A One-Dimensional Tearing Mode Equation for Pedestal Stability Studies in Tokamaks

TL;DR

This paper derives a one-dimensional tearing mode equation tailored for realistic tokamak pedestal conditions, enabling better analysis of stability influenced by steep profiles, bootstrap currents, and shaping effects.

Contribution

It introduces a simplified one-dimensional tearing mode model applicable to realistic tokamak equilibria near the separatrix, extending previous models to include more complex shaping effects.

Findings

The model captures the influence of steep profiles and bootstrap currents on tearing mode stability.

Comparison shows the model's assumptions are valid for certain tokamak configurations.

Provides a basis for future stability analysis in shaped, finite aspect ratio tokamaks.

Abstract

Starting from expressions in Connor et al. (1988) [1], we derive a one-dimensional tearing equation similar to the approximate equation obtained by Hegna and Callen (1984) [2] and by Nishimura et al (1998) [3], but for more realistic toroidal equilibria. The intention is to use this approximation to explore the role of steep profiles, bootstrap currents and strong shaping in the vicinity of a separatrix, on the stability of tearing modes which are resonant in the H-mode pedestal region of finite aspect ratio, shaped cross-section tokamaks, e.g. JET. We discuss how this one-dimensional model for tearing modes, which assumes a single poloidal harmonic for the perturbed poloidal flux, compares with a model that includes poloidal coupling by Fitzpatrick et al (1993) [4].