Solving the problem of overdetermination of quasisymmetric equilbrium solutions by near-axis expansions: I. Generalised force balance
arXiv:2008.04715 · doi:10.1063/5.0027574
Abstract
It is well known that the process of construction of quasisymmetric magnetic fields in magnetostatic equilibrium with isotropic pressure suffers from the problem of overdetermination. This has led to the widespread belief that global quasisymmetric solutions are likely not to exist. We develop a general near-axis expansion procedure that does not rely on the assumption of magnetostatic equilibria with isotropic pressure. We then demonstrate that in equilibria with anisotropic pressure, it is possible to circumvent the problem of overdetermination and carry out the power-series solutions to higher order. This suggests, contrary to current belief, that the existence of globally quasisymmetric fields is likely if one relaxes the assumption of magnetostatic equilibria with isotropic pressure.
References in corpus (7)
- Properties of a new quasi-axisymmetric configuration
- Direct construction of optimized stellarator shapes. I. Theory in cylindrical coordinates
- Constructing stellarators with quasisymmetry to high order
- Direct construction of optimized stellarator shapes. II. Numerical quasisymmetric solutions
- Necessary and Sufficient Conditions for Quasisymmetry
- Quasi-axisymmetric magnetic fields: weakly non-axisymmetric case in a vacuum
- Near-Axis Expansion of Stellarator Equilibrium at Arbitrary Order in the Distance to the Axis
Cited by in corpus (15)
- The DESC Stellarator Code Suite Part III: Quasi-symmetry optimization
- Measures of quasisymmetry for stellarators
- Phases and phase-transitions in quasisymmetric configuration space
- Permanent magnet optimization for stellarators as sparse regression
- 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
- Generalized Boozer coordinates: a natural coordinate system for quasisymmetry
- Vacuum magnetic fields with exact quasisymmetry near a flux surface. Part 1: Solutions near an axisymmetric surface
- Islands and current singularities in quasisymmetric toroidal plasmas
- Adjoint methods for quasisymmetry of vacuum fields on a surface
- Existence of weakly quasisymmetric magnetic fields in asymmetric toroidal domains with non-tangential quasisymmetry
- Connection between quasi-symmetric magnetic fields and anisotropic pressure equilibria in fusion plasmas
- Quasisymmetric magnetic fields in asymmetric toroidal domains
- Weakly Quasisymmetric Near-Axis Solutions to all Orders