraints that inform the design and operation of future fusion power plants.

Contribution

It extends Boozer coordinate theory to tokamaks, deriving expressions for Faraday's Law, safety factor, and inductance relevant to fusion reactor design.

Findings

Derived expressions for Faraday's Law, safety factor, and inductance in tokamaks.

Identified constraints that could optimize tokamak power plant design.

Explained the reasons behind common disruptions and the necessity of pulsed operation.

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.''