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The interest in the modeling of laboratory and astrophysical plasma behavior from mid up to strong non-ideality (NI), e.g., plasma in which a Coulomb interaction becomes dominant, led us to further investigate the optical properties of such systems. An expanded set of results and properties like wave functions, dipole matrix elements, etc., for such systems is presented in this submission. The methodologies of our research, as well as the current and future elements of their applications, are explained. In addition to being helpful to other researchers for achieving a variety of goals, the data from this study could be useful the interdisciplinary fields of machine learning, astrochemistry and fusion physics. The dataset is available online at the repository Figshare. [ABSTRACT FROM AUTHOR]

In this work we consider the problem of optimizing a stellarator subject to hard constraints on the design variables and physics properties of the equilibrium. We survey current numerical methods for handling these constraints, and summarize a number of methods from the wider optimization community that have not been used extensively for stellarator optimization thus far. We demonstrate the utility of new methods of constrained optimization by optimizing a quasi-axisymmetric stellarator for favourable physics properties while preventing strong shaping of the plasma boundary, which can be difficult to create with external current sources. [ABSTRACT FROM AUTHOR]

Quasilinear treatments are widely used for tokamaks to evaluate radio frequency (rf) heating and current drive. Even though the core of a tokamak plasma is weakly collisional, the solution of the linearized kinetic equation is evaluated using unperturbed collisionless trajectories while often treating successive poloidal circuits of the passing (and trapped) particles as uncorrelated or nearly so. In addition, the most important effect of tokamak geometry, the mirror force, is usually mistreated or ignored when obtaining the solution. These concerning aspects of rf treatments are clarified by considering lower hybrid heating and current drive to illustrate that the electrons in resonance with the applied rf are enclosed by narrow collisional boundary layers, and that tokamak geometry makes it necessary to retain poloidal variation when solving a weakly collisional linearized kinetic equation. Other aspects such as collisional boundary layers at the trapped–passing boundary, cyclotron resonances, and the limitations of quasilinear theory are also considered. The new insights lead to a fundamentally different formulation and interpretation of the solution of the linearized Fokker–Planck equation used for rf quasilinear theory in a tokamak, while retaining many of the features that have contributed to its successful application to rf heating and current drive. [ABSTRACT FROM AUTHOR]

The paper considers the electron transport in toroidal systems taking into account relativistic effects for electrons. The treatment is based on the relativistic drift-kinetic equation with the thermodynamic equilibrium given by the relativistic Maxwell–Jüttner distribution function. The definition of relativistic fluxes is given in a classic-like form using the same set of thermodynamic forces as in the classical (non-relativistic) approach. Such a formulation allows us to apply the currently used non-relativistic solvers for calculation of relativistic mono-energetic transport coefficients. As an example, the procedure for calculating electron fluxes is proposed, in which relativistic effects are taken into account using the DKES code. The model can be easily implemented in various transport codes, developed for the non-relativistic limit, making them accurate also for hot plasmas with non-negligible relativistic effects. [ABSTRACT FROM AUTHOR]

Hot electrons produced by parametric instabilities can negatively affect the thermonuclear gain of a direct-drive inertial confinement fusion capsule. A Monte Carlo transport is coupled to the hydrodynamics MULTI-IFE code in order to study the hot electron transport in a high-gain target implosion. The thermonuclear energy produced by the directly driven implosion of a reference target drops from 27 MJ without hot electrons to 13.5 kJ when the hot electrons are taken into account. A clear relationship is established between the level of hot electrons produced and the degradation of the thermonuclear yield produced by the target. It is shown that adding a relatively short laser spike (shock ignition) to the main pulse restores the thermonuclear energy released by the implosion. Different shock-ignition windows are presented depending on the duration of the spike. It appears that the longer the duration of the spike, the lower the power required for shock ignition. Finally, a 300 ps-duration spike requires only 50 TW to restore a thermonuclear energy output of 20 MJ. [ABSTRACT FROM AUTHOR]

We derive an advanced surrogate model for predicting turbulent transport at the edge of tokamaks driven by electron temperature gradient (ETG) modes. Our derivation is based on a recently developed sensitivity-driven sparse grid interpolation approach for uncertainty quantification and sensitivity analysis at scale, which informs the set of parameters that define the surrogate model as a scaling law. Our model reveals that ETG-driven electron heat flux is influenced by the safety factor $q$ , electron beta $\beta _e$ and normalized electron Debye length $\lambda _D$ , in addition to well-established parameters such as the electron temperature and density gradients. To assess the trustworthiness of our model's predictions beyond training, we compute prediction intervals using bootstrapping. The surrogate model's predictive power is tested across a wide range of parameter values, including within-distribution testing parameters (to verify our model) as well as out-of-bounds and out-of-distribution testing (to validate the proposed model). Overall, validation efforts show that our model competes well with, or can even outperform, existing scaling laws in predicting ETG-driven transport. [ABSTRACT FROM AUTHOR]

We have derived a necessary condition for the achievement of breakeven in axisymmetric plasmas with zero toroidal field and confined by a dipole magnetic field (B. Lehnert, Nature , vol. 181, 1958, p. 4605; A. Hasegawa, Comments Plasma Phys. Control. Fusion , vol. 11, no. 3, 1987). Excellent MHD stability, high values of $\beta$ (up to $26$  %) and good confinement properties awaken the interest of private investors after years of neglect due to lack of public funding and competing alternative lines of research like the tokamak. Starting from a requirement of self-consistency between the balances of momentum and energy in a dipole-confined, two-species plasma and assuming a Maxwellian distribution function for ions and electrons, we derive a necessary condition for breakeven. This condition is more stringent than the Lawson criterion because of the lack of a stabilizing toroidal field. For a given current flowing across the toroidal coil internal to the plasma, the crucial factor at stake is the ratio between the radius of the main toroidal coil and the radius of the vacuum chamber. [ABSTRACT FROM AUTHOR]

A systematic theory of the asymptotic expansion of the magnetohydrostatics (MHS) equilibrium in the distance from the magnetic axis is developed to include arbitrary smooth currents near the magnetic axis. Compared with the vacuum and the force-free system, an additional magnetic differential equation must be solved to obtain the pressure-driven currents. It is shown that there exist variables in which the rest of the MHS system closely mimics the vacuum system. Thus, a unified treatment of MHS fields is possible. The mathematical structure of the near-axis expansions to arbitrary order is examined carefully to show that the double-periodicity of physical quantities in a toroidal domain can be satisfied order by order. The essential role played by the leading-order Birkhoff–Gustavson normal form in solving the magnetic differential equations is highlighted. Several explicit examples of vacuum, force-free and MHS equilibrium in different geometries are presented. [ABSTRACT FROM AUTHOR]

Microinstabilities drive turbulent fluctuations in inhomogeneous, magnetised plasmas. In the context of magnetic confinement fusion devices, this leads to an enhanced transport of particles, momentum and energy, thereby degrading confinement. In this work, we describe an application of the adjoint method to efficiently determine variations of gyrokinetic linear growth rates on a general set of external parameters in the local $\delta f$ -gyrokinetic model. We then offer numerical verification of this approach. When coupled with gradient-based techniques, this methodology can facilitate the optimisation process for the microstability of the confined plasmas across a high-dimensional parameter space. We present a numerical demonstration wherein the ion-temperature-gradient instability growth rate in a tokamak plasma is minimised with respect to flux surface shaping parameters. The adjoint method approach demonstrates a significant computational speed-up compared with a finite-difference gradient calculation. [ABSTRACT FROM AUTHOR]

Electrostatic gyrokinetic instabilities and turbulence in the Wendelstein 7-X stellarator are studied. Particular attention is paid to the ion-temperature-gradient (ITG) instability and its character close to marginal stability [Floquet-type turbulence (Zocco et al. , Phys. Rev. E , vol. 106, 2022, p. L013202) with no electron temperature gradient]. The flux tube version of the $\delta f$ code stella (Barnes et al. , J. Comput. Phys. , vol. 391, 2019, pp. 365–380) is used to run linear and nonlinear gyrokinetic simulations with kinetic electrons. The nature of the dominant instability depends on the wavelength perpendicular to the magnetic field, and the results are conveniently displayed in stability diagrams that take this dependence into account. This approach highlights the presence of universal instabilities, which are less unstable but have longer wavelengths than other modes. A quasi-linear estimate of the heat flux suggests they are relevant for transport. Close to the stability threshold, the linear eigenmodes and turbulence form highly extended structures along the computational domain if the magnetic shear is small. Numerical experiments and diagnostics are undertaken to assess the resulting radial localisation of the turbulence, which affects the interaction of the latter with zonal flows. Increasing the amplitude of the magnetic shear (e.g.through current drive) has a stabilising effect on the turbulence and, thus, reduces the nonlinear energy transport. [ABSTRACT FROM AUTHOR]

GX is a code designed to solve the nonlinear gyrokinetic system for low-frequency turbulence in magnetized plasmas, particularly tokamaks and stellarators. In GX, our primary motivation and target is a fast gyrokinetic solver that can be used for fusion reactor design and optimization along with wide-ranging physics exploration. This has led to several code and algorithm design decisions, specifically chosen to prioritize time to solution. First, we have used a discretization algorithm that is pseudospectral in the entire phase space, including a Laguerre–Hermite pseudospectral formulation of velocity space, which allows for smooth interpolation between coarse gyrofluid-like resolutions and finer conventional gyrokinetic resolutions and efficient evaluation of a model collision operator. Additionally, we have built GX to natively target graphics processors (GPUs), which are among the fastest computational platforms available today. Finally, we have taken advantage of the reactor-relevant limit of small $\rho _*$ by using the radially local flux-tube approach. In this paper we present details about the gyrokinetic system and the numerical algorithms used in GX to solve the system. We then present several numerical benchmarks against established gyrokinetic codes in both tokamak and stellarator magnetic geometries to verify that GX correctly simulates gyrokinetic turbulence in the small $\rho _*$ limit. Moreover, we show that the convergence properties of the Laguerre–Hermite spectral velocity formulation are quite favourable for nonlinear problems of interest. Coupled with GPU acceleration, which we also investigate with scaling studies, this enables GX to be able to produce useful turbulence simulations in minutes on one (or a few) GPUs and higher fidelity results in a few hours using several GPUs. GX is open-source software that is ready for fusion reactor design studies. [ABSTRACT FROM AUTHOR]

A surrogate model of the runaway electron avalanche growth rate in a magnetic fusion plasma is developed. This is accomplished by employing a physics-informed neural network (PINN) to learn the parametric solution of the adjoint to the relativistic Fokker–Planck equation. The resulting PINN is able to evaluate the runaway probability function across a broad range of parameters in the absence of any synthetic or experimental data. This surrogate of the adjoint relativistic Fokker–Planck equation is then used to infer the avalanche growth rate as a function of the electric field, synchrotron radiation and effective charge. Predictions of the avalanche PINN are compared against first principle calculations of the avalanche growth rate with excellent agreement observed across a broad range of parameters. [ABSTRACT FROM AUTHOR]

A study of multi‐ion species plasmas in divertor region through kinetic simulation helps us understand particle transports and wall interactions. We analyzed plasma sheath behavior without collisions involving electrons, hydrogen isotopes, and helium ions using a one‐dimensional spatial space and three‐dimensional velocity space (1D3V) Particle‐In‐Cell (PIC) simulation. The PIC simulation model follows Maxwellian velocity distributions with the pre‐sheath acceleration for each particle species in the plasma source, and the plasmas move to the absorption wall with equal and constant flux. This revealed spatial potential variations due to differences in masses and charges of multi‐ion species plasmas, including independent sound velocities of each ion species. Increasing ion masses result in a more negative wall potential. The electrostatic force repels electrons and accelerates multi‐ions to reach the absorption wall. This information is found in the phase spaces of velocity in the sheath. [ABSTRACT FROM AUTHOR]

This work presents the synthesis of tungsten nanoparticles (W NPs) using a cluster source based on magnetron sputtering combined with gas aggregation (MSGA), operated with up to 81% H2 in the hydrogen/argon mixture used as a working gas. The results show that, with up to 41% H2 in discharge, the synthesis rate increases by more than 60 times, rapidly decreasing for over 50% H2 in discharge. The W dust is still produced for H2-dominated discharges (81%), and its deposition rate is small but not negligible (0.02 mg/h). The obtained W NPs are isolated, with the diameter decreasing from 50 nm to 15 nm when the amount of H2 in discharge is smaller than 41%. Over this value, the particles tend to agglomerate, forming structures similar to film-like deposits. Also, the diameter of the dust spots deposited on substrates depends on the H2 content of the discharge. This allows the efficient coating of substrates up to 26 mm wide by translating them in front of the MSGA cluster source exit aperture. Additionally, for 41% H2 in discharge, the influence of synthetic air leaks (0%–8.2%) in discharge was investigated. The deposition rate decreases rapidly (ceasing for around 6% air in discharge), and the obtained nanoparticles tend to agglomerate on the substrate (at 3.3% air content, the dust deposit has the aspect of a near-continuous film). Chemical composition investigations show a pronounced tendency for oxidation, nitridation, and oxynitride formation in the presence of air leaks. [ABSTRACT FROM AUTHOR]

When simulating runaway electron dynamics in tokamak disruptions, fluid models with lower numerical cost are often preferred to more accurate kinetic models. The aim of this work is to compare fluid and kinetic simulations of a large variety of different disruption scenarios in ITER. We consider both non-activated and activated scenarios; for the latter, we derive and implement kinetic sources for the Compton scattering and tritium beta decay runaway electron generation mechanisms in our simulation tool Dream (Hoppe et al. , Comput. Phys. Commun. , vol. 268, 2021, 108098). To achieve a diverse set of disruption scenarios, Bayesian optimization is used to explore a range of massive material injection densities for deuterium and neon. The cost function is designed to distinguish between successful and unsuccessful disruption mitigation based on the runaway current, current quench time and transported fraction of the heat loss. In the non-activated scenarios, we find that fluid and kinetic disruption simulations can have significantly different runaway electron dynamics, due to an overestimation of the runaway seed by the fluid model. The primary cause of this is that the fluid hot-tail generation model neglects superthermal electron transport losses during the thermal quench. In the activated scenarios, the fluid and kinetic models give similar predictions, which can be explained by the significant influence of the activated sources on the runaway dynamics and the seed. [ABSTRACT FROM AUTHOR]

The problem of the assimilation of a cryogenic fuel pellet injected into a hot plasma is considered. Due to the transparency to ambient particles of the plasmoid, the localised region of high-density plasma created by ionisation of the ablated pellet material, electrons reach a 'quasiequilibrium' (QE) state which is characterised by a steady-state on the fastest collisional time scale. The simplified electron kinetic equation of the QE state is solved. Taking a velocity moment of the higher-order electron kinetic equation, which is valid on the expansion time scale, permits a fluid closure, yielding an evolution equation for the macroscopic parameters describing the QE distribution function. In contrast to the Braginskii equations, the closure does not require that electrons have a short mean free path compared with the size of density perturbations, and permits an anisotropic and highly non-Maxwellian distribution function. As the QE distribution function accounts for both trapped and passing electrons, the self-consistent electric potential that causes the expansion can be properly described, in contrast to earlier models of pellet plasmoid expansion with an unbounded potential. The plasmoid expansion is simulated using both a Vlasov model and a cold-fluid model for the ions. During the expansion plasmoid ions and electrons obtain nearly equal amounts of energy; as hot ambient electrons provide this energy in the form of collisional heating of plasmoid electrons, the expansion of a pellet plasmoid is expected to be a potent mechanism for the transfer of energy from electrons to ions on a time scale shorter than that of ion–electron thermalisation. [ABSTRACT FROM AUTHOR]

We present a stellarator configuration optimized for a large threshold ('critical gradient') for the onset of the ion temperature gradient (ITG) driven mode, which achieves the largest critical gradient we have seen in any stellarator. Above this threshold, gyrokinetic simulations show that the configuration has low turbulence levels over an experimentally relevant range of the drive strength. The applied optimization seeks to maximize the drift curvature, leading to enhanced local-shear stabilization of toroidal ITG modes, and the associated turbulence. These benefits are combined with excellent quasi-symmetry, yielding low neoclassical transport and vanishingly small alpha particle losses. Analysis of the resulting configuration suggests a trade-off between magnetohydrodynamic (MHD) and ITG stability, as the new configuration possesses a vacuum magnetic hill. [ABSTRACT FROM AUTHOR]

Filament-based coil optimizations are performed for several quasi-helical stellarator configurations, beginning with the one from Landreman & Paul (Phys. Rev. Lett. , vol. 128, 2022, 035001), demonstrating that precise quasi-helical symmetry can be achieved with realistic coils. Several constraints are placed on the shape and spacing of the coils, such as low curvature and sufficient plasma–coil distance for neutron shielding. The coils resulting from this optimization have a maximum curvature 0.8 times that of the coils of the Helically Symmetric eXperiment (HSX) and a mean squared curvature 0.4 times that of the HSX coils when scaled to the same plasma minor radius. When scaled up to reactor size and magnetic field strength, no fast particle losses were found in the free-boundary configuration when simulating 5000 alpha particles launched at $3.5\,\mathrm {MeV}$ on the flux surface with a normalized toroidal flux of $s=0.5$. An analysis of the tolerance of the coils to manufacturing errors is performed using a Gaussian process model, and the coils are found to maintain low particle losses for smooth, large-scale errors up to amplitudes of approximately $0.15\,\mathrm {m}$. Another coil optimization is performed for the Landreman–Paul configuration with the additional constraint that the coils are purely planar. Visual inspection of the Poincaré plot of the resulting magnetic field-lines reveal that the planar modular coils alone do a poor job of reproducing the target equilibrium. Additional non-planar coil optimizations are performed for the quasi-helical configuration with $5\,\%$ volume-averaged plasma beta from Landreman et al. (Phys. Plasma , vol. 29, issue 8, 2022, 082501), and a similar configuration also optimized to satisfy the Mercier criterion. The finite beta configurations had larger fast-particle losses, with the free-boundary Mercier-optimized configuration performing the worst, losing approximately $5.5\,\%$ of alpha particles launched at $s=0.5$. [ABSTRACT FROM AUTHOR]

The interest in the modeling of laboratory and astrophysical plasma behavior from mid up to strong non-ideality (NI), e.g., plasma in which a Coulomb interaction becomes dominant, led us to further investigate the optical properties of such systems. An expanded set of results and properties like wave functions, dipole matrix elements, etc., for such systems is presented in this submission. The methodologies of our research, as well as the current and future elements of their applications, are explained. In addition to being helpful to other researchers for achieving a variety of goals, the data from this study could be useful the interdisciplinary fields of machine learning, astrochemistry and fusion physics. The dataset is available online at the repository Figshare.

This paper is based on a report at the 2nd International Fusion Plasma Conference & 13th International Conference on Open Magnetic Systems for Plasma Confinement (iFPC & OS 2023), August 21–25, 2023, Busan, Korea and provides a brief overview of the status of work at the Budker Institute on the study of hot plasma confinement in open-type magnetic traps with a linear axisymmetric configuration. The main attention is paid to key problems: magnetohydrodynamics (MHD) stability in regimes with extremely high relative pressure, longitudinal electronic thermal conductivity, stability with respect to the development of kinetic modes and transverse transport. This paper provides an overview of the methods we are developing to address these problems, the experimental and theoretical results achieved and plans for future development. The last section of the article provides brief information about the preliminary design of the gas-dynamic multiple-mirror trap device, the development of which has been completed. [ABSTRACT FROM AUTHOR]

Isothermal fluid turbulence simulations have been performed in the edge and scrape-off layer (SOL) of an analytic stellarator configuration with an island divertor, thereby providing numerical insight into edge turbulence in regions around islands in a stellarator. The steady-state transport follows the a curvature drive that is inverse to the major radius ($1/R$) toward the outboard side, but large fluctuations are present throughout the island divertor region, with the average wavelength of similar size to the island width. The system exhibits a prominent $m=2$ , $n=5$ mode, where m is the poloidal mode number and n is the toroidal mode number, although other modes are present. The amplitude and radial extent of the density fluctuations are similar throughout the edge and SOL, but can decrease near island O-points. The fluctuations exhibit a predominantly positive skewness on the outboard midplane, indicating blob-like perturbations for the transport into the outer SOL. It is determined that a point on the separatrix is generally more correlated with regions outside of the SOL than a nearby reference point which does not lie on the separatrix. [ABSTRACT FROM AUTHOR]

The centrifugal mirror confinement scheme incorporates supersonic rotation of a plasma into a magnetic mirror device. This concept has been shown experimentally to drastically decrease parallel losses and increase plasma stability as compared with prior axisymmetric mirrors. MCTrans++ is a dimensionless (0-D) scoping tool which rapidly models experimental operating points in the Centrifugal Mirror Fusion Experiment (CMFX) at the University of Maryland. In the low-collisionality regime, parallel losses can be modelled analytically. A confining potential is set up that is partially ambipolar and partially centrifugal. Due to the stabilizing effects of flow shear, the perpendicular losses can be modelled as classical. Radiation losses such as bremsstrahlung and cyclotron emission are taken into account. A neutrals model is included, and, in some circumstances, charge-exchange losses are found to exceed all other loss mechanisms. We use the SUNDIALS ARKODE library to solve the underlying equations of this model; the resulting software is suitable for scanning large parameter spaces, and can also be used to model time-dependent phenomena such as a capacitive discharge. MCTrans++ has been used to verify results from prior centrifugal mirrors, create an experimental plan for CMFX and find configurations for future reactor-scale fusion devices. [ABSTRACT FROM AUTHOR]

Some stellarators tend to benefit from favourable average magnetic curvature for trapped particles when the plasma pressure is sufficiently high. This so-called maximum- $J$ property has several positive implications, such as good fast-particle confinement, magnetohydrodynamic stability and suppression of certain trapped-particle instabilities. This property cannot be attained in quasisymmetric stellarators, in which deeply trapped particles experience average bad curvature and therefore precess in the diamagnetic direction close to the magnetic axis. However, quasi-isodynamic stellarators offer greater flexibility and allow the average curvature to be favourable and the precession to be reversed. We find that it is possible to design such stellarators so that the maximum- $J$ condition is satisfied for the great majority of all particles, even when the plasma pressure vanishes. The qualitative properties of such a stellarator field can be derived analytically by examining the most deeply and the most shallowly trapped particles, although some small fraction of the latter will inevitably not behave as desired. However, through numerical optimisation, we construct a vacuum field in which 99.6 % of all trapped particles satisfy the maximum- $J$ condition. [ABSTRACT FROM AUTHOR]

Recent developments in the design of magnetic confinement fusion devices have allowed the construction of exceptionally optimized stellarator configurations. The near-axis expansion in particular has been proven to enable the construction of magnetic configurations with good confinement properties while taking only a fraction of the usual computation time to generate optimized magnetic equilibria. However, not much is known about the overall features of fast-particle orbits computed in such analytical, yet simplified, equilibria when compared with those originating from accurate equilibrium solutions. This work aims to assess and demonstrate the potential of the near-axis expansion to provide accurate information on particle orbits and to compute loss fractions in moderate to high aspect ratios. The configurations used here are all scaled to fusion-relevant parameters and approximate quasi-symmetry to various degrees. This allows us to understand how deviations from quasi-symmetry affect particle orbits and what are their effects on the estimation of the loss fraction. Guiding-centre trajectories of fusion-born alpha particles are traced using gyronimo and SIMPLE codes under the NEAT framework, showing good numerical agreement. Discrepancies between near-axis and magnetohydrodynamic fields have minor effects on passing particles but significant effects on trapped particles, especially in quasi-helically symmetric magnetic fields. Effective expressions were found for estimating orbit widths and passing–trapped separatrix in quasi-symmetric near-axis fields. Loss fractions agree in the prompt losses regime but diverge afterwards. [ABSTRACT FROM AUTHOR]

We present new stellarator equilibria that have been optimized for reduced turbulent transport using nonlinear gyrokinetic simulations within the optimization loop. The optimization routine involves coupling the pseudo-spectral GPU-native gyrokinetic code GX with the stellarator equilibrium and optimization code DESC. Since using GX allows for fast nonlinear simulations, we directly optimize for reduced nonlinear heat fluxes. To handle the noisy heat flux traces returned by these simulations, we employ the simultaneous perturbation stochastic approximation (SPSA) method that only uses two objective function evaluations for a simple estimate of the gradient. We show several examples that optimize for both reduced heat fluxes and good quasi-symmetry as a proxy for low neoclassical transport. Finally, we run full transport simulations using the T3D stellarator transport code to evaluate the changes in the macroscopic profiles. [ABSTRACT FROM AUTHOR]

Quasisymmetry (QS), a hidden symmetry of the magnetic field strength, is known to support nested flux surfaces and provide superior particle confinement in stellarators. In this work, we study the ideal magnetohydrodynamic (MHD) equilibrium and stability of high-beta plasma in a large-aspect-ratio stellarator. In particular, we show that the lowest-order description of a near-axisymmetric equilibrium vastly simplifies the problem of three-dimensional quasisymmetric MHD equilibria, which can be reduced to a standard elliptic Grad–Shafranov equation for the flux function. We show that any large-aspect-ratio tokamak, deformed periodically in the vertical direction, is a stellarator with approximate volumetric QS. We discuss exact analytical solutions and numerical benchmarks. Finally, we discuss the ideal ballooning and interchange stability of some of our equilibrium configurations. [ABSTRACT FROM AUTHOR]

The paper presents an overview of experimental results of an investigation of different energy loss channels in the gas dynamic trap (GDT), which is a magnetic mirror plasma confinement device in the Budker Institute of Nuclear Physics. Energy losses along magnetic field lines are considered as well as losses onto radial limiters, which restrict the plasma column radius and provide its magnetohydrodynamic stability via the 'vortex confinement' mechanism. The losses along the field lines were measured using a set of pyroelectric bolometers on the plasma absorber and the losses onto the limiters were determined with thermistors from their temperature rise. Additionally, the losses due to charge exchange of fast plasma ions on the residual neutral gas in the GDT were measured using a longitudinal array of pyroelectric bolometers mounted on the wall of the central cell. An attempt was made to draw up the energy balance in the GDT in order to identify the predominant loss channels and reduce those losses in the future. [ABSTRACT FROM AUTHOR]

The gyrokinetic theory of the residual flow, in the electrostatic limit, is revisited, with optimized stellarators in mind. We consider general initial conditions for the problem, and identify cases that lead to a non-zonal residual electrostatic potential, i.e. one having a significant component that varies within a flux surface. We investigate the behaviour of the 'intermediate residual' in stellarators, a measure of the flow that remains after geodesic acoustic modes have damped away, but before the action of the slower damping that is caused by unconfined particle orbits. The case of a quasi-isodynamic stellarator is identified as having a particularly large such residual, owing to the small orbit width achieved by optimization. [ABSTRACT FROM AUTHOR]

In the limit of sufficiently fast rotation, rotating mirror traps are known to be stable against the loss-cone modes associated with conventional (non-rotating) mirrors. This paper calculates how quickly a mirror configuration must rotate in order for several of these modes to be stabilized (in particular, the high-frequency convective loss cone, drift cyclotron loss cone and Dory–Guest–Harris modes). Commonalities in the stabilization conditions for these modes then motivate a modified formulation of the Gardner free energy and diffusively accessible free energy to be used for systems in which the important modes have wavevectors that are orthogonal or nearly orthogonal to the magnetic field, as well as a modification to include the effects of a loss region in phase space. [ABSTRACT FROM AUTHOR]

We solve the linearized gyrokinetic equation, quasineutrality condition and Ampere's law to obtain the dispersion relation of microtearing modes (MTMs) in collisionless low- $\beta$ toroidal plasmas. Consistent with past studies, we find that MTMs are driven unstable by the electron temperature gradient and that this instability drive is mediated by magnetic drifts. The dispersion relation that we derive can be evaluated numerically very quickly and may prove useful for devising strategies to mitigate MTM instability in fusion devices. [ABSTRACT FROM AUTHOR]

In view of the ultimate goal of producing long-lasting quasi-stationary discharges required for future fusion power stations, the numerical study of steady-state solutions of equations describing the particle and energy balance rightfully gets ample attention. Transient states may, however, differ significantly from the steady state ultimately reached and will – in practice – impact on the actual fate of the discharge. Using brutally simple models, the present paper highlights a number of aspects to illustrate this dynamics. It e.g. shows the different signature of wave and beam heating, potentially giving room to transiently trigger desirable effects that may allow us to better steer a discharge. [ABSTRACT FROM AUTHOR]

BOUT++ turbulence simulations were performed to investigate the impact of turbulence spreading on the edge localized mode (ELM) size and divertor heat flux width $({\lambda _q})$ broadening in small ELM regimes. This study is motivated by EAST experiments. BOUT++ linear simulations of a pedestal radial electric field (Er) scan show that the dominant toroidal number mode (n) shifts from high- n to low- n , with a narrow mode spectrum, and the maximum linear growth rate increases as the pedestal Er well deepens. The nonlinear simulations show that as the net E  × B pedestal flow increases, the pressure fluctuation level and its inward penetration beyond the top of the pedestal both increase. This leads to a transition from small ELMs to large ELMs. Both inward and outward turbulence spreading are sensitive to the scrape-off-layer (SOL) plasma profiles. The inward turbulence spreading increases for the steep SOL profiles, leading to increasing pedestal energy loss in the small ELM regime. The SOL width $({\lambda _q})$ is significantly broadened progressing from the ELM-free to small ELM regime, due to the onset of strong radial turbulent transport. The extent of the SOL width $({\lambda _q})$ broadening depends strongly on outward turbulence spreading. The fluctuation energy intensity flux ${\varGamma _\varepsilon }$ at the separatrix can be enhanced by increasing either pedestal Er flow shear or local SOL pressure gradient. The ${\lambda _q}$ is broadened as the fluctuation energy intensity flux ${\varGamma _\varepsilon }$ at the last close flux surface (LCFS) increases. Local SOL E  × B flow shear will restrain outward turbulence spreading and the associated heat flux width broadening. Operating in H-mode with small ELMs has the potential to solve two critical problems: reducing the ELM size and broadening the SOL width. [ABSTRACT FROM AUTHOR]

Omnigenity is a desirable property of toroidal magnetic fields that ensures confinement of trapped particles. Confining charged particles is a basic requirement for any fusion power plant design, but it can be difficult to satisfy with the non-axisymmetric magnetic fields used by the stellarator approach. Every ideal magnetohydrodynamic equilibrium previously found to approximate omnigenity has been either axisymmetric, quasi-symmetric or has poloidally closed contours of magnetic field strength $B$. However, general omnigenous equilibria are a much larger design space than these subsets. A new model is presented and employed in the DESC stellarator optimization suite to represent and discover the full parameter space of omnigenous equilibria. Although exact omnigenity aside from quasi-symmetry is impossible, these results reveal that excellent particle confinement can be achieved in practice. Examples far from quasi-symmetry with poloidally, helically and toroidally closed $B$ contours are attained with DESC and shown to have low neoclassical collisional transport and fast particle losses. [ABSTRACT FROM AUTHOR]

The impact of an edge radial electric field on the particle orbits and the orbital spectrum in an axisymmetric toroidal magnetic equilibrium is investigated using a guiding centre canonical formalism. Poloidal and bounce/transit-averaged toroidal precession frequencies are calculated, highlighting the role of the radial electric field. The radial electric field is shown to drastically modify the resonance conditions between particles with certain kinetic characteristics and specific perturbative non-axisymmetric modes, and to enable the formation of transport barriers. The locations of the resonances and the transport barriers that determine the particle, energy and momentum transport are shown to be accurately pinpointed in the phase space by employing the calculated orbital frequencies. [ABSTRACT FROM AUTHOR]

This document is a correction notice for a paper titled "Magnetohydrodynamic stability and the effects of shaping: a near-axis view for tokamaks and quasisymmetric stellarators" by E. Rodriguez. The erratum addresses typographical errors in the equations of the paper, specifically in Figure 5 and Table 1. The errors have been rectified, and supplementary computational and numerical materials are provided for thoroughness and precision. The corrections do not impact the conclusions and discussions presented in the original work. The paper discusses the dependence of the Mercier criterion on lower-order near-axis quantities and the Shafranov shift, and it also provides the correct expression for the geometry at the stellarator symmetric point. [Extracted from the article]

Recently, stochastic motion of 3.5-MeV alpha particles with orbits that vary between locally trapped and locally passing states (transitioning particles) in a Helias reactor was observed numerically. This validated the theoretical predictions that (i) the stochastic diffusion represents a mechanism of considerable delayed loss of fast ions in quasi-isodynamic stellarators and (ii) it is possible to prevent the escape of particles to the wall by closing the separatrix between the locally trapped and passing states. It was concluded that, in principle, the separatrix could be made closed, resulting in a reduction of fast ion losses, by compensating for the effect of the helical component of the magnetic field $(1, 1)$ with an enhanced 'anti-helical' harmonic $(1, -1)$ ; the enlargement of this harmonic was proposed previously for other reasons. This possibility is explored in this work. Equations of previous relevant works were generalised to include the $(1, -1)$ harmonic. Calculations were carried out for several magnitudes of the ratio of anti-helical to helical magnetic field harmonics. Positive effects were found already at the smallest anti-helical harmonic considered: when the latter ratio is 0.25, transitioning particles with the smallest and intermediate pitch parameters are confined and, moreover, their fraction decreased. When the ratio is 0.85, almost all transitioning particles are confined and their fraction is minimal; well-confined localised orbits dominate at the smallest pitch parameters. [ABSTRACT FROM AUTHOR]

The paper presents an investigation of the plasma fluctuation in the SMOLA helical mirror, which is suspected to be responsible for anomalous scattering. The helical mirror confinement is effective when the ion mean free path is equal to the helix pitch length. This condition can be satisfied in hot collisionless plasma only by anomalous scattering. The wave, which scatters the passing ions, is considered to receive energy from the trapped ions. The oscillations of the electric field in the helically symmetric plasma were observed in experiment. The oscillations have both regular highly correlated and chaotic components. The dependency of the regular component frequency on the Alfvén velocity is linear for $V_{\rm A} and constant for higher values. It is shown experimentally that the condition for the wave to be in phase resonance with the trapped ions is satisfied in a specific region of the plasma column for the highly correlated component. The amplitude of the chaotic component (up to $3\ \text {V}\ \text {cm}^{-1}$) is higher than the estimated electric field required for the ion scattering. [ABSTRACT FROM AUTHOR]

This paper explores the feasibility of a break-even-class mirror referred to as BEAM (break-even axisymmetric mirror): a neutral-beam-heated simple mirror capable of thermonuclear-grade parameters and $Q\sim 1$ conditions. Compared with earlier mirror experiments in the 1980s, BEAM would have: higher-energy neutral beams, a larger and denser plasma at higher magnetic field, both an edge and a core and capabilities to address both magnetohydrodynamic and kinetic stability of the simple mirror in higher-temperature plasmas. Axisymmetry and high-field magnets make this possible at a modest scale enabling a short development time and lower capital cost. Such a $Q\sim 1$ configuration will be useful as a fusion technology development platform, in which tritium handling, materials and blankets can be tested in a real fusion environment, and as a base for development of higher- $Q$ mirrors. [ABSTRACT FROM AUTHOR]

Electron-cyclotron resonance heating (ECRH) is the main heating mechanism in the Wendelstein 7-X (W7-X) stellarator. Although second-harmonic ECRH (X2) has been used routinely for plasma startup, startup at third harmonic (X3) is known to be much more difficult. In this work, we investigate the energy gain of particles during nonlinear wave–particle interaction for conditions relevant to second- and third-harmonic startups in W7-X. We take into account both the beam and the ambient magnetic field inhomogeneities. The latter is shown to significantly increase the mean energy gain resulting from a single wave–particle resonant interaction. In W7-X-like conditions, the improvement in maximum gained energy is up to 4 times the analogous uniform magnetic field case. However, this improvement is not enough to ensure X3 startup. The optimal magnetic field inhomogeneity length scale for average energy gain and start up in W7-X-like conditions is found to be in the range of $1$ to $3\ {\rm km}^{-1}$. A possibility of using multiple beams with neighbouring resonances is also considered. A considerable enhancement of the energy gain is demonstrated. [ABSTRACT FROM AUTHOR]

Beam–target reactions in fusion plasmas play an important role in both magnetic confinement fusion and inertial confinement fusion in the condition of low-density plasmas with high-velocity interactions. The traditional method for calculating beam–target reaction rate neglects the transport process of incident particles in inhomogeneous plasmas, leading to errors providing that the temperature and density in the transport path of incident particles vary obviously. An improved method considering the transport process is proposed in this paper to eliminate the deficiencies. Then the method is employed in high-speed plasma collision studies. When the initial plasma density and temperature are set to $0.5\,{\rm g}\,{\rm cm}^{-3}$ and 100 eV, it is found that the beam–target reaction rate calculated by the traditional method is almost identical to that by our method if the collision velocity is less than 600 km s $^{-1}$. However, the traditional method is not suitable for study as the collision velocity gets higher, inducing obvious differences, which can reach 70 % at 1000 km s $^{-1}$. The improved method will make large corrections to evaluate the importance of the non-negligible beam–target reaction for inertial confinement fusion schemes with large implosion velocity such as double-cone ignition and impact ignition, in which the high-speed plasmas collide with each other to realize plasma ignition. [ABSTRACT FROM AUTHOR]

Abstract The theory of turbulent transport of parallel momentum and ion heat by the interaction of stochastic magnetic fields and turbulence is presented. Attention is focused on determining the kinetic stress and the compressive energy flux. A critical parameter is identified as the ratio of the turbulent scattering rate to the rate of parallel acoustic dispersion. For the parameter large, the kinetic stress takes the form of a viscous stress. For the parameter small, the quasilinear residual stress is recovered. In practice, the viscous stress is the relevant form, and the quasilinear limit is not observable. This is the principal prediction of this paper. A simple physical picture is developed and shown to recover the results of the detailed analysis.

In this study, a high sampling rate data acquisition system with the ability to provide timestamp, pulse shape information, and waveform simultaneously under a sub megahertz pulse counting rate was developed for radiation diagnostics for magnetic confinement nuclear fusion plasma research. The testing of the data acquisition system under the high pulse counting rate condition using real signals was performed in an accelerator-based deuterium-deuterium fusion neutron source (Fast Neutron Source) at the Japan Atomic Energy Agency. We found that the pulse counts acquired by the system linearly increased up to 6 × 105 cps, and the count loss at 106 cps was estimated to be ~10%. The data acquisition system was applied to deuterium-deuterium neutron profile diagnostics in the deuterium gas operation of a helical-type magnetic confinement plasma device, called the Large Helical Device, to observe the radial profile of neutron emissivity for the first time in a three-dimensional magnetic confinement fusion device. Time-resolved measurements of the deuterium-deuterium fusion emission profile were performed. The experimentally observed radial neutron emission profile was consistent with numerical predictions based on the orbit-following models using experimental data. The data acquisition system was shown to have the desired performance. [ABSTRACT FROM AUTHOR]

Available energy (Æ), which quantifies the maximum amount of thermal energy that may be liberated and converted into instabilities and turbulence, has shown to be a useful metric for predicting saturated energy fluxes in trapped-electron-mode-driven turbulence. Here, we calculate and investigate the Æ in the analytical tokamak equilibria introduced by Miller et al. (Phys. Plasmas , vol. 5, issue, 4, 1998, pp. 973–978). The Æ of trapped electrons reproduces various trends also observed in experiments; negative shear, increasing Shafranov shift, vertical elongation and negative triangularity can all be stabilising, as indicated by a reduction in Æ, although it is strongly dependent on the chosen equilibrium. Comparing Æ with saturated energy flux estimates from the TGLF (trapped gyro-Landau fluid) model, we find fairly good correspondence, showcasing that Æ can be useful to predict trends. We go on to investigate Æ and find that negative triangularity is especially beneficial in vertically elongated configurations with positive shear or low gradients. Furthermore, we extract a gradient-threshold-like quantity from Æ and find that it behaves similarly to gyrokinetic gradient thresholds: it tends to increase linearly with magnetic shear, and negative triangularity leads to an especially high threshold. We next optimise the device geometry for minimal Æ and find that the optimum is strongly dependent on equilibrium parameters, for example, magnetic shear or pressure gradient. Investigating the competing effects of increasing the density gradient, the pressure gradient, and decreasing the shear, we find regimes that have steep gradients yet low Æ, and that such a regime is inaccessible in negative-triangularity tokamaks. [ABSTRACT FROM AUTHOR]

A collisionless plasma possesses a certain amount of 'available energy', which is that part of the thermal energy that can be converted into kinetic energy of plasma motion and electromagnetic fluctuations. In this paper we present a calculation of the available energy carried by trapped electrons in a slender non-omnigenous flux tube of plasma. This quantity is compared with gyrokinetic simulations of the nonlinear saturated radial energy flux resulting from turbulence driven by collisionless trapped-electron modes in various stellarators and a tokamak. The numerical calculation of available energy is fast and shows a strong correlation with the turbulent energy fluxes found in the gyrokinetic simulations. Indeed, the energy flux is found to be proportional to the available energy to the power of approximately $3/2$ , which is what one would expect from a simple argument. We furthermore investigate how available energy is distributed across different bounce wells, and it is found that deeply trapped electrons typically contribute most to the available energy. Finally, we investigate the dependence of available energy on gradient strength, and we find important differences between weakly and strongly driven regimes for stellarators and tokamaks. [ABSTRACT FROM AUTHOR]

Significant progress has been made in designing magnetic fields that provide excellent confinement of the guiding-centre trajectories of alpha particles using quasisymmetry (QS). Given the reduction in this transport channel, we assess the impact of resonant Alfvén eigenmodes (AEs) on the guiding-centre motion. The AE amplitudes are chosen to be consistent with experimental measurements and large-scale simulations. We evaluate the drift resonance condition, phase-space island width and island overlap criterion for quasisymmetric configurations. Kinetic Poincaré plots elucidate features of the transport, including stiff transport above a critical perturbation amplitude. Our analysis highlights key departures from the AE-driven transport in tokamaks, such as the avoidance of phase-space island overlap in quasihelical configurations and the enhanced transport due to wide phase-space islands in low magnetic shear configurations. In configurations that are closer to QS, with QS deviations $\delta B/B_0 \lesssim 10^{-3}$ , the transport is primarily driven by the AE, while configurations that are further from QS, $\delta B/B_0 \sim 10^{-2}$ , experience significant transport due to the QS-breaking fields in addition to the AE. [ABSTRACT FROM AUTHOR]

Tokamak start-up is strongly dependent on the state of the initial plasma formed during plasma breakdown. To acquire a better understanding of the process and to estimate the influence of the impurity of beryllium on the ohmic heating tokamak start-up process, one-dimensional particle-in-cell coupled with a Monte Carlo collision method has been developed. The main aim is to investigate the plasma performance under various amounts of beryllium with different discharge parameters. Tokamak breakdown with the impurity of beryllium in the ohmic heating strategy has been simulated. The simulation results show that with the impurity of beryllium, the increase of plasma density is suppressed compared with the case without beryllium. The breakdown time is delayed by the impurity. Moreover, the successful breakdown has a much higher requirement on discharge parameters with a low electric field operational scenario, since in the low electric field discharge the influence of beryllium impurity is greater. As the plasma density increases, the effect of beryllium impurity on plasma becomes more critical. It indicates that impurities cannot be neglected in the high plasma density. [ABSTRACT FROM AUTHOR]

We demonstrate a fast adjoint-based method to optimise tokamak and stellarator equilibria against a pressure-driven instability known as the infinite- $n$ ideal ballooning mode. We present three finite- $\beta$ (the ratio of thermal to magnetic pressure) equilibria: one tokamak equilibrium and two stellarator equilibria that are unstable against the ballooning mode. Using the self-adjoint property of ideal magnetohydrodynamics, we construct a technique to rapidly calculate the change in the eigenvalue, a measure of ideal ballooning instability. Using the SIMSOPT optimisation framework, we then implement our fast adjoint gradient-based optimiser to minimise the eigenvalue and find stable equilibria for each of the three originally unstable equilibria. [ABSTRACT FROM AUTHOR]

We show that the saturation of resistive tearing modes in a cylindrical tokamak, as well as the corresponding island width, can be directly calculated with a magnetohydrodynamics (MHD) equilibrium code without solving the dynamics and without considering resistivity. The results are compared with initial-value resistive MHD simulations and to an analytical nonlinear theory. For small enough islands, the agreement is remarkable. For sufficiently large islands, the equilibrium calculations, which assume a flat current profile inside the island, overestimate the saturation amplitude. On the other hand, excellent agreement between nonlinear resistive MHD simulations and nonlinear theory is observed for all the considered tearing unstable equilibria. [ABSTRACT FROM AUTHOR]

If the electrons in a plasma are suddenly heated, the resulting change in Debye shielding causes the ion kinetic energy to quickly increase. For the first time, this correlation heating , which is much faster than collisional energy exchange, is rigorously derived for a moderately coupled, electron–ion plasma. The electron–ion mass ratio is taken to be the smallest parameter in the Bogoliubov–Born–Green–Kirkwood–Yvon hierarchy, smaller even than the reciprocal of the plasma parameter. This ordering differs from conventional kinetic theory by making the electron collision rates faster than the ion plasma frequency, which allows stronger coupling and makes the ion heating a function only of the total energy supplied to the electrons. The calculation uses known formulae for correlations in a two-temperature plasma, for which a new, elementary derivation is presented. Suprathermal ions may be created more rapidly by this mechanism than by ion–electron Coulomb collisions. This means that the use of a femtosecond laser pulse could potentially help to achieve ignition in certain fast ignition approaches to inertial confinement fusion. [ABSTRACT FROM AUTHOR]