Diffusion wall time in toroidally segmented shell aka Armadillo

TL;DR

This paper derives an analytical formula for the diffusion wall time of a segmented toroidal shell, accounting for non-axisymmetric currents and segmentation effects, validated against numerical simulations.

Contribution

It extends the continuous-shell model to include segmentation effects, providing a practical formula for estimating wall time in segmented conducting structures.

Findings

Analytical formula agrees within 10% with 3D numerical calculations.

Segmentation reduces wall time more significantly for low-n modes.

The formula helps estimate MHD stability and control in fusion devices.

Abstract

An analytical expression for the diffusion wall time of a toroidally segmented conducting shell (the Armadillo configuration) is derived by extending the continuous-shell formulation to include the non-axisymmetric current pattern imposed by the presence of toroidal gaps. The segmentation constrains the toroidal current to follow a standing-wave structure that vanishes at the gap locations, introducing a correction to the effective resistivity that grows quadratically with the number of gaps and competes with the intrinsic toroidal scale of the mode. As a result, the wall time decreases rapidly for low toroidal-number modes, more gradually for intermediate ones, and only for sufficiently large segmentation in the high-n regime. The analytical formula shows agreement within 10% against 3D electromagnetic numerical calculations. The resulting expression provides a compact tool for estimating the wall time of segmented conducting structures surrounding the plasma, with direct applications to MHD stability and control in both RFPs and tokamaks.