Misha Padidar

The non-resonant divertor (NRD) offers a promising exhaust solution for stellarators, combining topological simplicity with resilience to magnetic field perturbations. To experimentally validate the robustness of NRDs in a quasi-axisymmetric (QA) configuration, we introduce STAR_Lite, a new stellarator experiment at Hampton University. This paper details the design and analysis of the first STAR_Lite coil configuration, STAR_Lite-A. The two-field-period configuration manifests an NRD through X-points with zero rotational transform, at the top and bottom of the device. The divertor legs extruding from the X-points are topologically similar to the poloidal divertors of tokamaks. To expand the experimental range, STAR_Lite-A is optimised for experimental flexibility, producing a wide range of distinct QA configurations by only varying the currents in the modular coils. The NRDs not only persist across these configurations, but numerical strike-line simulations confirm that heat exhaust remains resilient to changes in coil currents, with plasma following the divertor legs and creating a toroidal, discontinuous, strike pattern. We further examine the resilience of the NRD to magnetic perturbations caused by manufacturing errors in the modular coils. We find that quasi-symmetry and the existence of X-points are well preserved under these magnetic field changes, but the rotational transform may vary substantially and displacements of the divertor X-points may lead to one X-point having a dominant effect on edge transport. Overall, our analysis indicates that a compact, modular design can likely generate a resilient NRD structure while satisfying the practical constraints of a university-scale experiment.

Due to their simultaneous optimization for radial and parallel neoclassical transport, quasi-isodynamic (QI) fields have been the main choice of stellarator magnetic configuration for most fusion reactor candidates in recent years. However, achieving a high degree of quasi-isodynamicity often comes at the cost of a strong shaping of the flux surfaces of the stellarator and complex coil geometries. In this work, the concepts of quasi-isodynamicity and piecewise omnigenity (pwO) are combined to form QI-pwO fields. These fields are QI in the low-field region of the magnetic surface, whereas they significantly depart from quasi-isodynamicity in the high-field region without sacrificing the neoclassical transport properties of QI fields. This departure could make it easier to integrate the optimization of neoclassical transport with other physical and technological aspects of a stellarator reactor.

In designing stellarators, any design decision ultimately comes with a trade-off. Improvements in particle confinement, for instance, may increase the burden on engineers to build more complex coils, and the tightening of financial constraints may simplify the design and worsen some aspects of transport. Understanding trade-offs in stellarator designs is critical in designing high performance devices that satisfy the multitude of physical, engineering and financial criteria. In this study, we show how multi-objective optimization (MOO) can be used to investigate trade-offs and develop insight into the role of design parameters. We discuss the basics of MOO, as well as practical solution methods for solving MOO problems. We apply these methods to bring insight into the selection of two common design parameters: the aspect ratio of an ideal magnetohydrodynamic equilibrium and the total length of the electromagnetic coils.

Confining energetic ions such as alpha particles is a prime concern in the design of stellarators. However, directly measuring alpha confinement through numerical simulation of guiding-center trajectories has been considered to be too computationally expensive and noisy to include in the design loop, and instead has been most often used only as a tool to assess stellarator designs post hoc. In its place, proxy metrics, simplified measures of confinement, have often been used to design configurations because they are computationally more tractable and have been shown to be effective. Despite the success of proxies, their correlation with direct trajectory calculations is known to be imperfect. In this study, we optimize stellarator designs for improved alpha particle confinement without the use of proxy metrics. In particular, we numerically optimize an objective function that measures alpha particle losses by simulating alpha particle trajectories. While this method is computationally expensive, we find that it can be used successfully to generate configurations with low losses.

In designing stellarators, any design decision ultimately comes with a trade-off. Improvements in particle confinement, for instance, may increase the burden on engineers to build more complex coils, and the tightening of financial constraints may simplify the design and worsen some aspects of transport. Understanding trade-offs in stellarator designs is critical in designing high performance devices that satisfy the multitude of physical, engineering, and financial criteria. In this study we show how multi-objective optimization (MOO) can be used to investigate trade-offs and develop insight into the role of design parameters. We discuss the basics of MOO, as well as practical solution methods for solving MOO problems. We apply these methods to bring insight into the selection of two common design parameters: the aspect ratio of an ideal magnetohydrodynamic equilibrium, and the total length of the electromagnetic coils.

We explore novel approaches for solving nonlinear optimization problems with unrelaxable bound constraints, which must be satisfied before the objective function can be evaluated. Our method reformulates the unrelaxable bound-constrained problem as an unconstrained optimization problem that is amenable to existing unconstrained optimization methods. The reformulation relies on a domain warping to form a merit function; the choice of the warping determines the level of exactness with which the unconstrained problem can be used to find solutions to the bound-constrained problem, as well as key properties of the unconstrained formulation such as smoothness. We develop theory when the domain warping is a multioutput sigmoidal warping, and we explore the practical elements of applying unconstrained optimization methods to the formulation. We develop an algorithm that exploits the structure of the sigmoidal warping to guarantee that unconstrained optimization algorithms applied to the merit function will find a stationary point to the desired tolerance.