Related papers: Computing local sensitivity and tolerances for ste…
Coil complexity is a critical consideration in stellarator design. The traditional two-step optimization approach, in which the plasma boundary is optimized for physics properties and the coils are subsequently optimized to be consistent…
The shape gradient is a local sensitivity function that provides the change in a figure of merit associated with a perturbation to the shape of the object. The shape gradient can be used for gradient-based optimization, sensitivity…
The design of a stellarator with acceptable confinement properties requires optimization of the magnetic field in the non-convex, high-dimensional spaces describing their geometry. Another major challenge facing the stellarator program is…
In fusion reactor design, steels under consideration for the blanket are ferromagnetic, so the steel's effect on the plasma physics must be examined. For efficient calculation of these fields, we can exploit the fact that the magnetic…
The shape gradient quantifies the change in some figure of merit resulting from differential perturbations to a shape. Shape gradients can be applied to gradient-based optimization, sensitivity analysis, and tolerance calculation. An…
This study proposes a versatile and efficient optimisation method for discrete coils that induce a magnetic field by their steady currents. The prime target is gradient coils for MRI (Magnetic Resonance Imaging). The derivative (gradient)…
We present a method for stellarator coil design via gradient-based optimization of the coil-winding surface. The REGCOIL (Landreman 2017 Nucl. Fusion 57 046003) approach is used to obtain the coil shapes on the winding surface using a…
Using recently developed adjoint methods for computing the shape derivatives of functions that depend on MHD equilibria (Antonsen et al. 2019; Paul et al. 2020), we present the first example of analytic gradient-based optimization of…
Stellarators confine fusion plasmas using three-dimensional magnetic fields composed of nested toroidal magnetic surfaces. In generic stellarators, trapped particles can drift across these surfaces and degrade plasma confinement. Certain…
In the construction of a stellarator, the manufacturing and assembling of the coil system is a dominant cost. These coils need to satisfy strict engineering tolerances, and if those are not met the project could be canceled as in the case…
Access to the plasma chamber in a stellarator reactor is essential for maintenance and diagnostics. However, the complex geometry of stellarator coils, often characterized by their strong twisting, can severely limit the space available for…
This paper describes a new and efficient method of defining an annular region of a curl-free magnetic field with specific physics and coil properties that can be used in stellarator design. Three statements define the importance: (1) Codes…
Shape calculus concerns the calculation of directional derivatives of some quantity of interest, typically expressed as an integral. This article introduces a type of shape calculus based on localized dilation of boundary faces through…
It was recently shown in [Wechsung et. al., Proc. Natl. Acad. Sci. USA, 2022] that there exist electromagnetic coils that generate magnetic fields which are excellent approximations to quasi-symmetric fields and have very good particle…
In stellarator optimization studies, the boundary of the plasma is usually described by Fourier series that are not unique: several sets of Fourier coefficients describe approximately the same boundary shape. A simple method for eliminating…
Calibration of large-scale differential equation models to observational or experimental data is a widespread challenge throughout applied sciences and engineering. A crucial bottleneck in state-of-the art calibration methods is the…
The magnetic field that supports tokamak and stellarator plasmas must be produced by coils well separated from the plasma. However the larger the separation, the more difficult it is to produce a given magnetic field in the plasma region,…
This article deals with a particular class of shape and topology optimization problems: the optimized design is a region $G$ of the boundary $\partial \Omega$ of a given domain $\Omega$, which supports a particular type of boundary…
The reduction of magnetic forces on electromagnetic coils is an important consideration in the design of high-field devices such as the stellarator or tokamak. Unfortunately, these forces may be too time-consuming to evaluate by…
In this paper we investigate and compare different gradient algorithms designed for the domain expression of the shape derivative. Our main focus is to examine the usefulness of kernel reproducing Hilbert spaces for PDE constrained shape…