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The tearing mode stability of an inverse aspect-ratio expanded tokamak plasma equilibrium of general shape is investigated using asymptotic matching techniques. Particular emphasis is placed on the conservation of toroidal electromagnetic angular momentum. The TJ code, which is a specific implementation of the results of the investigation, is described.
Gyrokinetic simulations of the fishbone instability in DIII-D tokamak plasmas find that self-generated zonal flows can dominate the nonlinear saturation by preventing coherent structures from persisting or drifting in the energetic particle phase space when the mode frequency down-chirps. Results from the simulation with zonal flows agree quantitatively, for the first time, with experimental measurements of the fishbone saturation amplitude and energetic particle transport. Moreover, the fishbone-induced zonal flows are likely responsible for the formation of an internal transport barrier that was observed after fishbone bursts in this DIII-D experiment. Finally, gyrokinetic simulations of a related ITER baseline scenario show that the fishbone induces insignificant energetic particle redistribution and may enable high performance scenarios in ITER burning plasma experiments. Published by the American Physical Society 2024
The tokamak approach, utilizing a toroidal magnetic field configuration to confine a hot plasma, is one of the most promising designs for developing reactors that can exploit nuclear fusion to generate electrical energy. To reach the goal of an economical reactor, most tokamak reactor designs simultaneously require reaching a plasma line-averaged density above an empirical limit—the so-called Greenwald density and attaining an energy confinement quality better than the standard high-confinement mode. However, such an operating regime has never been verified in experiments. In addition, a long-standing challenge in the high-confinement mode has been the compatibility between a high-performance core and avoiding large, transient edge perturbations that can cause very high heat loads on the plasma-facing-components in tokamaks. Here we report the demonstration of stable tokamak plasmas with a line-averaged density approximately 20% above the Greenwald density and an energy confinement quality of approximately 50% better than the standard high-confinement mode, which was realized by taking advantage of the enhanced suppression of turbulent transport granted by high density-gradients in the high-poloidal-beta scenario. Furthermore, our experimental results show an integration of very low edge transient perturbations with the high normalized density and confinement core. The operating regime we report supports some critical requirements in many fusion reactor designs all over the world and opens a potential avenue to an operating point for producing economically attractive fusion energy.
We report x-ray transitions of the very high-n Rydberg series in Ar 16+ have been observed from Alcator C-Mod tokamak plasmas. Individual emission lines up to 1s16p-1s 2 have been resolved and the central chord line brightnesses with principal quantum number n between 7 and 16 are generally found to decay as 1/n α , with α slightly larger than 3. In the plasma periphery, emission from 1s9p-1s 2 and 1s10p-1s 2 are found to be significantly enhanced relative to this decrease, indicative of selected population of these levels through charge exchange between background neutral deuterium in the ground state and Ar 17+ . An unresolved feature between the wavelengths of 1s27p-1s 2 and 1s30p-1s 2 is also present, which arises through charge exchange with neutral deuterium in the n* = 3 excited state. The brightnesses of transitions populated by charge exchange are spatially up/down asymmetric, with an excess on the side of the magnetic surface X-point. The relative brightness of the unresolved very high-n feature compared to 1s7p-1s 2 is found to increase with electron temperature and decrease with electron density. Simulations of line emission just on the long wavelength side of the Ar 16+ ionization limit indicate that the principal quantum number decay exponent is closer to α = 4 at very high n. The brightness dependence on n below 16 is in excellent agreement with calculations from the flexible atomic code package.
We introduce a new approach to measure the magnetic pitch angle profile in tokamak plasmas with Doppler backscattering (DBS), a technique traditionally used for measuring flows and density fluctuations. The DBS signal is maximised when its probe beam's wavevector is perpendicular to the magnetic field at the cutoff location, independent of the density fluctuations [Hillesheim \emph{et al} 2022 \emph{Nucl. Fusion} \textbf{55} 073024]. Hence, if one could isolate this effect, DBS would then yield information about the magnetic pitch angle. By varying the toroidal launch angle, the DBS beam reaches cutoff with different angles with respect to the magnetic field, but with other properties remaining similar. Hence, the toroidal launch angle which gives maximum backscattered power is thus that which is matched to the pitch angle at the cutoff location, enabling inference of the magnetic pitch angle. We performed systematic scans of the DBS toroidal launch angle for repeated DIII-D tokamak discharges. Experimental DBS data from this scan were analysed and combined with Gaussian beam-tracing simulations using the Scotty code [Hall-Chen \emph{et al} 2022 \emph{Plasma Phys. Control. Fusion} \textbf{64} 095002]. The pitch-angle inferred from DBS is consistent with that from magnetics-only and motional-Stark-effect-constrained (MSE) equilibrium reconstruction in the edge. In the core, the pitch angles from DBS and magnetics-only reconstructions differ by one to two degrees, while simultaneous MSE measurements were not available. The uncertainty in these measurements was under a degree; we show that this uncertainty is primarily due to the error in toroidal steering, the number of toroidally separated measurements, and shot-to-shot repeatability. We find that the error of pitch-angle measurements can be reduced by optimising the poloidal launch angle and initial beam properties. Since DBS has high spatial and temporal resolutions, is non-perturbative, does not require neutral beams, and is likely robust to neutron damage of and debris on the first mirrors, using DBS to measure the pitch angle in future fusion energy systems is especially appealing.
This paper provides a comprehensive review of the TRANSP code, a sophisticated tool for interpretive and predictive analysis of tokamak plasmas, detailing its major capabilities and features. It describes the equations for particle, power, and momentum balance analysis, as well as the poloidal field diffusion equations. The paper outlines the spatial and time grids used in TRANSP and details the equilibrium assumptions and solvers. Various models for heating and current drive and radiation, including updates to the NUBEAM model, are discussed. The handling of large-scale events such as sawtooth crashes and pellet injections is examined, along with the predictive capabilities for advancing plasma profiles. The integration of TRANSP with the ITER Integrated Modeling and Analysis Suite (IMAS) is highlighted, demonstrating enhanced data access and analysis capabilities. Additionally, the paper discusses best practices and continuous integration techniques to enhance TRANSP's robustness. The suite of TRANSP tools, designed for efficient data analysis and simulation, further supports the optimization of tokamak operations and coupling with other tokamak codes. Continuous development and support ensure that TRANSP remains a major code for the analysis of experimental data for controlled thermonuclear fusion, maintaining its critical role in supporting the optimization of tokamak operations and advancing fusion research.
Considerable interest in the observation of forbidden spectral lines from highly ionized atoms in tokamak plasmas is related to the significance of such observations for plasma diagnostic applications. Atomic data for the elements Ti Cr, Mn, Fe, Ni, and Kr have been published by Feldman et al. (1980) and Bhatia et al. (1980). The present investigation is concerned with collisional excitation rate coefficients and radiative decay rates, which are interpolated for ions of elements between calcium, and krypton and for levels of the 2s2 2pk, 2s 2p(k+1), and 2p(k+2) configurations, and for the O I, N I, C I, B I, and Be I isoelectronic sequences. The provided interpolated atomic data can be employed to calculate level populations and relative line intensities for ions of the considered sequences, taking into account levels of the stated configurations. Important plasma diagnostic information provided by the forbidden lines includes the ion temperature
Three-dimensional MHD instabilities, including edge-localized modes (ELMs) and internal reconnection events (IREs), have been observed to precipitate loss of vertical stability in tokamak plasmas, resulting in vertical displacement events (VDEs). This vertical destabilization can occur due to toroidal current redistributions and/or shape changes resulting from these phenomena. Using a recently introduced method for rapidly reconstructing the two-dimensional toroidal plasma current density profile in real-time, results are presented that demonstrate the specific current distribution changes that occur during ELMs (on KSTAR) and IREs (on MAST-U) that lead to loss of vertical control. The method most efficiently reconstructs the toroidal current density profile by doing so on a basis of principal components of historical profiles. These principal components isolate dominant current profile dynamics, improving interpretability, increasing speed, and reducing dimensionality of the profile computation. On KSTAR, this computation is executed in the real-time plasma control system at a rate of 10 kHz (limited by available CPU cycle times), allowing the current profile evolution to be assessed at several times over the course of each ELM event. Further, by incorporating the reconstructions into a novel vertical stability metric, the contribution of specific current profile dynamics to the loss of vertical stability can be assessed in real-time for VDE avoidance and improved understanding of the causal relationship between three-dimensional MHD phenomena and VDEs. The success of this method in approximating toroidal current density profiles from kinetic equilibrium reconstructions is also presented ($R^2=0.990$), along with its capability to produce other equilibrium quantities of interest in real-time at high time resolution.
This study investigates the impact of various impurity species on peeling–ballooning (PB) modes and microturbulence in tokamak plasmas through the extension of traditional two-fluid and gyro-landau-fluid (GLF) models. By incorporating finite Larmor radius (FLR) effects, the analysis provides a comprehensive understanding of impurity-driven impact and its interaction with plasma turbulence. Depending on charge state and local plasma conditions, heavy impurities may exhibit gyro-radii larger than those of main ions, which are captured in the extended GLF model presented. Following the presentation of modified two-fluid equations incorporating impurity effects, we systematically analyze the distinctions between impurity and main ion dynamics and their resultant feedback mechanisms on plasma behavior. Derivation of the linear dispersion relation enables quantification of impurity-mediated modifications to: plasma vorticity, diamagnetic drift and gyroviscous effects, electron Hall physics, and FLR effects. BOUT++ – based linear simulations corroborate this formalism, demonstrating systematic stabilization of PB modes upon impurity seeding. And then operational implications for practical impurity control strategies in tokamak devices are proposed. The results underscore the necessity of impurity management to maintain stability and optimize plasma confinement, with specific focus on how FLR effects contribute to transport dynamics. This work paves the way for enhanced modeling and simulation efforts, supporting the development of strategies to control impurity-induced turbulence and improve overall reactor performance.
Gyrokinetic simulations of electrostatic micro-turbulence have been carried out for transport barriers (TBs) in tokamak plasmas. It is found that the ion temperature gradient (ITG) mode is dominant in the pedestal with medium density gradient and steep temperature gradient. The mode width shrinks with increase of the ratio of the density and temperature gradients, which is in good agreement with the analytic theory. Unstable mode with herringbone-like structure is excited in the simulation annulus. The simulation results also indicate that multiple ITG modes are induced by a high temperature gradient. Radial electric field shear decreases the mode growth rate while increases the real frequency. Lastly, the generation of the GAM and its interaction with the turbulence are also observed in the nonlinear simulation.
The paper considers the spectroscopy and atomic physics for some highly ionized Cr, Fe, and Ni ions produced in tokamak plasmas. Forbidden and intersystem wavelengths for Cr and Ni ions are extrapolated and interpolated using the known wavelengths for Fe lines identified in solar-flare plasmas. Tables of transition probabilities for the B I, C I, N I, O I, and F I isoelectronic sequences are presented, and collision strengths and transition probabilities for Cr, Fe, and Ni ions of the Be I sequence are given. Similarities of tokamak and solar spectra are discussed, and it is shown how the atomic data presented may be used to determine ion abundances and electron densities in low-density plasmas.
Magnetic islands are believed to be responsible for triggering the internal transport barrier (ITB) around the rational surface and hence improves confinement in magnetic confinement fusion plasma, for more than two decades. Although some recent theoretical or modelling works support this hypothesis, the direct experimental demonstration on the ITB triggered by a magnetic island is still missing. Here, we report the first experimental observation that the increase in the magnetic island width triggers the bifurcation of the plasma transport state from a low confinement mode (L-mode) to an ITB mode in tokamak plasma. At medium island widths, the bifurcation appears with a dithering phase, i.e. plasma transitions from L-mode to ITB or vice versa quasi-periodically. As the island width further increases, the dithering ITB transitions into a steady ITB. The electron temperature gradient inside the ITB increases with island width. The trigger of the ITB and further enhancement of the ITB performance are also demonstrated by locking the island via applying a resonant magnetic perturbation field. The reduction of density fluctuations in the ITB region is observed and indicates turbulence suppression during ITB formation. These findings offer new insights for understanding ITB formation and robust ITB control.
A major challenge in tokamak fusion research is first-wall erosion caused by steady heat loads and sudden energy bursts known as edge-localized modes. Divertor detachment reduces steady-state heat flux, while resonant magnetic perturbations can suppress these instabilities. However, integrating the two has been difficult because they require conflicting operating conditions. Here we demonstrate simultaneous achievement of resonant magnetic perturbations mitigated small edge-localized modes and impurity seeded partial divertor detachment in plasmas with an ITER-similar shape on the DIII-D tokamak. Experiments and simulations show that resonant magnetic perturbations facilitate detachment by redistributing particles, lowering the core density and increasing the scrape-off layer density, thereby reducing the amount of injected gas required. Cooling-gas injection eliminates the secondary heat-flux peak created by three-dimensional magnetic lobes, while edge cooling weakens the plasma response to the applied magnetic fields. These advances illustrate a viable pathway for integrating edge stability control with power exhaust in future fusion reactors.
In nuclear fusion reactors, plasmas are heated to very high temperatures of more than 100 million kelvin and, in so-called tokamaks, they are confined by magnetic fields in the shape of a torus. Light nuclei, such as deuterium and tritium, undergo a fusion reaction that releases energy, making fusion a promising option for a sustainable and clean energy source. Tokamak plasmas, however, are prone to disruptions as a result of a sudden collapse of the system terminating the fusion reactions. As disruptions lead to an abrupt loss of confinement, they can cause irreversible damage to present-day fusion devices and are expected to have a more devastating effect in future devices. Disruptions expected in the next-generation tokamak, ITER, for example, could cause electromagnetic forces larger than the weight of an Airbus A380. Furthermore, the thermal loads in such an event could exceed the melting threshold of the most resistant state-of-the-art materials by more than an order of magnitude. In this work, to prevent disruptions or at least mitigate their detrimental effects, empirical models obtained with artificial intelligence methods, of which an overview is given here, are commonly employed to predict their occurrence—and ideally give enough time to introduce counteracting measures.
X-ray transitions of the very high-n Rydberg series in Ar^16+ have been observed from Alcator C-Mod tokamak plasmas. Individual emission lines up to 1s16p - 1s^2 have been resolved and the central chord line brightnesses with principal quantum number n between 7 and 16 are generally found to decay as 1/n^alpha, with alpha slightly larger than 3. In the plasma periphery, emission from 1s9p - 1s^2 and 1s10p - 1s^2 are found to be significantly enhanced relative to this decrease, indicative of selected population of these levels through charge exchange between background neutral deuterium in the ground state and Ar^17+. An unresolved feature between the wavelengths of 1s27p - 1s^2 and 1s30p - 1s^2 is also present, which arises through charge exchange with neutral deuterium in the n^* = 3 excited state. The brightnesses of transitions populated by charge exchange are spatially up/down asymmetric, with an excess on the side of the magnetic surface X-point. The relative brightness of the unresolved very high-n feature compared to 1s7p - 1s^2 is found to increase with electron temperature and decrease with electron density. Simulations of line emission just on the long wavelength side of the Ar^16$ ionization limit indicate that the principal quantum number decay exponent is closer to alpha = 4 at very high n. The brightness dependence on n below 16 is in excellent agreement with calculations from the Flexible Atomic Code package.
Minority relativistic electron populations can occur in a range of complex plasmas. Of specific interest is when runaway electrons form among the presence of high-atomic-number ion species in a tokamak plasma discharge. It has been recently demonstrated that ion charge state distributions and radiation losses at low bulk electron temperatures can be dominated by relativistic electrons, even though their density is orders of magnitude lower. Furthermore, this was attributed to the relativistic enhancement of electron impact inelastic cross sections. In this work, we provide a closer inspection of the atomic physics underpinning this effect. We also demonstrate the consequences of runaway enhanced scattering on post-disruption tokamak fusion discharges with neon and argon impurities present. Effects on charge state distributions, radiation and spectral characteristics, and reduced-order modeling considerations are discussed.
A concise and transparent second order ordinary differential equation (ODE) describing the radial structure of the global geodesic acoustic mode (GAM) is analytically presented in a low-β tokamak plasma. The large-aspect-ratio and circular cross section are assumed to linearize the ideal magnetohydrodynamic equations. We show clearly how finite β-dependent terms affect the global GAM frequency and radial mode structure. Here, a typical Wentzel–Kramers–Brillouin form of solution is found for some reversed shear equilibria. For some other equilibria with lower β, even also in a reversed shear tokamak, the GAM continuum is upraised by the high order β-dependent terms so that its maximum is beyond ω G , where ω G is the classical local frequency of GAM. As a result, no self-consistent solution to the ODE can be found.
Abstract The favorable average curvature effect, also known as the GGJ effect (Glasser et al 1975 Phys. Fluids 18 875), is intrinsically associated with parallel sound wave propagation in a tokamak plasma. This work investigates how the GGJ effect is modified by changing the parallel sound wave behavior. Two physics models beyond the standard single fluid theory, i.e. an anisotropic thermal transport model and a parallel sound wave damping model, are employed to change parallel sound waves in a toroidal plasma, and the consequence on the GGJ effect is demonstrated for two important classes of problems, i.e. the resistive plasma response to the applied resonant magnetic perturbation and the stability of the tearing mode. Toroidal modeling reveals that the GGJ effect is significantly altered by both of the aforementioned physics effects. Compared to the thermal transport physics, which completely removes the GGJ effect, the sound wave damping effect only offers partial mitigation. The differences between these two models are further illustrated in terms of the radial structure of the shielding current and the eigenfunction of the tearing instability. In particular, a fundamental reason for complete suppression of the GGJ effect by the thermal transport is identified as an extra toroidal coupling of the poloidal harmonics.