Abstract
It is demonstrated that finite-pressure, approximately quasi-axisymmetric stellarator equilibria can be directly constructed (without numerical optimization) via perturbations of given axisymmetric equilibria. The size of such perturbations is measured in two ways, via the fractional external rotation and, alternatively, via the relative magnetic field strength, i.e. the average size of the perturbed magnetic field, divided by the unperturbed field strength. It is found that significant fractional external rotational transform can be generated by quasi-axisymmetric perturbations, with a similar value of the relative field strength, despite the fact that the former scales more weakly with the perturbation size. High mode number perturbations are identified as a candidate for generating such transform with local current distributions. Implications for the development of a general non-perturbative solver for optimal stellarator equilibria are discussed.
Highlights
Quasi-symmetry is a property of magnetic fields that ensures the confinement of collisionless particle orbits
The close relationship between axisymmetry and QAS suggests that the second class may be continuously connected to the first, and in particular that QAS stellarators may be obtained by deformation of axisymmetric equilibria (Boozer 2008)
It has been suggested that modifying tokamak equilibria by non-axisymmetric shaping might help overcome the stability issues that plague them, and a previous study, using conventional numerical optimization, has demonstrated that suitable QAS may be found as deformed tokamak equilibria (Ku & Boozer 2009)
Summary
Quasi-symmetry is a property of magnetic fields that ensures the confinement of collisionless particle orbits. In a previous paper (Plunk & Helander 2018), it was proved that nearly axisymmetric magnetic fields can be constructed to satisfy the condition of quasi-axisymmetry on a single magnetic surface. These solutions, apply only to vacuum conditions, where the plasma itself does not contribute significantly to the magnetic field. This, as we find, gives evidence that the same problem as solved in the vacuum limit by Plunk & Helander (2018), namely the problem of finding a perturbation of specified toroidal mode number N that satisfies the condition of QAS on a single magnetic surface, is well posed, at least in some practical sense. The VMEC (Hirshman & Whitson 1983) and BOOZ_XFORM (Sanchez et al 2000) codes are used to demonstrate that the solutions can satisfy the appropriate level of QAS as predicted by the theory
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