Conditions for up-down asymmetry in the core of tokamak equilibria

TL;DR

This paper investigates the conditions that lead to up-down asymmetry in the core of tokamak plasmas, linking it to current density ratios and external field perturbations, with validation through analytical and numerical models.

Contribution

It identifies key parameters, especially the ratio of on-axis toroidal current density to external field perturbation, that determine core asymmetry in tokamaks, including the role of hollow current profiles.

Findings

Asymmetry is primarily governed by the ratio of on-axis current density to external field perturbation.

Hollow current-density profiles are crucial for achieving core asymmetry similar to edge conditions.

Analytical and numerical models confirm the importance of reverse magnetic shear for asymmetry.

Abstract

A local magnetic equilibrium solution is sought around the magnetic axis in order to identify the key parameters defining the magnetic-surface's up-down asymmetry in the core of tokamak plasmas. The asymmetry is found to be determined essentially by the ratio of the toroidal current density flowing on axis to the fraction of the external field's odd perturbation that manages to propagate from the plasma boundary into the core. The predictions are tested and illustrated first with an analytical Solovev equilibrium and then using experimentally relevant numerical equilibria. Hollow current-density distributions, and hence reverse magnetic shear, are seen to be crucial to bring into the core asymmetry values that are usually found only near the plasma edge.