ESTELL: A Quasi‐Toroidally Symmetric Stellarator

Drevlak, M.; Brochard, F.; Helander, P.; Kißlinger, J.; Михайлов, М. И.; Nührenberg, C.; Nührenberg, J.; Turkin, Y.

doi:10.1002/ctpp.201200055

Cited by 44 publications

(53 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…(The ι profile for QAS2 given in [14] implies a nonzero current on axis; we use a configuration with slightly shifted current profile in which the on-axis current density vanishes.) The ESTELL configuration [15], also discussed in section 6 of [16], is shown in figure 8. A free-boundary β = 0 configuration of the Chinese First Quasi-axisymmetric Stellarator (CFQS) [17,18] is shown in figure 9.…”

Section: Methods and Resultsmentioning

confidence: 99%

See 1 more Smart Citation

Optimized quasisymmetric stellarators are consistent with the Garren–Boozer construction

Landreman

2019

Plasma Phys. Control. Fusion

View full text Add to dashboard Cite

Most quasisymmetric stellarators to date have been designed by numerically optimizing the plasma boundary shape to minimize symmetrybreaking Fourier modes of the magnetic field strength B. At high aspect ratio, a faster approach is to directly construct the plasma shape from the equations of quasisymmetry near the magnetic axis derived by Garren and Boozer [Phys Fluids B 3, 2805]. Here we show that the core shape and rotational transform of many optimization-based configurations can be accurately described by this direct-construction approach. This consistency supports use of the near-axis construction as an accurate analytical model for modern stellarator configurations.

show abstract

Section: Methods and Resultsmentioning

confidence: 99%

“…Shapes of the magnetic surfaces at ρ = √ s = 0.1 and 0.2 for ESTELL[15,16] (dark dashed curves) at 8 toroidal locations, and the same surfaces of the corresponding direct-construction quasisymmetric configuration (solid curves).…”

mentioning

confidence: 99%

Optimized quasisymmetric stellarators are consistent with the Garren–Boozer construction

Landreman

2019

Plasma Phys. Control. Fusion

View full text Add to dashboard Cite

show abstract

“…This condition places an important upper bound on the field strength achievable by arranging the magnets according to this method. We now turn to a concrete example, an optimized stellarator configuration published a few years ago [6], which was orginally obtained by deforming a classical l = 2 stellarator with aspect ratio A = 5 into a shape that makes the magnetic field quasi-axisymmetric. (This means that the field strength is nearly independent of the toroidal angle in Boozer or Hamada coordinates, which ensures good orbit confinement [7][8][9].)…”

mentioning

confidence: 99%

“…Magnetic-field coils and plasma boundary for ES-TELL, a two-period quasisymmetric stellarator[6]. The 8 coils are all identical and circular.…”

mentioning

confidence: 99%

Stellarators with Permanent Magnets

et al. 2020

Self Cite

View full text Add to dashboard Cite

It is shown that the magnetic-field coils of a stellarator can, at least in principle, be substantially simplified by the use of permanent magnets. Such magnets cannot create toroidal magnetic flux but they can be used to shape the plasma and thus to create poloidal flux and rotational transform, thereby easing the requirements on the magnetic-field coils. As an example, a quasiaxisymmetric stellarator configuration is constructed with only 8 circular coils (all identical) and permanent magnets.Stellarators, tokamaks and other devices for fusion plasma confinement use electromagnets to create the magnetic field. In the case of stellarators, the required magnetic-field coils can be very complicated and contribute significantly to the overall cost of the device [2]. In the present Letter, we suggest that permanent magnets could be used to shape the plasma and drastically simplify the coils. Our emphasis is on mathematical aspects of this problem whereas other issues are discussed in a companion paper [1].A magnetic field B tracing out toroidal surfaces can never be created by permanent magnets alone, because it follows from Ampère's law that the loop integral of the magnetic field taken once toroidally around the torus is proportional to the linked current of free charges,This conclusion follows from one of Maxwell's equations,if the integration contour C is chosen to lie within the plasma, where the magnetization M vanishes. In other words, permanent magnets cannot create a net toroidal magnetic flux, but they can (perhaps surprisingly) create poloidal flux and thus twist the magnetic field lines in a stellarator (though not in an axisymmetric device such as tokamak).To see how this can be accomplished, we write the magnetic field as a sumrepresents the field created by coils and B m that from the permanent magnets. The magnetization M vanishes outside a bounded domain Ω but is generally finite on the boundary ∂Ω and produces a magnetic fieldwhere n is the unit vector pointing outward from Ω. Our aim is to find a magnetization field M that creates a desired magnetic field B m within the plasma region, which we denote by P . Since many different choices of M produce the same magnetic field, the solution is not unique and there is considerable freedom to find the simplest one. One way to solve the problem is to reduce it to one already routinely solved in stellarator design. This problem was first described by Merkel [3] and proceeds from the observation that the magnetic field within the plasma is uniquely determined by the shape of the plasma boundary ∂P and the current and pressure profiles within the plasma [4]. Suppose, therefore, that a desired plasma surface ∂P is prescribed and consider the problem of finding the surface current K = n × ∇Φ(2) on another toroidal surface ∂D, some distance from the plasma, that creates a magnetic field tangential to ∂P . In the method of Merkel, this is done by choosing the scalar function Φ on ∂D so as to minimize the surface integral ∂P |n · B| 2 dS.(This problem is ill-pose...

show abstract

“…Recent examples of such use include [10][11][12][13][14]. Second, the convergence of a nonlinear coil optimizer is expedited by using a good initial guess for the coil shapes, and NESCOIL has been used to provide this initial condition [12]. Third, NESCOIL is sometimes called in the first stage of plasma optimization, to guide the fixed-boundary plasma optimization towards configurations consistent with realistic coils [15].…”

Section: Introductionmentioning

confidence: 99%

An improved current potential method for fast computation of stellarator coil shapes

Landreman

2017

Nucl. Fusion

133

View full text Add to dashboard Cite

Several fast methods for computing stellarator coil shapes are compared, including the classical NESCOIL procedure [Merkel, Nucl. Fusion 27, 867 (1987)], its generalization using truncated singular value decomposition, and a Tikhonov regularization approach we call REGCOIL in which the squared current density is included in the objective function. Considering W7-X and NCSX geometries, and for any desired level of regularization, we find the REGCOIL approach simultaneously achieves lower surface-averaged and maximum values of both current density (on the coil winding surface) and normal magnetic field (on the desired plasma surface). This approach therefore can simultaneously improve the free-boundary reconstruction of the target plasma shape while substantially increasing the minimum distances between coils, preventing collisions between coils while improving access for ports and maintenance. The REGCOIL method also allows finer control over the level of regularization, it preserves convexity to ensure the local optimum found is the global optimum, and it eliminates two pathologies of NESCOIL: the resulting coil shapes become independent of the arbitrary choice of angles used to parameterize the coil surface, and the resulting coil shapes converge rather than diverge as Fourier resolution is increased. We therefore contend that REGCOIL should be used instead of NESCOIL for applications in which a fast and robust method for coil calculation is needed, such as when targeting coil complexity in fixed-boundary plasma optimization, or for scoping new stellarator geometries.

show abstract

ESTELL: A Quasi‐Toroidally Symmetric Stellarator

Cited by 44 publications

References 8 publications

Optimized quasisymmetric stellarators are consistent with the Garren–Boozer construction

Optimized quasisymmetric stellarators are consistent with the Garren–Boozer construction

Stellarators with Permanent Magnets

An improved current potential method for fast computation of stellarator coil shapes

Contact Info

Product

Resources

About