Phases and phase-transitions in quasisymmetric configuration space

Abstract

We explore the structure of the space of quasisymmetric configurations identifying them by their magnetic axes, described as 3D closed curves. We demonstrate that this topological perspective divides the space of all configurations into well-separated quasisymmetric phases. Each phase is characterized by the self-linking number (a topological invariant), defining different symmetry configurations (quasi-axisymmetry or quasi-helical symmetry). The phase-transition manifolds correspond to quasi-isodynamic configurations. By considering some models for closed curves (most notably torus unknots), general features associated with these phases are explored. Some general criteria are also built and leveraged to provide a simple way to describe existing quasisymmetric designs. This constitutes the first step in a program to identify quasisymmetric configurations with a reduced set of functions and parameters, to deepen understanding of configuration space, and offer an alternative approach to stellarator optimization that begins with the magnetic axis and builds outward.

References in corpus (8)

• Magnetic fields with precise quasisymmetry for plasma confinement
• Necessary and Sufficient Conditions for Quasisymmetry
• Measures of quasisymmetry for stellarators
• Solving the problem of overdetermination of quasisymmetric equilbrium solutions by near-axis expansions: I. Generalised force balance
• Solving the problem of overdetermination of quasisymmetric equilbrium solutions by near-axis expansions. II. Circular axis stellarators
• Generalized Boozer coordinates: a natural coordinate system for quasisymmetry
• Approximate symmetries of guiding-centre motion
• Islands and current singularities in quasisymmetric toroidal plasmas

Cited by in corpus (11)

• Mapping the space of quasisymmetric stellarators using optimized near-axis expansion
• Direct stellarator coil design using global optimization: application to a comprehensive exploration of quasi-axisymmetric devices
• Constructing the space of quasisymmetric stellarators
• MHD stability and the effects of shaping: a near-axis view for tokamaks and quasisymmetric stellarators
• Higher order theory of quasi-isodynamicity near the magnetic axis of stellarators
• Stellarator coil optimization supporting multiple magnetic configurations
• Exploration of the parameter space of quasisymmetric stellarator vacuum fields through adjoint optimisation
• Collisionless zonal-flow dynamics in quasisymmetric stellarators
• The zonal-flow residual does not tend to zero in the limit of small mirror ratio
• Optimization of quasisymmetric stellarators with self-consistent bootstrap current and energetic particle confinement
• Near-axis quasi-isodynamic database