Biquadratic Nontwist Map: a model for shearless bifurcations

TL;DR

This paper introduces a simple, symmetric area-preserving map as a model to study shearless bifurcations, phenomena important in physical systems like plasma confinement, and demonstrates its ability to replicate complex bifurcation scenarios.

Contribution

The paper derives a new, simple map that models shearless bifurcations, providing a clearer understanding of these phenomena in nontwist systems.

Findings

Multiple shearless curves are identified in the map.

The map reproduces shearless bifurcation scenarios observed in original models.

The model's symmetry and simplicity facilitate the study of shearless phenomena.

Abstract

Area-preserving nontwist maps are used to describe a broad range of physical systems. In those systems, the violation of the twist condition leads to nontwist characteristic phenomena, such as reconnection-collision sequences and shearless invariant curves that act as transport barriers in the phase space. Although reported in numerical investigations, the shearless bifurcation, i.e., the emergence scenario of multiple shearless curves, is not well understood. In this work, we derive an area-preserving map as a local approximation of a particle transport model for confined plasmas. Multiple shearless curves are found in this area-preserving map, with the same shearless bifurcation scenario numerically observed in the original model. Due to its symmetry properties and simple functional form, this map is proposed as a model to study shearless bifurcations.