On the electrostatic field of a tokamak in the limit of large aspect ratio and concentric circular flux surfaces

TL;DR

This paper derives the electrostatic potential and field in a large aspect ratio tokamak with circular flux surfaces, analyzing the resulting charge density and electron temperature profile predictions.

Contribution

It provides an analytical approach to calculate the electrostatic potential and fields in tokamaks under specific geometric assumptions, linking these to plasma parameters.

Findings

Electrostatic potential satisfies Laplace's equation in the simplified geometry.

Estimated boundary charge density based on radial electrostatic field.

Predicted electron temperature profile does not match typical tokamak observations.

Abstract

From a common expression for the poloidal electrostatic field of a tokamak, in the limit of large aspect ratio and concentric circular flux surfaces, one may determine the associated potential. This potential satisfies Poisson's equation, which reduces to Laplace's equation when the medium has vanishing charge density, in axial geometry but not toroidal geometry. A simple transformation takes the potential over to the correct harmonic form for tokamak coordinates, and the resulting electrostatic field is calculated. From the radial field one may estimate the supporting charge density on the boundary, and from the poloidal field one may determine a prediction for the radial dependence of the electron temperature, which does not compare well with a rough estimate of the profile often seen in a tokamak.