Direct construction of optimized stellarator shapes. Part 3. Omnigenity near the magnetic axis

Plunk, G. G.; Landreman, Matt; Helander, P.

doi:10.1017/s002237781900062x

Cited by 31 publications

(107 citation statements)

References 19 publications

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“…We have argued recently Landreman, Sengupta & Plunk 2019;Jorge, Sengupta & Landreman 2020a) that this asymptotic approach deserves further attention, as it complements numerical optimization. The asymptotic approach allows equilibria to be evaluated orders of magnitude faster, and it provides a practical way to generate new initial conditions for numerical optimization Plunk, Landreman & Helander 2019). In the present paper, we extend our asymptotic approach, which has focused previously on neoclassical confinement, to MHD stability.…”

Section: Introductionmentioning

confidence: 98%

Magnetic well and Mercier stability of stellarators near the magnetic axis

Landreman

Jorge

2020

J. Plasma Phys.

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We have recently demonstrated that by expanding in small distance from the magnetic axis compared with the major radius, stellarator shapes with low neoclassical transport can be generated efficiently. To extend the utility of this new design approach, here we evaluate measures of magnetohydrodynamic interchange stability within the same expansion. In particular, we evaluate the magnetic well, Mercier's criterion, and resistive interchange stability near a magnetic axis of arbitrary shape. In contrast to previous work on interchange stability near the magnetic axis, which used an expansion of the flux coordinates, here we use the ‘inverse expansion’ in which the flux coordinates are the independent variables. Reduced expressions are presented for the magnetic well and stability criterion in the case of quasisymmetry. The analytic results are shown to agree with calculations from the VMEC equilibrium code. Finally, we show that near the axis, Glasser, Greene and Johnson's stability criterion for resistive modes approximately coincides with Mercier's ideal condition.

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Section: Introductionmentioning

confidence: 98%

Magnetic well and Mercier stability of stellarators near the magnetic axis

Landreman

Jorge

2020

J. Plasma Phys.

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“…'direct construction' of optimal solutions), is potentially beneficial due to the speedup offered (Landreman, Sengupta & Plunk 2019). So far, the only ways to do this have involved approximations to the problem such as a small distance from the magnetic axis (Garren & Boozer 1991a,b;Landreman & Sengupta 2018;Landreman et al 2019;Plunk, Landreman & Helander 2019), or a small deviation from axisymmetry (Plunk & Helander 2018). However, solving these approximate problems can also lead to fundamental insights into the properties of the solutions, and the size of the solution space.…”

Section: Introductionmentioning

confidence: 99%

Perturbing an axisymmetric magnetic equilibrium to obtain a quasi-axisymmetric stellarator

Plunk

2020

J. Plasma Phys.

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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.

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“…(2019) and Plunk et al. (2019). However, this approach of setting turns out to require modification when applied to the equations.…”

Section: Generating a Finite-minor-radius Boundarymentioning

confidence: 97%

“…The near-axis expansion, although it is an approximation, is always accurate in the core of any stellarator, even stellarators for which the aspect ratio of the outermost surface is not large. In a recent series of papers (Landreman & Sengupta 2018; Landreman, Sengupta & Plunk 2019; Plunk, Landreman & Helander 2019), the near-axis expansion was developed into practical procedures for constructing fields with quasisymmetry, or the more general condition of omnigenity. It was also shown that, close to the axis, quasisymmetric configurations obtained by conventional optimization closely match configurations generated by the construction (Landreman 2019).…”

Section: Introductionmentioning

confidence: 99%

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Constructing stellarators with quasisymmetry to high order

2019

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A method is given to rapidly compute quasisymmetric stellarator magnetic fields for plasma confinement, without the need to call a three-dimensional magnetohydrodynamic equilibrium code inside an optimization iteration. The method is based on direct solution of the equations of magnetohydrodynamic equilibrium and quasisymmetry using Garren and Boozer's expansion about the magnetic axis (Phys Fluids B 3, 2805 (1991)), and it is several orders of magnitude faster than the conventional optimization approach. The work here extends the method of Landreman, Sengupta and Plunk (J Plasma Phys 85, 905850103 (2019)), which was limited to flux surfaces with elliptical cross-section, to higher order in the aspect ratio expansion. As a result, configurations can be generated with strong shaping that achieve quasisymmetry to high accuracy. Using this construction, we give the first numerical demonstrations of Garren and Boozer's ideal scaling of quasisymmetry-breaking with the cube of inverse aspect ratio. We also demonstrate a strongly nonaxisymmetric configuration (vacuum ι > 0.4) in which symmetry-breaking mode amplitudes throughout a finite volume are < 2 × 10 −7 , the smallest ever reported. To generate boundary shapes of finite-minor-radius configurations, a careful analysis is given of the effect of substituting a finite minor radius into the near-axis expansion. The approach here can provide analytic insight into the space of possible quasisymmetric stellarator configurations, and it can be used to generate good initial conditions for conventional stellarator optimization. †

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Direct construction of optimized stellarator shapes. Part 3. Omnigenity near the magnetic axis

Cited by 31 publications

References 19 publications

Magnetic well and Mercier stability of stellarators near the magnetic axis

Magnetic well and Mercier stability of stellarators near the magnetic axis

Perturbing an axisymmetric magnetic equilibrium to obtain a quasi-axisymmetric stellarator

Constructing stellarators with quasisymmetry to high order

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