Analytic equilibrium of “straight tokamak” plasma bounded by a magnetic separatrix

Franco Porcelli,Adil Yolbarsop

doi:10.1063/1.5096838

Abstract

Theoretical and experimental considerations suggest that axisymmetric perturbations that are resonant at the X-point(s) of a magnetic divertor separatrix may play a role in the understanding of Edge Localized Modes in tokamak experiments and their active control via so-called vertical kicks. With this motivation in mind, the first step in the development of an analytical model for resistive axisymmetric X-point modes is presented, i.e., finding an adequate, but at the same time relatively simple analytical magnetohydrodynamic equilibrium for a plasma column with a noncircular cross section bound by a magnetic separatrix. An early example is Gajewski's equilibrium solution [R. Gajewski, Phys. Fluids 15, 70 (1972)], which, however, has the shortcoming that infinite external currents placed at an infinite distance from the X-points produce the elliptical elongation of the plasma column. In this article, Gajewski's solution is extended to the case where external currents are located at a finite distance from the boundary of the plasma current density and the latter is distributed uniformly over a domain bound by a nearly elliptical magnetic flux surface.

Highlights

Theoretical and experimental considerations suggest that axisymmetric perturbations that are resonant at the X-point(s) of a magnetic divertor separatrix may play a role in the understanding of Edge Localized Modes in tokamak experiments and their active control via socalled vertical kicks
With this motivation in mind, the first step in the development of an analytical model for resistive axisymmetric X-point modes is presented, i.e., finding an adequate, but at the same time relatively simple analytical magnetohydrodynamic equilibrium for a plasma column with a noncircular cross section bound by a magnetic separatrix
A puzzling experimental fact was the rather large shift of the strike points on divertor target plates observed during giant Edge Localized Modes (ELMs) in JET experiments

Summary

Introduction

Gajewski’s solution is extended to the case where external currents are located at a finite distance from the boundary of the plasma current density and the latter is distributed uniformly over a domain bound by a nearly elliptical magnetic flux surface. We are concerned with the first step in the development of an analytical model for resistive axisymmetric X-point modes, i.e., finding an adequate, but at the same time relatively simple analytical MHD equilibrium for a plasma column with a noncircular cross section bound by a magnetic separatrix.

Results

Conclusion