Tokamak Edge Research Articles

Advanced surrogate model for electron-scale turbulence in tokamak pedestals

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.

Tokamak edge-SOL turbulence in H-mode conditions simulated with a global, electromagnetic, transcollisional drift-fluid model

Abstract The design of commercially feasible magnetic confinement fusion reactors strongly relies on the reduced turbulent transport in the plasma edge during operation in the high confinement mode (H-mode). We present first global turbulence simulations of the ASDEX Upgrade tokamak edge and scrape-off layer in ITER baseline H-mode conditions. Reasonable agreement with the experiment is obtained for outboard mid-plane measurements of plasma density, electron and ion temperature, as well as the radial electric field. The radial heat transport is underpredicted by roughly 1/3. These results were obtained with the GRILLIX code implementing a transcollisional, electromagnetic, global drift-fluid plasma model, coupled to diffusive neutrals. The transcollisional extensions include neoclassical corrections for the ion viscosity, as well as either a Landau-fluid or free-streaming limited model for the parallel heat conduction. Electromagnetic fluctuations are found to play a critical role in H-mode conditions. We investigate the structure of the significant E × B flow shear, finding both neoclassical components as well as zonal flows. But unlike in L-mode, geodesic acoustic modes are not observed. The turbulence mode structure is mostly that of drift-Alfvén waves. However, in the upper part of the pedestal, it is very weak and overshadowed by neoclassical transport. At the pedestal foot, on the other hand, we find instead the (electromagnetic) kinetic ballooning mode, most clearly just inside the separatrix. Our results pave the way towards predictive simulations of fusion reactors.

Electron transport barrier and high confinement in configurations with internal islands close to the plasma edge of W7-X

Abstract The low magnetic shear in the Wendelstein 7-X (W7-X) stellarator makes it feasible to shape the separatrix by the large islands constituting an island-divertor, and this can be exploited to access various magnetic configurations, including samples of different internal island sizes and locations. To investigate the configuration effects on the plasma confinement, a configuration scan was performed by changing the coil currents to vary the rotational transform between values 5 / 4 and 5 / 6 at the plasma boundary with different power levels (2, 4, 6 MW) of electron cyclotron resonance heating (ECRH) at a maximum plasma density of 8 × 10 19 m − 2 . neutral beam injection (NBI) heating was also applied during some configurations of the scan to create a density ramp and access high densities beyond the X2 ECRH cutoff. For the magnetic configurations, where the 5 / 5 and 5 / 6 island chains were moved closer to separatrix but remaining inside the last closed flux surface, the electron cyclotron emission shows that an electron temperature, T e , pedestal develops already during ECRH heated plasma buildup phase indicating a transport barrier, and the barrier sustains irrespective of changed plasma heating conditions such as NBI in the later part of discharge. The transport barrier is broken by subsequent fast crashes, observed with multiple plasma diagnostics with characteristics such as tokamak edge localized modes, and the corresponding crash amplitude and frequency vary with plasma pressure. The impact of the transport barrier on plasma confinement can be seen through the increased core T e profile, which could be responsible for the overall increase in the stored diamagnetic energy by approximately 10% for these configurations. After the plasma heating is terminated, a backwards transition to a degraded confinement state is also observed. These observations indicate a configuration triggered high confinement mode in low shear W7-X. This work focuses on the occurrence of this transport barrier for different magnetic configurations and its relation to internal magnetic islands.

Applicability of alkali beam emission spectroscopy on NSTX-U.

Understanding fast pedestal dynamics and turbulent transport in the edge and scrape-off layer (SOL) plasma of spherical tokamaks is crucial for the design and operation of future fusion reactors. The alkali beam emission spectroscopy diagnostic technique offers a means to measure the absolute electron density radial profile and fluctuation amplitude in these regions. In this study, we demonstrate that injecting a sodium neutral beam radially into the plasma and analyzing the light emission from its 3p-3s atomic transition using near-orthogonal viewing angles allows for accurate measurement of the electron density profile and fluctuations in the National Spherical Torus Experiment (NSTX) Upgrade spherical tokamak. Our findings indicate a peak signal-to-noise ratio of 118 in the pedestal and 12 in the SOL under typical NSTX plasma conditions. The spatial resolution for the electron density profile is estimated to be between 2 and 8mm, while for fluctuation measurements, it ranges from 12 to 15mm.

Symmetries of the Electromagnetic Turbulence in a Tokamak Edge

We construct the low-frequency formulation of the turbulence characterizing the plasma in a Tokamak edge. Under rather natural assumptions, we demonstrate that, even in the presence of poloidal magnetic fluctuations, it is possible to deal with a reduced model for turbulence dynamics. This model relies on a single equation for the electric potential from which all the physical turbulent properties can be calculated. The main result of the present analysis concerns the existence of a specific Fourier branch for the dynamics which demonstrate the attractive character of the two-dimensional turbulence with respect to non-axisymmetric fluctuations. The peculiar nature of this instability, affecting the non-axially symmetric modes, is discussed in some detail by recovering two different physical regimes.

HL‐2A's ELM cycle simulations by integrating BOUT++'s drift MHD and transport code

AbstractA new integrating model has been developed to couple tokamak edge multiscale magnetohydrodynamic (MHD) events and transport simulations, such as edge‐localized mode (ELM) cycles. As a proof of principle, we first start from a set of three‐field two‐fluid model equations, which includes the pressure, current, and vorticity. The equations are separated into the slowly evolving part of the axisymmetric component by taking a time average of the axisymmetric component. The time‐averaged fluxes, which are quadratic in fluctuating quantities, act as driven terms for the time‐averaged axisymmetric quantities that determine the plasma transport, and therefore the large‐scale evolution of the plasma profiles. Then the HL‐2A's ELM cycles are simulated using the model. Good agreements of ELM size and pedestal recovery time have been achieved for the solutions obtained from the coupled simulation compared with experiment. For one ELM cycle simulation, the coupled code can achieve a speedup of a factor of up to 30 over standalone code.

Retraction Note to: Effects of External Resonant Fields on the Tokamak Edge Plasma Fluctuations

Retraction Note to: Effects of External Resonant Fields on the Tokamak Edge Plasma Fluctuations

Retraction Note to: Turbulent Transport in the Tokamak Edge Plasma and SOL Region

Retraction Note to: Turbulent Transport in the Tokamak Edge Plasma and SOL Region

Tokamak edge localized mode onset prediction with deep neural network and pedestal turbulence

A neural network, BES-ELMnet, predicting a quasi-periodic disruptive eruption of the plasma energy and particles known as edge localized mode (ELM) onset is developed with observed pedestal turbulence from the beam emission spectroscopy system in DIII-D. BES-ELMnet has convolutional and fully-connected layers, taking two-dimensional plasma fluctuations with a temporal window of size 128 µs and generating a scalar output which can be interpreted as a probability of the upcoming ELM onset. As approximately labeled inter-ELM broadband ( 15kHz⩽f⩽150kHz ) fluctuations are given to the network, BES-ELMnet learns by itself ELM-related precursors arising before the onsets through supervised learning scheme. BES-ELMnet achieves the gradually increasing ELM onset probabilities between two consecutive ELMs during the inter-ELM phases and can forecast the first ELM onsets which occur after the high confinement mode transition. We further investigate the network generality in terms of the selected frequency band to ensure the use of BES-ELMnet for various operation regimes without changing the trained architecture. Therefore, our novel prediction method will enhance a proactive high confinement mode control of fusion-grade plasmas.

Breakdown of Quasilinear Theory in the Tokamak Edge.

In the edge of an L-mode tokamak plasma, particle transport and ion energy transport are shown to follow a strong microturbulence (SMT) scaling, whereas in the plasma core the transport is shown to follow quasilinear turbulence scaling. The dependence of diffusivity on potential fluctuation amplitude is linear in the SMT regime, and quadratic in the quasilinear regime. The transition to strong microturbulence results from larger E×B drift velocities in the edge compared to the plasma core. At these larger velocities, ions traverse the spatially correlated range faster than the stochastic evolution of the electric potential. Hence, these particles do not experience a time-stochastic field as required by the quasilinear approximation. Instead, scattering of particles in the SMT regime is caused by spatial stochasticity. In contrast, electron energy transport remains quasilinear due to decorrelations caused by collisions and fast parallel motion. Improved understanding of transport beyond quasilinear theory opens the path to more accurate modeling of transport in the tokamak plasma edge.

The effect of divertor particle sources on scrape-off-layer turbulence

Tokamak edge turbulence is crucial for the cross-field transport of particles and energy away from the separatrix. A better understanding of what affects the turbulence helps to control the heat flux to the divertor targets and the wall. One potentially important factor is the ion particle source in the divertor, as the neutral pathways and the ionisation source distributions are different depending on the divertor geometry, e.g. vertical- and horizontal-target configurations. Numerically, how to represent the sources and mimic the effects on the SOL in the simulations is still an open question. In this paper, we use a 3D turbulence code STORM, based on drift-reduced Braginskii equations, to study the effects of the divertor particle source distribution on turbulence in a simplified 3D slab geometry. The results show that it requires a large amount of divertor particle source to be peaked near the separatrix to alter the heat flux deposited on the target in attached conditions. This large non-uniform particle source can locally enhance the turbulence in the divertor volume, which redistributes the energy flux to the target and reduces the maximum amplitude. Meanwhile, the plasma profiles evaluated at the outboard midplane, such as the amplitudes and fluctuations of the density and temperature, are marginally changed. Another consequence of our results is that the prediction of the temperature difference between the outboard midplane and the target would be underestimated, if the calculation only considers the conductive heat flux and ignores this enhanced cross-field transport in the divertor.

Simulation of ion temperature gradient driven modes with 6D kinetic Vlasov code

With the increase in computational capabilities over the last few years, it becomes possible to simulate more and more complex and accurate physical models. Gyrokinetic theory has been introduced in the 1960s and 1970s in the need of describing a plasma with more accurate models than fluid equations but eliminating the complexity of the fast gyration about the magnetic field lines. Although results from current gyrokinetic computer simulations are in fair agreement with experimental results in core physics, crucial assumptions made in the derivation make it unreliable in regimes of higher fluctuations and stronger gradient, such as the tokamak edge. With our novel optimized and scalable semi-Lagrangian solver, we are able to simulate ion temperature gradient modes with the 6D kinetic model including the turbulent saturation. After thoroughly testing our simulation code against analytical computations and gyrokinetic simulations (with the gyrokinetic code GYRO), it has been possible to show first plasma properties that go beyond standard gyrokinetic simulations. This includes the explicit description of the complete perpendicular energy fluxes and the excitation of high-frequency waves (around the Larmor frequency) in the nonlinear saturation phase.

Effects of resonant magnetic perturbations on turbulence and flows in the edge of HL-2A plasmas

The influence of resonant magnetic perturbations (RMPs) on the dynamics of turbulence and flows at the edge of the HL-2A tokamak is analyzed utilizing transfer entropy technique. The results have shown that the RMP damps the poloidal flows as well as the E × B shearing rate, whereas enhances the toroidal flows and leads to a broadened particle spectrum with increased small scale turbulence transport. The causality analysis indicates that the regulation impact of poloidal flow on turbulent fluctuations and particle flux is weakened, while that of the toroidal rotation on the latter is strengthened by the RMP field. The impact of the changes in poloidal flow dominates over that of the modified toroidal flow on turbulent transport in the edge. The magnetic perturbation and the flows generally show predator–prey oscillations, where the causal effect between the former and the toroidal flow transits to a synchronization relation in the presence of RMP. In addition, the RMP field will weaken the causal effect on poloidal Reynolds stress while strengthening the parallel-radial component simultaneously. The present findings provide a possible explanation on the effects of external fields on the edge transport, which is suggested to be dominated by the complex interactions among external perturbations, flows, and ambient microturbulence.

Simulations of tokamak edge plasma turbulent fluctuations based on a minimal 3D model

A new simulation model for tokamak boundary plasma, SOLT3D, is implemented in the BOUT++ framework (Dudson et al 2009 Comput. Phys. Commun. 180 1467). The simulation model includes a set of dynamic equations describing collisional boundary plasma and neutral gas in the tokamak scrape-off layer and divertor region. The model is verified against standard linear plasma instabilities and available nonlinear results. For L-mode like conditions, SOLT3D reproduces characteristics of boundary plasma turbulent fluctuations that are similar to published experimental data, in terms of the amplitude and spatial dependence of the fluctuations. It also reproduces realistic plasma fluxes on material surfaces and expected Bohm-like effective radial transport. Plasma fluctuations inferred from the simulations imply inevitably a significant level of intrinsic ‘noise’ for axisymmetric tokamak plasma transport modeling, introducing errors on the order of unity. In particular, the toroidally averaged atomic rates below 5–10 eV are strongly modified by turbulent plasma fluctuations, which should significantly affect the standard axisymmetric modeling of the tokamak edge plasma and divertor.

A Gaussian process guide for signal regression in magnetic fusion

Extracting reliable information from diagnostic data in tokamaks is critical for understanding, analyzing, and controlling the behavior of fusion plasmas and validating models describing that behavior. Recent interest within the fusion community has focused on the use of principled statistical methods, such as Gaussian process regression (GPR), to attempt to develop sharper, more reliable, and more rigorous tools for examining the complex observed behavior in these systems. While GPR is an enormously powerful tool, there is also the danger of drawing fragile, or inconsistent conclusions from naive GPR fits that are not driven by principled treatments. Here we review the fundamental concepts underlying GPR in a way that may be useful for broad-ranging applications in fusion science. We also revisit how GPR is developed for profile fitting in tokamaks. We examine various extensions and targeted modifications applicable to experimental observations in the edge of the DIII-D tokamak. Finally, we discuss best practices for applying GPR to fusion data.

Pedestal main ion particle transport inference through gas puff modulation with experimental source measurements

Transport in the DIII-D high confinement mode (H-mode) pedestal is investigated through a periodic edge gas puff modulation (GPM) which perturbs the deuterium density and source profiles. By using absolutely calibrated experimental edge ionization profile measurements, radial profiles of diffusion (D) and convection (v) are calculated into the pedestal region without depending on modeling the edge ionization source. An analytic approach with closed-form expressions for the D and v profiles and a more advanced Bayesian approach show evidence of an inward particle convection on the order of 1 m s−1 extending to normalized poloidal flux ( ΨN ) of 0.98. Meanwhile, diffusion reaches a minimum value of (0.03±0.02) m2 s−1 in the pedestal region. Notably, the Bayesian approach, which utilizes the Aurora 1.5 D forward model inside the IMPRAD OMFIT module, provides radially resolved transport profiles with associated uncertainty without requiring an explicit form for the perturbation to the density profile or source. The combination of experimental ionization measurements and Bayesian inference provides an enhanced robust framework for investigating edge particle transport coefficients to experimentally test transport physics in order to improve predictive capabilities in the tokamak edge.

New Method for Spectroscopic Diagnostics of Tokamak Edge Plasmas Based on a Peculiar Stark Broadening of Hydrogen or Deuterium Spectral Lines Emitted by the Injected Neutral Beam

New Method for Spectroscopic Diagnostics of Tokamak Edge Plasmas Based on a Peculiar Stark Broadening of Hydrogen or Deuterium Spectral Lines Emitted by the Injected Neutral Beam

Robust Avoidance of Edge-Localized Modes alongside Gradient Formation in the Negative Triangularity Tokamak Edge.

In a series of high performance diverted discharges on DIII-D, we demonstrate that strong negative triangularity (NT) shaping robustly suppresses all edge-localized mode (ELM) activity over a wide range of plasma conditions: ⟨n⟩=0.1-1.5×10^{20} m^{-3}, P_{aux}=0-15 MW, and |B_{t}|=1-2.2 T, corresponding to P_{loss}/P_{LH08}∼8. The full dataset is consistent with the theoretical prediction that magnetic shear in the NT edge inhibits access to ELMing H-mode regimes; all experimental pressure profiles are found to be at or below the infinite-n ballooning stability limit. Our present dataset also features edge pressure gradients in strong NT that are closer to an H-mode than a typical L-mode plasma, supporting the consideration of NT for reactor design.

Unstable drift waves in presence of dust

The well-known stability of the drift wave in a sheared slab geometry does not hold in the presence of dust particles. Due to the presence of dust particles, the magnetic shear damping is reduced drastically. As a result, collisionless drift modes become unstable under typical parameter regimes of tokamak. Consequently, drift wave must still be considered as an underlying dynamic of anomalous transport in tokamak edges, where dust particles are found to be abundant, the same physics is expected in the spacial environments as well.

Supervised machine learning-based multivariate regression of parallel closures for a high-collisionality deuterium-carbon plasma

Many plasmas of interest in laboratory experiments and space consist of multiple ion species. In tokamak edge plasmas, for instance, ionized impurities expelled from the vessel wall influence plasma transport. When describing multi-species plasmas using fluid equations, we need accurate closure relations to close the set of fluid equations. In this study, we introduce the development of fitting formulas for parallel closures using supervised machine learning, in conjunction with the recent closure theory [J.-Y. Ji, Plasma Phys. Controlled Fusion 65, 075014 (2023)], considering multi-ion collisions and arbitrary ion temperatures. We apply this approach to a high-collisionality deuterium-carbon plasma and demonstrate its effectiveness. The machine learning-based method for developing practical and accurate closures can be extended to a wider range of plasmas.