The case of the trapped singularities

A case study in bifurcation and stability analysis is presented, in which reduced dynamical system modelling yields substantial new global and predictive information about the behaviour of a complex system. The first smooth pathway, free of pathological and persistent degenerate singularities, is surveyed through the parameter space of a nonlinear dynamical model for a gradient-driven, turbulence-shear flow energetics in magnetized fusion plasmas. Along the route various obstacles and features are identified and treated appropriately. An organizing centre of low codimension is shown to be robust, several trapped singularities are found and released, and domains of hysteresis, threefold stable equilibria, and limit cycles are mapped. Characterization of this rich dynamical landscape achieves unification of previous disparate models for plasma confinement transitions, supplies valuable intelligence on the big issue of shear flow suppression of turbulence, and suggests targeted experimental design, control and optimization strategies.Comment: 21 pages, 12 figures, 34 postscript figure file

1997 international Sherwood fusion theory conference

Papers presented during the conference are indexed separately

GENE-3D - ein globaler gyrokinetischer Turbulenzcode für Stellaratoren und gestörte Tokamaks

This thesis describes the development and application of GENE-3D, a global gyrokinetic turbulence HPC code for stellarators. The gyrokinetic equations as well as their implementation and the use of field-aligned coordinates in non-axisymmetric geometries are discussed. GENE-3D is benchmarked for validity and performance. Different geometries of Wendelstein 7-X are investigated for their influence on turbulent properties. Also the influence of the machine size on linear growth rates is studied.Diese Arbeit beschreibt die Entwicklung und Anwendung von GENE-3D, ein globaler gyrokinetischer Turbulenzcode für Stellaratoren. Die gyrokinetischen Gleichungen sowie deren Implementierung und das am Feld ausgerichtete Koordinatensystem werden für nicht-axisymmetrische Geometrien vorgestellt. GENE-3D wird auf Korrektheit getestet.Der Einfluß unterschiedlicher Wendelstein 7-X Geometrien auf den turbulenten Transport und der Einfluß der Maschinengröße auf die linearen Anwachsraten wird untersucht

The JOREK non-linear extended MHD code and applications to large-scale instabilities and their control in magnetically confined fusion plasmas

JOREK is a massively parallel fully implicit non-linear extended magneto-hydrodynamic (MHD) code for realistic tokamak X-point plasmas. It has become a widely used versatile simulation code for studying large-scale plasma instabilities and their control and is continuously developed in an international community with strong involvements in the European fusion research programme and ITER organization. This article gives a comprehensive overview of the physics models implemented, numerical methods applied for solving the equations and physics studies performed with the code. A dedicated section highlights some of the verification work done for the code. A hierarchy of different physics models is available including a free boundary and resistive wall extension and hybrid kinetic-fluid models. The code allows for flux-surface aligned iso-parametric finite element grids in single and double X-point plasmas which can be extended to the true physical walls and uses a robust fully implicit time stepping. Particular focus is laid on plasma edge and scrape-off layer (SOL) physics as well as disruption related phenomena. Among the key results obtained with JOREK regarding plasma edge and SOL, are deep insights into the dynamics of edge localized modes (ELMs), ELM cycles, and ELM control by resonant magnetic perturbations, pellet injection, as well as by vertical magnetic kicks. Also ELM free regimes, detachment physics, the generation and transport of impurities during an ELM, and electrostatic turbulence in the pedestal region are investigated. Regarding disruptions, the focus is on the dynamics of the thermal quench (TQ) and current quench triggered by massive gas injection and shattered pellet injection, runaway electron (RE) dynamics as well as the RE interaction with MHD modes, and vertical displacement events. Also the seeding and suppression of tearing modes (TMs), the dynamics of naturally occurring TQs triggered by locked modes, and radiative collapses are being studied.Peer ReviewedPostprint (published version