A method is given to rapidly compute quasisymmetric stellarator magnetic fields for plasma confinement, without the need to call a three-dimensional magnetohydrodynamic equilibrium code inside an optimization iteration. The method is based on direct solution of the equations of magnetohydrodynamic equilibrium and quasisymmetry using Garren & Boozer’s expansion about the magnetic axis (Phys Fluids B, vol. 3, 1991, p. 2805), and it is several orders of magnitude faster than the conventional optimization approach. The work here extends the method of Landreman et al. (J. Plasma Phys., vol. 85, 2019, 905850103), which was limited to flux surfaces with elliptical cross-section, to higher order in the aspect-ratio expansion. As a result, configurations can be generated with strong shaping that achieve quasisymmetry to high accuracy. Using this construction, we give the first numerical demonstrations of Garren and Boozer’s ideal scaling of quasisymmetry breaking with the cube of the inverse aspect ratio. We also demonstrate a strongly non-axisymmetric configuration (vacuum rotational transform $\unicode[STIX]{x1D704}>0.4$) in which symmetry-breaking mode amplitudes throughout a finite volume are ${<}2\times 10^{-7}$, the smallest ever reported. To generate boundary shapes of finite-minor-radius configurations, a careful analysis is given of the effect of substituting a finite minor radius into the near-axis expansion. The approach here can provide analytic insight into the space of possible quasisymmetric stellarator configurations, and it can be used to generate good initial conditions for conventional stellarator optimization.

Accelerated statistical computation of collisionless fusion alpha particle losses in stellarator configurations is presented based on direct guiding-centre orbit tracing. The approach relies on the combination of recently developed symplectic integrators in canonicalized magnetic flux coordinates and early classification into regular and chaotic orbit types. Only chaotic orbits have to be traced up to the end, as their behaviour is unpredictable. An implementation of this technique is provided in the code SIMPLE (symplectic integration methods for particle loss estimation, Albert et al., 2020b, doi:10.5281/zenodo.3666820). Reliable results were obtained for an ensemble of 1000 orbits in a quasi-isodynamic, a quasi-helical and a quasi-axisymmetric configuration. Overall, a computational speed up of approximately one order of magnitude is achieved compared to direct integration via adaptive Runge–Kutta methods. This reduces run times to the range of typical magnetic equilibrium computations and makes direct alpha particle loss computation adequate for use within a stellarator optimization loop.

Following up on earlier work which demonstrated an improved numerical stellarator coil design optimization performance by the use of stochastic optimization (Lobsien et al., Nucl. Fusion, vol. 58 (10), 2018, 106013), it is demonstrated here that significant further improvements can be made – lower field errors and improved robustness – for a Wendelstein 7-X test case. This is done by increasing the sample size and applying fully three-dimensional perturbations, but most importantly, by changing the design sequence in which the optimization targets are applied: optimization for field error is conducted first, with coil shape penalties only added to the objective function at a later step in the design process. A robust, feasible coil configuration with a local maximum field error of 3.66 % and an average field error of 0.95 % is achieved here, as compared to a maximum local field error of 6.08 % and average field error of 1.56 % found in our earlier work. These new results are compared to those found without stochastic optimization using the FOCUS and ONSET suites. The relationship between local minima in the optimization space and coil shape penalties is also discussed.

The core toroidal plasma intrinsic rotation has been studied by experiments and simulations in the Joint Texas Experimental Tokamak (J-TEXT). The direction of core intrinsic rotation in the J-TEXT plasma is counter-current. As the plasma density ramps up, the rotation velocity increases in the counter-current direction. By comparing four different electron densities, linear local gyrokinetic simulations have been performed by the Gyrokinetic Electromagnetic Numerical Experiment code for the first time on J-TEXT. It is found that the most dominant turbulence is the ion temperature gradient at $0.2a$, where $a$ is the minor radius of the plasma and this is unchanged during the plasma density ramp up. By scanning the radial wave vectors, it is found that the residual stress term reverses from negative to positive when the plasma density exceeds a certain threshold. The pinch term is larger than the residual stress term at all four electron densities, which means that the pinch term is always dominant in the core of a J-TEXT plasma.

The modelling of edge carbon transport and emission on EAST tokamak under resonant magnetic perturbation (RMP) fields has been conducted with the three-dimensional edge transport code EMC3-EIRENE. The measured vertical distribution of CVI emission by the extreme ultraviolet spectrometer system for the perturbed case shows a reduction in the CVI emission by 20 % compared to the equilibrium case. The chord-integrated CVI emission can be reconstructed by EMC3-EIRENE modelling, which presents an increase in the CVI emission with RMP fields. The discrepancy between experiments and simulations has been investigated by parameter study to examine the sensitivity of the simulation results on the edge plasma conditions and the impurity perpendicular transport. It is found that the variation of edge plasma conditions for the equilibrium case cannot resolve the discrepancy in the CVI emission between simulations and measurements. The simulations with enhanced impurity perpendicular transport coefficient allows a reasonable agreement with the measured reduction of CVI emission.

Using transport models, the impacts of trapped electrons on zonal flows and turbulence in helical field configurations are studied. The effect of the trapped electrons on the characteristic quantities of the linear response for zonal flows is investigated for two different field configurations in the Large Helical Device. The turbulent potential fluctuation, zonal flow potential fluctuation and ion energy transport are quickly predicted by the reduced models for which the linear and nonlinear simulation results are used to determine dimensionless parameters related to turbulent saturation levels and typical zonal flow wavenumbers. The effects of zonal flows on the turbulent transport for the case of the kinetic electron response are much smaller than or comparable to those in an adiabatic electron condition for the two different field configurations. It is clarified that the effect of zonal flows on the turbulent transport due to the trapped electrons changes, depending on the field configurations.

The linear MHD (magnetohydrodynamic) stability for high beta plasmas in the inward shifted Large Helical Device (LHD) configurations has been investigated for a wide range of magnetic Reynolds numbers $S$ using numerical simulations based on the kinetic MHD model with kinetic thermal ions where the beta is the ratio of the plasma pressure to the magnetic pressure. It is found that the dependence of the linear growth rate of the resistive ballooning modes on the $S$ number changes from $\unicode[STIX]{x1D6FE}\propto S^{-1/3}$ to $\unicode[STIX]{x1D6FE}\propto S^{-1}$ by the kinetic thermal ion effects so that the resistive ballooning modes are significantly suppressed as the $S$ number increases. For a high $S$ number comparable to experimental values, the most unstable modes are interchange modes. The kinetic thermal ion effects change the most unstable interchange mode from the ideal mode to the resistive mode. This transition of the interchange modes by kinetic thermal ion effects is consistent with the shift of the marginal stability boundary for the ideal interchange modes observed in the LHD experiments.

The neutral beam (NB) fast ion confinement in the Large Helical Device (LHD) is studied for several full field ($B_{t}\sim 2.75~\text{T}$) magnetic configurations by a combination of neutron measurement and simulations. To investigate the NB fast ion confinement, we have performed a series of short-pulse NB injection experiments. The experiment results are analysed by the integrated code TASK3D-a. From this investigation, the effective particle diffusion coefficients of the tangential and perpendicular NBs are approximately $D^{\text{eff}}\sim 0.1~\text{m}^{2}~\text{s}^{-1}$ and $D^{\text{eff}}\sim 1~\text{m}^{2}~\text{s}^{-1}$ in the standard configuration. It is clarified that the NB fast ion confinement improves when the plasmas are shifted inward. Moreover, it is also found that the simulation, which considers the deuteron dilution effect due to the presence of impurity ions, can describe a neutron emission rate consistent with the measurement.

This work presents updates in the diagnostics systems, magnetohydrodynamics (MHD) calculations and simulations of microwave heating scenarios of the small modular Stellarator of Costa Rica 1 (SCR-1). Similarly, the design of a flexible bolometer and magnetic diagnostics (a set of Mirnov coils, Rogowski coils and two diamagnetic loops) are introduced. Furthermore, new MHD equilibrium calculations for the plasma of the SCR-1 device were performed using the VMEC code including the poloidal cross-section of the magnetic flux surfaces at different toroidal positions, profiles of the rotational transform, magnetic well, magnetic shear and total magnetic field norm. Charged particle orbits in vacuum magnetic field were computed by the magnetic field solver BS-SOLCTRA (Vargas et al. In 27th IAEA Fusion Energy Conference (FEC 2018), 2018. IAEA). A visualization framework was implemented using Paraview (Solano-Piedra et al. In 23rd IAEA Technical Meeting on the Research Using Small Fusion Devices (23rd TM RUSFD), 2017) and compared with magnetic mapping results (Coto-Vílchez et al. In 16th Latin American Workshop on Plasma Physics (LAWPP), 2017, pp. 43–46). Additionally, simulations of microwave heating scenarios were performed by the IPF-FDMC full-wave code. These simulations calculate the conversion of the ordinary waves to extraordinary waves and allow us to identify the location where the conversion takes place. Finally, the microwave heating scenarios for the $330^{\circ }$ toroidal position are presented. The microwave heating scenarios showed that the O–X–B mode conversion is around 12–14 %. It was possible to identify the spatial zone where the conversion takes place (upper hybrid frequency).

A magnetic field configuration of an island divertor for a quasi-axisymmetric stellarator (CFQS) is proposed. The configuration incorporates large islands surrounding the core confinement region. The interface between the core region and the peripheral region of the island divertor is a clear magnetic separatrix similar to a tokamak divertor. The structure of divertor magnetic field lines is very regular without stochasticity and the connection length is sufficiently long for good divertor performance. Such a divertor configuration is produced in the magnetic field configuration for the CFQS device, which is now under construction in China.

The rapidly emerging technology of high-temperature superconductors (HTS) opens new opportunities for the development of non-planar non-insulated HTS magnets. This type of HTS magnet offers attractive features via its simplicity and robustness, and is well suited for modest size steady-state applications such as a mid-scale stellarator. In non-planar coil applications the HTS tape may be subject to severe hard-way bending strain ($\epsilon _{\textrm {bend}}$), torsional strains ($\epsilon _{\textrm {tor}}$) and magnetic field components transverse to the HTS tape plane ($B_{\perp }$), all of which can limit the magnet operating space. A novel method of winding angle optimization is here presented to overcome these limitations for fixed input non-planar coil filamentary geometry. Essentially, this method: (i) calculates the peak $\epsilon _{\textrm {bend}}$ and $B_{\perp }$ for arbitrary winding angle along an input coil filamentary trajectory, (ii) defines a cost function including both and then (iii) uses tensioned splines to define a winding angle that reduces $\epsilon _{\textrm {tor}}$ and optimizes the $\epsilon _{\textrm {bend}}$ and $B_{\perp }$ cost function. As strain limits are present even without $B_{\perp }$, this optimization is able to provide an assessment of the minimum buildable size of an arbitrary non-planar non-insulating HTS coil. This optimization finds that for standard 4 mm wide HTS tapes the minimum size coils of the existing HSX, NCSX and W7-X stellarator geometries are around 0.3–0.5 m in mean coil radius. Identifying the minimum size provides a path to specify a mid-scale stellarator capable of achieving high-field or high-temperature operation with minimal HTS tape length. For coils larger than this size, strain optimization allows use of wider (higher current capacity) HTS tapes or alternatively permitting a finite (yet tolerable) strain allows reduction of $B_{\perp }$. Reduced $B_{\perp }$ enables a reduction of the HTS tape length required to achieve a given design magnetic field or equivalently an increase in the achievable magnetic field for fixed HTS tape length. The distinct considerations for optimizing a stellarator coilset to further ease compatibility with non-insulated HTS magnets are also discussed, highlighting relaxed curvature limits and the introduction of limits to the allowable torsion.

The multiphase simulations are conducted with the kinetic-magnetohydrodynamics hybrid code MEGA to investigate the spatial and the velocity distributions of lost fast ions due to the Alfvén eigenmode (AE) bursts in the Large Helical Device plasmas. It is found that fast ions are lost along the divertor region with helical symmetry both before and during the AE burst except for the promptly lost particles. On the other hand, several peaks are present in the spatial distribution of lost fast ions along the divertor region. These peaks along the divertor region can be attributed to the deviation of the fast-ion orbits from the magnetic surfaces due to the grad-B and the curvature drifts. For comparison with the velocity distribution of lost fast ions measured by the fast-ion loss detector (FILD), the ‘numerical FILD’ which solves the Newton–Lorentz equation is constructed in the MEGA code. The velocity distribution of lost fast ions detected by the numerical FILD during AE burst is in good qualitative agreement with the experimental FILD measurements. During the AE burst, fast ions with high energy (100–180 keV) are detected by the numerical FILD, while co-going fast ions lost to the divertor region are the particles with energy lower than 50 keV.