Symplectic Maps for Diverted Plasmas

TL;DR

This paper develops analytical symplectic maps to model magnetic field lines in diverted tokamaks, aiding understanding of plasma confinement and edge chaos with potential experimental relevance.

Contribution

It introduces new symplectic maps for diverted plasmas, including a divertor map, tokamap, Ullmann map, and an explicit integrable magnetic field line map, linking theory with experimental parameters.

Findings

Derived area-preserving maps for diverted plasma configurations.

Demonstrated onset of chaotic field lines at plasma edge.

Linked magnetic surface models with experimental control parameters.

Abstract

Nowadays, divertors are used in the main tokamaks to control the magnetic field and to improve the plasma confinement. In this article, we present analytical symplectic maps describing Poincar\'e maps of the magnetic field lines in confined plasmas with a single null poloidal divertor. Initially, we present a divertor map and the tokamap for a diverted configuration. We also introduce the Ullmann map for a diverted plasma, whose control parameters are determined from tokamak experiments. Finally, an explicit, area-preserving and integrable magnetic field line map for a single-null divertor tokamak is obtained using a trajectory integration method to represent toroidal equilibrium magnetic surfaces. In this method, we also give examples of onset of chaotic field lines at the plasma edge due to resonant perturbations.