相关论文: Adjoint methods for quasisymmetry of vacuum fields…

Optimising stellarators for quasisymmetry leads to strongly reduced collisional transport and energetic particle losses compared to unoptimised configurations. Though stellarators with precise quasisymmetry have been obtained in the past,…

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…

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…

Stellarators are a promising route to steady-state fusion power. However, to achieve the required confinement, the magnetic geometry must be highly optimized. This optimization requires navigating high-dimensional spaces, often…

For a given {\it misfit function}, a specified optimality measure of a model, its gradient describes the manner in which one may alter properties of the system to march towards a stationary point. The adjoint method, arising from…

A continuous system of moment equations is introduced that models the transverse dynamics of a beam of charged particles as it passes through an arbitrary lattice of quadrupoles and solenoids in the presence of self-fields. Then, figures of…

The auxiliary field method is a technique to obtain approximate closed formulae for the solutions of both nonrelativistic and semirelativistic eigenequations in quantum mechanics. For a many-body Hamiltonian describing identical particles,…

While several results have pointed to the existence of exactly quasisymmetric fields on a surface (Garren & Boozer 1991a,b; Plunk & Helander 2018), we have obtained the first such solutions using a vacuum surface expansion formalism. We…

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…

A method is demonstrated to optimize a stellarator's geometry to eliminate magnetic islands and achieve other desired physics properties at the same time. For many physics quantities that have been used in stellarator optimization,…

Adjoint variable method in combination with gradient descent optimization has been widely used for the inverse design of nanophotonic devices. In many of such optimizations, the design region is only a small fraction of the total…

Quasisymmetric stellarators are appealing intellectually and as fusion reactor candidates since the guiding center particle trajectories and neoclassical transport are isomorphic to those in a tokamak, implying good confinement. Previously,…

The adjoint method is an efficient way to numerically compute gradients in optimization problems with constraints, but is only formulated to differentiable cost and constraint functions on real variables. With the introduction of complex…

This paper presents a novel computational scheme for sensitivity analysis of the velocity field in the level set method using the discrete adjoint method. The velocity field is represented in B-spline space, and the adjoint equations are…

In this article we consider an optimization problem where the objective function is evaluated at the fixed-point of a contraction mapping parameterized by a control variable, and optimization takes place over this control variable. Since…

As more and more multiphysics effects are entering the field of CFD simulations, this raises the question how they can be accurately captured in gradient computations for shape optimization. The latter has been successfully enriched over…

A new technique for approximating eigenvalues and eigenvectors of a self-adjoint operator is presented. The method does not incur spectral pollution, uses trial spaces from the form domain, has a self-adjoint algorithm, and exhibits…

Adjoint methods form a class of importance sampling methods that are used to accelerate Monte Carlo (MC) simulations of transport equations. Ideally, adjoint methods allow for zero-variance MC estimators provided that the solution to an…

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…

Quasi-symmetry of a steady magnetic field means integrability of first-order guiding-centre motion. Here we derive many restrictions on the possibilities for a quasi-symmetry. We also derive an analogue of the Grad-Shafranov equation for…