Generalised ballooning theory of two dimensional tokamak modes

TL;DR

This paper develops a comprehensive analytical framework called the generalized ballooning theory (GBT) to describe various global modes in tokamak plasmas, including their behavior under sheared flow, with implications for plasma stability and intrinsic rotation.

Contribution

The paper introduces the GBT that unifies different ballooning mode limits and analyzes their behavior under flow, advancing understanding of tokamak mode structures and plasma rotation.

Findings

Isolated mode (IM) can transform into a mixed mode (MM) and then into a general mode (GM) with increasing flow.

The theory explains the transition of mode structures under flow, relevant to ELM behavior.

Global mode structures influence intrinsic rotation through Reynolds stress.

Abstract

In this work, using solutions from a local gyrokinetic flux-tube code combined with higher order ballooning theory, a new analytical approach is developed to reconstruct the global linear mode structure with associated global mode frequency. In addition to the isolated mode (IM), which usually peaks on the outboard mid-plane, the higher order ballooning theory has also captured other types of less unstable global modes: (a) the weakly asymmetric ballooning theory (WABT) predicts a mixed mode (MM) that undergoes a small poloidal shift away from the outboard mid-plane, (b) a relatively more stable general mode (GM) balloons on the top (or bottom) of the tokamak plasma. In this paper, an analytic approach is developed to combine these disconnected analytical limits into a single generalised ballooning theory (GBT). This is used to investigate how an IM behaves under the effect of sheared toroidal flow. For small values of flow an IM initially converts into a MM where the results of WABT are recaptured, and eventually, as the flow increases, the mode asymptotically becomes a GM on the top (or bottom) of the plasma. This may be an ingredient in models for understanding why in some experimental scenarios, instead of large edge localised modes (ELMs), small ELMs are observed. Finally, our theory can have other important consequences, especially for calculations involving Reynolds stress driven intrinsic rotation through the radial asymmetry in the global mode structures. Understanding the intrinsic rotation is significant because external torque in a plasma the size of ITER is expected to be relatively low.