Critical evaluation of the neoclassical model for the equilibrium electrostatic field in a tokamak

TL;DR

This paper critically examines the neoclassical approach to calculating the equilibrium electrostatic field in tokamak plasmas, revealing fundamental issues and proposing an alternative dynamic electric field explanation.

Contribution

It identifies flaws in two common expressions for the equilibrium electrostatic field and offers a new perspective that no static field is necessary for a neutral plasma.

Findings

One expression fails formal scrutiny.

The other does not respect the vector nature of diamagnetic current.

Dynamic electric fields arise from shifts in magnetic flux, explaining measurements.

Abstract

The neoclassical prescription to use an equation of motion to determine the electrostatic field within a tokamak plasma is fraught with difficulties. Herein we examine two popular expressions for the equilibrium electrostatic field so determined and show that one fails to withstand a formal scrutiny thereof while the other fails to respect the vector nature of the diamagnetic current. Reconsideration of the justification for the presence of the equilibrium electrostatic field indicates that no field is needed for a neutral plasma when considering the net bound current defined as the curl of the magnetization. With any shift in the toroidal magnetic flux distribution, a dynamic electric field is generated with both radial and poloidal components, providing an alternate explanation for any measurements thereof.