The shear Alfvén wave (SAW) continuum plays a critical role in the stability of energetic particle-driven Alfvén eigenmodes. We develop a theoretical framework to analyze the SAW continuum in three-dimensional (3-D) quasisymmetric magnetic fields, focusing on its implications for stellarator design. By employing a near-axis model and degenerate perturbation theory, the continuum equation is solved, highlighting unique features in 3-D configurations, such as the interactions between spectral gaps. Numerical examples validate the theory, demonstrating the impact of flux-surface shaping and quasisymmetric field properties on continuum structure. The results provide insights into optimizing stellarator configurations to minimize resonance-driven losses of energetic particles. This work establishes a basis for incorporating Alfvénic stability considerations into the stellarator design process, demonstrated through optimization of a quasihelical configuration to avoid high-frequency spectral gaps.

The DESC stellarator optimization code takes advantage of advanced numerical methods to search the full parameter space much faster than conventional tools. Only a single equilibrium solution is needed at each optimization step thanks to automatic differentiation, which efficiently provides exact derivative information. A Gauss–Newton trust-region optimization method uses second-order derivative information to take large steps in parameter space and converges rapidly. With just-in-time compilation and GPU portability, high-dimensional stellarator optimization runs take orders of magnitude less computation time with DESC compared to other approaches. This paper presents the theory of the DESC fixed-boundary local optimization algorithm along with demonstrations of how to easily implement it in the code. Example quasi-symmetry optimizations are shown and compared to results from conventional tools. Three different forms of quasi-symmetry objectives are available in DESC, and their relative advantages are discussed in detail. In the examples presented, the triple product formulation yields the best optimization results in terms of minimized computation time and particle transport. This paper concludes with an explanation of how the modular code suite can be extended to accommodate other types of optimization problems.

Good fast ion confinement in quasi-isodynamic stellarators still has to be demonstrated experimentally. In the absence of fusion alphas, auxiliary heating systems can be used to generate fast ions. For this purpose, W7-X has neutral beam injection and its newly installed ion cyclotron heating system. In practice, both systems can run simultaneously, the synergetic running of both is the focus of the current modelling development. With the upgrades to the SCENIC code described here, we find that, compared with pure neutral beam injection (NBI), the fast ion tail is significantly enhanced when radio frequency (RF) heating is enabled. But the effectiveness of heating and fast ion tail generation strongly depends on the plasma parameters and antenna frequency, which calls for further study, both numerical and experimental.

We present orbit classification schemes for use as fast metrics for fusion alpha particle losses implemented in the symplectic guiding-centre code SIMPLE. Two variants respectively based on conservation of the parallel adiabatic invariant, and topology of footprints in Poincaré sections are introduced. Like an existing approach based on the Minkowski fractal dimension, those methods estimate whether a guiding-centre orbit is regular and therefore expected to be confined for infinite time in the collisionless case, or chaotic, which might lead to its loss. Compared with the existing approach, the required orbit tracing time for the novel classifiers is shorter by at least an order of magnitude. This enables massive sampling of orbits across the whole phase space to identify regular and chaotic regions for the purpose stellarator optimization. Based on conservation of the perpendicular invariant, we demonstrate how extended regular regions may act as radial barriers for orbits from the chaotic regions on the radially inboard side. We propose to use a quantified version of this property as a new metric for collisionless fusion alpha losses. As pitch-angle scattering becomes only relevant after alphas have already deposited a significant fraction of their energy, such a metric remains useful also for the case with collisions. This is illustrated by comparison with collisional loss computations. Results are presented for applications to two quasi-isodynamic configurations, a quasi-helical configuration and two quasi-axisymmetric configurations. In addition, the Hamiltonian action-angle formalism is used in quasi-axisymmetric configurations to investigate the overlap of drift-orbit resonances leading to chaos. The respective analysis is performed with the NEO-RT code originally developed for investigation of neoclassical toroidal viscous torque in tokamak plasmas.

The impurity transport at Wendelstein 7-X during its most recent campaign is characterized and documented for a variety of different plasma scenarios. An overview of its dependence on several quantities is given, which allows identification of transport regimes and the major driver for impurity transport. Beyond this, a comparison with the impurity behavior in other fusion devices is now possible. In contrast to other stellarators, no density dependence of the impurity transport has been found. Additionally, the influence of the turbulence contribution to the overall transport is reflected in the dependence on various parameters, e.g. turbulent diffusion and density fluctuation amplitudes. With this database approach, one can now also apply scaling laws to make extrapolations about the impurity confinement in future plasma scenarios.

Three-dimensional equilibrium codes are vital for stellarator design and operation, and high-accuracy equilibria are also necessary for stability studies. This paper details comparisons of two three-dimensional equilibrium codes: VMEC, which uses a steepest-descent algorithm to reach a minimum-energy plasma state, and DESC, which minimizes the magnetohydrodynamic (MHD) force error in real space directly. Accuracy as measured by satisfaction of MHD force balance is presented for each code, along with the computation time. It is shown that DESC is able to achieve more accurate solutions, especially near axis. The importance of higher-accuracy equilibria is shown in DESC's better agreement of stability metrics with asymptotic formulae. DESC's global Fourier–Zernike basis also yields solutions with analytic derivatives explicitly everywhere in the plasma volume, provides improved accuracy in the radial direction versus conventional finite differences and allows for exponential convergence. Further, DESC can compute a solution with the same accuracy as VMEC in order-of-magnitude less time.

Global electromagnetic turbulence is simulated in stellarator geometry using the gyrokinetic particle-in-cell code EUTERPE. The evolution of the turbulent electromagnetic field and the plasma profiles is considered at different values of the plasma beta and for different magnetic configurations. It is found that turbulence is linearly driven at relatively high toroidal mode numbers. In the nonlinear regime, lower toroidal mode numbers, including zonal flows, are excited resulting in a quench of the linear instability drive. The turbulent heat flux is outward and leads to the nonlinear relaxation of the plasma temperature profile. The particle flux is inward for the parameters considered. The effect of the parallel perturbation of the magnetic field on the stellarator turbulence is addressed.

A new perturbation and continuation method is presented for computing and analysing stellarator equilibria. The method is formally derived from a series expansion about the equilibrium condition $\boldsymbol {F} \equiv \boldsymbol {J}\times \boldsymbol {B} - \boldsymbol {\nabla } p = 0$, and an efficient algorithm for computing solutions to second- and third-order perturbations is developed. The method has been implemented in the DESC stellarator equilibrium code, using automatic differentiation to compute the required derivatives. Examples are shown demonstrating its use for computing complicated equilibria, perturbing a tokamak into a stellarator and performing parameter scans in pressure, rotational transform and boundary shape in a fraction of the time required for a full solution.

The multiple-recycle fuel cycle for uranium-238 considered here, if practically realized, can bring revolutionary changes in nuclear energy. A full use of uranium-238 implies a practically infinite resource for power generation. Besides the energy, the fuel cycle net output is only fission products, which are co-products rather than waste. For the same amount of energy produced, the amount of fission products is two orders of magnitude less compared with the amount of spent nuclear fuel generated in currently exploited nuclear energy production scenarios. Using the simplest isotope balance model, key features of the multiple-recycle fuel cycle for uranium-238 are investigated. The repetition of this cycle results in smooth transformation of the initial fuel to ‘stationary’ fuel without strong variations in the fractional isotope content. Deficit of delayed neutrons is a threat of the fuel cycle considered as well as other fuel cycles that use plutonium. It has a dramatic impact on reactor controllability and safety. A solution to this threat could be a subcritical nuclear reactor with an external neutron source. In this paper, use of a stellarator–mirror (SM) fusion–fission hybrid for the multiple-recycle fuel cycle for uranium-238 is analysed. A summary of the experimental and theoretical studies on the SM hybrid is given. Preliminary results for principal design of a SM hybrid nuclear reactor for the multiple-recycle fuel cycle for uranium-238 are presented.

This paper documents the design and construction of MUSE, the world's first permanent magnet (PM) stellarator and the first quasi-axisymmetric experiment. The purpose of MUSE is to develop and assess a new way of building optimised stellarators that uses simple planar coils PMs. Our PM optimisation algorithm consists of initialising a geometry to pack dipoles densely, running the FAMUS code to minimise surface field error subject to PM constraints and applying discrete jumps to reach a physically realisable solution. FAMUS treats the PM system as a set of ideal point dipoles. From there we construct finite-volume magnet towers to be housed in 3D-printed PM holders. We describe the design of the PM holders, which were validated by laser metrology. We analyse the effects of finite permeability, sensitivity to perturbations and magnetostatic forces. An exact analytic formula for the magnetic field from a finite-volume PM tower is presented to compute PM–PM forces and stress on the PM holder. Stellarator construction is complete and experiments are underway.

Pellet injection is currently the primary candidate for achieving efficient plasma fuelling, one of the key issues for steady-state operation in large fusion devices. In this paper, pellet injection experiments are performed for several magnetic configurations of the TJ-II stellarator. The aim of this study is to increase the understanding of the role played by rational surfaces in plasmoid drift and deposition profiles in stellarators. The analysis of experimentally observed plasmoid drifts is supported by simulations of such cases made with the HPI2 code. Plasmoid drift is found to be significantly reduced, as in tokamaks, in the vicinity of rational surfaces. This is attributed to the fact that plasmoid external charge reconnection lengths are shorter near rational surfaces, resulting in a more effective damping of the plasmoid drift. Although the effect of plasmoid external currents on the drift is expected to be negligible in stellarators, compared with those caused by plasmoid internal currents, the effect observed in TJ-II is clearly measurable. In addition, simulations show that enhanced drift reductions near rational surfaces lead to significantly different deposition profiles for the magnetic configurations included in this study. This implies that it should be possible to select the magnetic configurations to obtain more efficient pellet fuelling.