A nontwist field line mapping in a tokamak with ergodic magnetic limiter

TL;DR

This paper introduces an analytical nontwist magnetic field line map for tokamaks with arbitrary safety factor profiles, capturing complex phenomena like twin islands and shearless curves, extending previous models to more general conditions.

Contribution

It develops a new analytical nontwist map based on the Martin-Taylor map, applicable to tokamaks with non-monotonic safety factor profiles, revealing characteristic degenerate system properties.

Findings

The nontwist map exhibits twin islands and shearless curves.

Island widths and shapes vary with limiter current.

Shearless curve position depends on control parameters.

Abstract

For tokamaks with uniform magnetic shear, Martin and Taylor have proposed a symplectic map has been used to describe the magnetic field lines at the plasma edge perturbed by an ergodic magnetic limiter. We propose an analytical magnetic field line map, based on the Martin-Taylor map, for a tokamak with arbitrary safety factor profile. With the inclusion of a non-monotonic profile, we obtain a nontwist map which presents the characteristic properties of degenerate systems, as the twin islands scenario, the shearless curve and separatrix reconnection. We estimate the width of the islands and describe their changes of shape for large values of the limiter current. From our numerical simulations about the shearless curve, we show that its position and aspect depend on the control parameters.