353 research outputs found
Generalised action-angle coordinates defined on island chains
Straight-field-line coordinates are very useful for representing magnetic
fields in toroidally confined plasmas, but fundamental problems arise regarding
their definition in 3-D geometries because of the formation of islands and
chaotic field regions, ie non-integrability. In Hamiltonian dynamical systems
terms these coordinates are a form of action-angle variables, which are
normally defined only for integrable systems. In order to describe 3-D magnetic
field systems, a generalisation of this concept was proposed recently by the
present authors that unified the concepts of ghost surfaces and
quadratic-flux-minimising (QFMin) surfaces. This was based on a simple
canonical transformation generated by a change of variable , where and are poloidal and toroidal
angles, respectively, with a new poloidal angle chosen to give
pseudo-orbits that are a) straight when plotted in the plane and
b) QFMin pseudo-orbits in the transformed coordinate. These two requirements
ensure that the pseudo-orbits are also c) ghost pseudo-orbits. In the present
paper, it is demonstrated that these requirements do not \emph{uniquely}
specify the transformation owing to a relabelling symmetry. A variational
method of solution that removes this lack of uniqueness is proposed.Comment: 10 pages. Accepted by Plasma Physics and Controlled Fusion as part of
a cluster of refereed papers in a special issue containing papers arising
from the Joint International Stellarator & Heliotron Workshop and
Asia-Pacific Plasma Theory Conference, held in Canberra and Murramarang
Resort, Australia, 30 January - 3 February, 201
Multi-region relaxed magnetohydrodynamics with anisotropy and flow
We present an extension of the multi-region relaxed magnetohydrodynamics
(MRxMHD) equilibrium model that includes pressure anisotropy and general plasma
flows. This anisotropic extension to our previous isotropic model is motivated
by Sun and Finn's model of relaxed anisotropic magnetohydrodynamic equilibria.
We prove that as the number of plasma regions becomes infinite, our anisotropic
extension of MRxMHD reduces to anisotropic ideal MHD with flow. The
continuously nested flux surface limit of our MRxMHD model is the first
variational principle for anisotropic plasma equilibria with general flow
fields.Comment: 11 pages, 2 figures. arXiv admin note: text overlap with
arXiv:1401.307
Relaxed plasma equilibria and entropy-related plasma self-organization principles
The concept of plasma relaxation as a constrained energy minimization is reviewed. Recent work by the authors on generalizing this approach to partially relaxed threedimensional plasma systems in a way consistent with chaos theory is discussed, with a view to clarifying the thermodynamic aspects of the variational approach used. Other entropy-related approaches to finding long-time steady states of turbulent or chaotic plasma systems are also briefly reviewed
Minimally Constrained Model of Self-Organized Helical States in Reversed-Field Pinches
We show that the self-organized single-helical-axis (SHAx) and double-axis (DAx) states in reversed field pinches can be reproduced in a minimally constrained equilibrium model using only five parameters. This is a significant reduction on previous repre
Identification of important error fields in stellarators using the Hessian matrix method
Error fields are predominantly attributed to inevitable coil imperfections. Controlling error fields during coil fabrication and assembly is crucial for stellarators. Excessively tight coil tolerance increases time and cost, and, in part, led to the cancellation of the National Compact Stellarator Experiment and delay of W7-X. In this paper, we improve the recently proposed Hessian matrix method to rapidly identify important coil deviations. Two of the most common figures of merit, magnetic island size and quasi-symmetry, are analytically differentiated over coil parameters. By extracting the eigenvectors of the Hessian matrix, we can directly identify sensitive coil deviations in the order of the eigenvalues. The new method is applied to the upcoming Chinese First Quasi-axisymmetric Stellarator configuration. Important perturbations that enlarge n/m  =  4/11 islands and deteriorate quasi-axisymmetry of the magnetic field are successfully determined. The results suggest each modular coil should have separate tolerance and some certain perturbation combinations will produce significant error fields. By relaxing unnecessary coil tolerance, this method will hopefully lead to a substantial reduction in time and cost
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