Tokamak Discharges Research Articles

Theory of edge localized mode suppression by static resonant magnetic perturbations in the DIII-D tokamak

According to a recent paper [Hu et al., Phys. Plasmas 26, 120702 (2019)], mode penetration at the top of the pedestal is a necessary and sufficient condition for the suppression of edge localized modes (ELMs) by a resonant magnetic perturbation (RMPs) in an H-mode tokamak discharge. This paper employs asymptotic matching theory to model a particular DIII-D discharge in which ELMs were suppressed by an externally generated, static, n = 2, RMP whose amplitude was modulated at a frequency of 1 Hz. It is demonstrated that the response of the plasma to the applied RMP, in the immediate vicinities of the rational (i.e., resonant) surfaces, is governed by nonlinear, rather than by linear, physics. This is the case because the magnetic island widths associated with driven reconnection exceed the linear layer widths, even in cases where driven reconnection is strongly suppressed by plasma rotation. The natural frequency at a given rational surface (i.e., the helical frequency at which the locally resonant component of the RMP would need to propagate in order to maximize driven reconnection) is found to be offset from the local E×B frame in the ion diamagnetic direction. The size of the offset is mostly determined by neoclassical poloidal rotation. Finally, the predictions of a fully nonlinear plasma response model are found to be broadly consistent with the DIII-D experimental data.

Modelling of nanometer scale dust grains in tokamak

AbstractDust poses a serious threat to tokamak operation and safety. It is important to study the behaviour of dust grains under tokamak's discharge conditions, which depends heavily on their size and charge. Existing simulations mainly address issues on dust grains with radii larger than 1 μm, in which case, the drift effect due to electromagnetic fields can be safely ignored. For nanometer scale dust grains, however, the drift effect becomes significant and a new model based on guiding‐centre system needs to be established. In this work, the NDS has been done under BOUT++ framework. The simulation contains two parts. Part one, NDS evaluates the charging and ablation processes of the dust grains. In the second part, the guiding‐centre orbits of dust particles are tracked in tokamak plasmas, whose parameters are obtained from BOUT++, a highly desirable C++ code package for performing parallel plasma fluid simulations with an arbitrary number of equations in 3D curvilinear coordinates. The orbit of nanodust dynamics is described by guiding centre equations for simplicity, and these equations are numerically solved by conventional fourth‐order Runge Kutta method. Simulations provide results such as trajectories and evolutions of dust particles with different sizes and velocities for different tokamak geometries. Results show tungsten dust grains with a radius of a few nanometers launched from outer midplane will oscillate before totally ablated in C‐Mod. The oscillation in this case is driven by the ion drag force. Larger Nanodust with a radius of 100 nm, on the contrary, cannot be completely constrained by the electromagnetic field. The high plasma temperature and density in the seperatrix region causes severe dust ablation, resulting in total ablation within several ms.

Kinetic modeling of seeded nitrogen in an ITER baseline scenario

ITER as the next-level fusion device is intended to reliably produce more fusion power than required for sustainably heating its plasma. Modeling has been an essential part of the ITER design and for planning of future experimental campaigns. In a tokamak or stellarator plasma discharge, impurities play a significant role, especially in the edge region. Residual gases, eroded wall material, or even intentionally seeded gases all heavily influence the confinement and, thus, the overall fusion performance. Nitrogen is such a gas envisaged to be seeded into a discharge plasma. By modeling the impurities kinetically using the full three-dimensional Monte-Carlo code package EMC3-EIRENE, we analyze the distribution of nitrogen charge-state resolved in a seeded ITER baseline scenario and draw conclusions for the hydrogen background plasma density. Lastly, we compare the influence of a more refined kinetic ion transport in EIRENE including additional physical effects on the impurity density.

Magnetohydrodynamics-induced internal crash near density limit in ohmic discharge on experimental advanced superconducting tokamak

The magnetohydrodynamics (MHD)-induced internal crash (IC) is one of the most fundamental dynamics of a tokamak discharge. Study of IC and the consequent formation of seed island (for neo-classical tearing modes) are still attractive in both experimental and numerical studies. In this work, a set of MHD-induced sawtooth like crashes (SLCs) have been observed in experimental advanced superconducting tokamak (EAST) ohmic discharge near density limit. With the tomography of high-resolution upgraded soft x-ray imaging system, it is observed that m/n = 2/1 tearing mode converts to a m/n = 1/1 instability, and it then triggers crash in the plasma core, here, m is the poloidal mode number and n is the toroidal mode number. Similar to sawtooth crash (SC), the crash of SLC here is due to m/n = 1/1 mode nonlinear dynamic. An extended MHD simulation code M3D is used to understand of the dynamics of m/n = 1/1 internal kink mode in SC in torus. A complex SC is reproduced from M3D nonlinear simulation under EAST realistic magnetic flux equilibrium and experimental resistivity. The rapid growth of unstable m/n = 1/1 kink and interaction with its higher harmonics, are responsible for SC. The simulation results show an existence of annular chaos belt outside q = 1 surface during SC. Furthermore, magnetic islands with higher poloidal mode number are found after SC. The formation of island after SC make plasma current profile flat in the core.

Classification of tokamak plasma confinement states with convolutional recurrent neural networks

During a tokamak discharge, the plasma can vary between different confinement regimes: low (L), high (H) and, in some cases, a temporary (intermediate state), called dithering (D). In addition, while the plasma is in H mode, edge localized modes (ELMs) can occur. The automatic detection of changes between these states, and of ELMs, is important for tokamak operation. Motivated by this, and by recent developments in deep learning, we developed and compared two methods for automatic detection of the occurrence of L-D-H transitions and ELMs, applied on data from the TCV tokamak. These methods consist in a convolutional neural network and a convolutional long short term memory neural network. We measured our results with regards to ELMs using ROC curves and Youden’s score index, and regarding state detection using Cohen’s Kappa index.

Simulation of Alfvénic avalanche onset in NSTX

In some tokamak discharges, a number of Alfvén eigenmodes (AEs) have been observed to cause a large-scale collapse of the high energy particle distribution, a phenomenon referred to as an avalanche. We examine the necessary conditions for an avalanche using the available experimental information from NSTX on the equilibrium and mode properties for two cases, one with a measurable but benign AE activity and one with an AE activity leading up to an avalanche. To produce an avalanche, the modes present in the discharge must possess resonances that can overlap with a modest increase in instability magnitude, providing a path to global particle stochastic motion. We find that the modes present in the avalanche-free discharge do not provide such a path even at a very large amplitude. During the discharge which subsequently produces an avalanche, the high energy population is growing and the Alfvén frequency is dropping due to increasing density, and we find that both these changes, producing a small increased drive or an increased resonance width for the Alfvén modes, can lead in this case to uncontrolled mode growth and large-scale beam particle loss.

Long pulse D2 and N2 seeded discharges on the upper actively cooled tungsten divertor of WEST

A series of L-mode discharges in upper single null configuration with more than 30 s duration were performed in the WEST tokamak with the strike line on actively cooled tungsten-coated divertor components. This series of discharges accumulated 20 min of plasma and a strike point fluence of in two days of operation in attached conditions. The discharges showed good density control, no tungsten accumulation and overall very benign thermal behaviour of the upper divertor. A subset of the discharges were seeded with nitrogen either in the divertor or midplane region to study plasma–wall interaction and associated ammonia formation in this weakly pumped scenario with all-tungsten plasma-facing components. While ammonia signals remained too weak for useful analysis, a strong dependence of nitrogen plasma penetration efficiency and residence time on the injection location was found. This hints towards a currently underestimated plasma-near nitrogen reservoir in these tokamak discharges in divertor configuration.

Robust Cascade LMI Design of MIMO Control System for Plasma Position, Current, and Shape Model with Time-Varying Parameters in a Tokamak

A new robust hierarchical plasma magnetic control system with time-varying parameters and cascade circuits for the Globus-M2 tokamak (Ioffe Institute) has been synthesized by means of the linear matrix inequalities (LMI) method. Each control cascade has a separate objective: placing poles of the closed-loop system in the D-region to guarantee robust performance, restriction of the H∞-norm of the transfer function between external disturbances and the plant outputs of the closed-loop system, tracking PF-currents, CS-current, plasma current, plasma position, gaps between the plasma separatrix and the first wall. Control cascades were synthesized for an array of plant linear models corresponding to reconstructed plasma equilibria at different time points of the tokamak discharges. The LMIs allow the synthesis of one LTI controller, providing the required performance and system stability margin for each model from a given array. Tracking cascades use new MIMO PID controllers adjusted by means of the LMIs.

Discharge simulation and volt-second consumption analysis during ramp-up on the CFETR tokamak**Project supported by the National Key Research and Development Program of China (Grant Nos. 2017YFE0300500 and 2017YFE0300501), the National Natural Science Foundation of China (Grant Nos. 11875290 and 11875253), and the Fundamental Research Funds for the Central Universities of China (Grant No. WK3420000004).

The plasma current ramp-up is an important process for tokamak discharge, which directly affects the quality of the plasma and the system resources such as volt-second consumption and plasma current profile. The China Fusion Engineering Test Reactor (CFETR) ramp-up discharge is predicted with the tokamak simulation code (TSC). The main plasma parameters, the plasma configuration evolution and coil current evolution are given out. At the same time, the volt-second consumption during CFETR ramp-up is analyzed for different plasma shaping times and different plasma current ramp rates dIP/dt with/without assisted heating. The results show that the earlier shaping time and the faster plasma current ramp rate with auxiliary heating will enable the volt-second to save 5%–10%. At the same time, the system ability to provide the volt-second is probably 470 V · s. These simulations will give some reference to engineering design for CFETR to some degree.

Mapping the sawtooth

The sawtooth oscillation involves a topological change of the magnetic field lines in the core of a tokamak discharge. We simulate a steady state sawtoothing discharge using the M3DC1-code. During the sawtooth the topological structure of the magnetic field is analyzed by tracking the fixed points of the field line map: the mapping induced by the field lines going once around the tokamak. We numerically locate the fixed points of the field line map (of which the magnetic axis is one) and use them construct a Poincaré section that resolves the core region and the (1, 1) island. By following the evolution of the magnetic field through the motion and bifurcation of the fixed points of the field line map we get an intuitive picture of the processes that take place during a Kadomtsev style sawtooth crash.

Implementation of cross-phase analysis for study of MHD instabilities arising on TUMAN-3M and Globus-M tokamaks

Following paper represents a method to resolve spatial mode structure of plasma MHD instabilities employing cross-phase correlation analysis applied to signals of magnetic probes, mounted on Globus-M and Tuman-3M tokamaks. The data on observations of toroidal Alfven eigenmodes (TAEs), which were formerly identified in Globus-M tokamak discharges, has been analyzed. Possible interpretation of the phase plot, acquired from analysis of NBI-stimulated ion-cyclotron emission (ICE) on Tuman-3M is given as well. The method described below turns out to be useful instrument for resolution of spatial structure of plasma instabilities, especially in D-shaped tokamaks with low aspect ratio.

Simulations of tokamak boundary plasma turbulence transport in setting the divertor heat flux width

The BOUT + + code has been used to simulate edge plasma electromagnetic (EM) turbulence and transport, and to study the role of EM turbulence in setting the scrape-off layer (SOL) heat flux width λq. More than a dozen tokamak discharges from C-Mod, DIII-D, EAST, ITER and CFETR have been simulated with encouraging success. The parallel electron heat fluxes onto the target from the BOUT + + simulations of C-Mod, DIII-D, and EAST follow the experimental heat flux width scaling of the inverse dependence on the poloidal magnetic field. Further turbulence statistics analysis shows that the blobs are generated near the pedestal pressure peak gradient region inside the separatrix and contribute to the transport of the particle and heat in the SOL region. Transport simulations indicate two distinct regimes: drift dominant regime and turbulence dominant regime. Goldston's heuristic drift-based (HD) model yields a consistent divertor heat flux width in the drift dominant regime. For C-Mod enhanced Dα H-mode discharges, drifts and turbulence are competing in setting the divertor heat flux width, possibly due to its compact machine size and good pedestal confinement.The simulations for ITER and CFETR indicate that divertor heat flux width λq of the future machines may no longer follows the 1/Bpol,OMP HD-based empirical (Eich) scalings and the HD model gives a pessimistic limit of divertor heat flux width. The simulation results show a transition from a drift dominant regime to a turbulence dominant regime from current machines to future machines such as ITER and CFETR for two reasons. (1) The magnetic drift-based radial transport decreases due to large CFETR and ITER machine sizes. (2) The SOL turbulence thermal diffusivity increases due to larger turbulent fluxes ejected from the pedestal into the SOL when operating in a different pedestal structure, from an ELM-free H-mode pedestal regime to a small and grassy ELM regime.

Extreme UV spectrometers for the tungsten 40–70 Å emission in the WEST tokamak

Since the decision to implement a tungsten (W) divertor in ITER, several tokamaks have introduced W in their plasma facing components. For these devices, W monitoring in the core plasma has thus become an important topic of research as its high radiation capability can lead to excessive radiative losses. We have used our extreme UV (EUV) grazing incidence spectrometer (GIS) to investigate the 40–70 Å range where W ions of intermediate charge emit in WEST tokamak discharges. The spectrometer is mounted on a mobile frame controlled with a jack so that it can measure the dependence of the brightness of any spectral feature lying in the observed wavelength interval as a function of the line of sight angle. The quasi-continuum and W line brightnesses in the 40–70 Å range are shown to be much larger when the observed region has a temperature above 3 keV . The brightness profiles as a function of the line of sight position also provides qualitative information on the emitting ions. The delivery and the current installation of a new imaging EUV spectrometer dedicated to the 40–70 Å range are reported. This spectrometer will allow to image the lower inner half of the plasma with an expected time resolution down to 10 ms. The absolute brightness calibration will be performed before the spectrometer is installed on the tokamak at the beginning of the coming experimental campaign.

Reduced energetic particle transport models enable comprehensive time-dependent tokamak simulations

Time-dependent integrated simulations through codes such as TRANSP are becoming an indispensable tool for the interpretation of existing experiments and predictions of optimized scenarios. For many practical cases, quantitative simulations need to include the effect of plasma instabilities on the evolution of a tokamak discharge. An example is the degradation in energetic particle (EP) confinement induced by instabilities, which in turn affects important source terms for heating, non-inductive current, and momentum in a simulation. The reduced-physics kick model provides phase-space resolved transport probability matrices to TRANSP that are used to account for enhanced EP transport by instabilities in addition to neoclassical transport. The model has recovered the measured Alfvén eigenmode (AE) spectrum on NSTX, NSTX-U and DIII-D, and has reproduced details of phase-space resolved fast ion diagnostic data measured on DIII-D for EP-driven modes and tearing modes. In general, the kick model has proven the potential of phase-space resolved EP simulations to unravel details of EP transport for detailed theory/experiment comparison and for scenario planning based on optimization of neutral beam injection parameters. In this work, the extension of the kick model to low-frequency instabilities such as tearing modes and fishbones, in addition to AEs, is assessed. The goal is to enable TRANSP simulations that retain the main effects of multiple types of instabilities through a common framework. Results from the NSTX/NSTX-U and DIII-D tokamaks show that the extension to multi-mode scenarios can expand the range of applicability of the model for more reliable, quantitative integrated simulations.

Liquid tin interactions with ISTTOK plasmas

Materials such as lithium, gallium and tin have been proposed as candidates for liquid metals plasma facing components. The properties of these materials introduce novel methods to cope with the high power loads on the divertor region of nuclear fusion reactors. Although several results have been reported using lithium less experiments were done using gallium or tin. With the purpose of comprehending the impact of the utilisation of tin on a tokamak's plasma performance it was deemed relevant to perform a series of experiments with particular emphasis on plasma contamination. In this work several diagnostics, such as Hα, bolometry, visible spectroscopy and electrostatic probes are used to characterise the interaction of plasmas with tin samples and impact this material had on the tokamak discharge performance. Liquid tin samples were exposed in the ISTTOK's edge and subject to deuterium plasmas. The sample's surface temperature was monitored by pyrometry from which plasma induced heat load was inferred. Heat loads in excess of 300 kWm−2 was regularly observed which are in agreement with Langmuir probe analysis. Hα, bolometry and plasma resistivity were used as proxies for plasma performance and these were found to remain unchanged throughout the sample exposure. The radial impurity content across the plasma column of ISTTOK is characterised by spectroscopic measurements of the Sn-II line 579.88 nm. The line intensity was found to exponentially decrease towards the plasma center with a decay length of ≈2.3 mm. These results suggest that, under specific experimental conditions, liquid tin had a negligible impact in the plasma performance of ISTTOK discharges.

Experimental validation of plasma tomography algorithms at ISTTOK

Plasma tomography is an ill-conditioned inversion problem. Algorithms based on Tikhonov regularization and minimum Fisher information try to overcome this issue by introducing regularization parameters that require empirical tuning. In general, to validate the implementation of these algorithms, either artificial phantoms are used, or one must rely on information provided by other diagnostics. In this work, an experimental setup was developed that allows the use of physical phantoms to tune and validate the reconstruction algorithms. The setup was assembled in a replica of the ISTTOK tokamak with a cylindrical cold cathode lamp placed perpendicular to the poloidal plane at multiple radial and angular positions. It is assumed that this physical phantom acts approximately as a point source in the emissivity profile. Knowing these profiles a priori, it is possible to compare them with the reconstructions produced by the algorithms, in order to tune and optimize the reconstruction parameters. After validation with these physical phantoms, several reconstructions were successfully computed for some tokamak discharges.

A high field side multijunction launcher with aperture impedance matching for lower hybrid current drive in DIII-D advanced tokamak plasmas

A high field side (HFS) lower hybrid current drive launch scenario improves wave accessibility, has single pass damping at r/a ~ 0.6–0.8 and good current drive efficiency in DIII-D advanced tokamak discharges. The DIII-D experiment is an opportunity to validate HFS wave propagation, absorption and scrape-off layer benefits. A HFS multi-junction launcher is designed and simulated in COMSOL over a range of plasma edge conditions to evaluate n|| spectrum, directivity, and return loss. The COMSOL model utilizes a lossy anisotropic dielectric modeled with the cold plasma dispersion relation cross validated against ALOHA and Petra-M codes. The COMSOL model seamlessly includes a realistic plasma model and coupler that allows for rapid optimization of a single launcher module, while Petra-M allows more complex simulation of an eight-module array including curvature, and warm plasma effects. The resulting design utilizes a traveling wave poloidal power divider to minimize peak electric fields in the vacuum region of the coupler, and an internal aperture matching structure provides an impedance match to the plasma over a wide range of plasma density and density gradient edge conditions.

Unified modeling of both resonant and non-resonant neoclassical transport under non-axisymmetric magnetic perturbations in tokamaks

A numerical model for neoclassical transport under nonaxisymmetric magnetic perturbations in low collisionality plasmas in tokamaks is developed. To take into account bounce-drift resonances and magnetic drift effects, a Fourier decomposition of the drift kinetic equation in new coordinates, rather than bounce average of it, is employed. A pitch angle scattering collisional operator is used to keep accuracy in the nonresonant regimes or resonant plateau regimes with resonant pitch near pitch space boundaries. Full toroidal geometry effects are also included to increase the accuracy in the modeling of neoclassical transport in the resonant regimes. Neoclassical transport in the most important collisionless regimes, including resonant super-banana plateau and bounce-drift resonances regimes, nonresonant 1/ν and ν−ν regimes, and the transitions between them, can be modeled simultaneously in this model by numerically solving the drift kinetic equation. By application to the neoclassical toroidal viscosity modeling in one discharge in the EAST tokamak, it is found that the bounce-drift resonances dominate the contributions near the plasma core where the plasma E→×B→ drift frequency is close to the bounce frequency, while the precessional resonance dominates the contribution near the edge pedestal top where the E→×B→ drift frequency is close to zero.

Effects of lithium coating of the chamber wall on the STOR-M tokamak discharges

Lithium (Li) coating of the inner wall of tokamaks has been considered a practical technique to reduce fuel recycling. Li-coating also improves the tokamak wall condition and reduces high-Z material release from the tokamak wall during discharges. In a recent campaign in the STOR-M tokamak (R/a = 0.46/0.12 m, Bt = 0.7 T, Ip = 25 kA), 100 mg of Li has been coated on the tokamak chamber using a physical vacuum evaporation applicator developed by General Fusion Inc. A reduction in the plasma impurity contents and increase in both the peak plasma current and duration have been observed after Li-coating. The line averaged electron density in the plasma reduced after Li-coating. An increase in hard x-ray radiation has also been observed, suggesting an enhanced production of suprathermal run-away electrons because of the reduced electron density. In addition the Li atom emission line has been used to measure the plasma flow velocity based on the Doppler shift of the emission.

Multiple Analytical Approach to Isotopic Transport Analysis in Magnetic Fusion Devices

High-Z impurities released from plasma-material interactions have been shown to limit the performance of fusion plasmas, and understanding these impurity transport mechanisms throughout the plasma scrape-off layer is a major challenge. Presented herein is a study of tungsten (W) erosion and transport by uniquely measuring absolute quantities of isotopic W in order to determine the source of natural and enriched 182W isotopes that have traveled throughout the tokamak discharges on the DIII-D National Fusion Facility at General Atomics. Two primary analysis methods have been implemented to characterize this W on graphite collector probes that were inserted into DIII-D’s outboard midplane. Results from experiments using Rutherford backscattering spectrometry (RBS) have measured W particle areal densities down the centerline of the probes as high as 6E14 atoms/cm2 with a detection limit of 1E12 atoms/cm2. Laser ablation inductively coupled plasma mass spectrometry (LAMS) has confirmed the elemental trends found with RBS and has provided additional insight into collector probe surface profiles. Two-dimensional elemental and isotopic maps from LAMS are used to reveal new collector probe features and further refine the source of collected W. Variations in isotopic profiles and total W content are coupled to (a) the face of the probe being analyzed, (b) the dimensions of the probe, and (c) the plasma pulse parameters that were used during probe exposure. These results provide one-of-a-kind empirical evidence that is now being utilized for validation of tokamak impurity transport through theoretical models and in codes such as 3D-LIM and OEDGE.