Tokamak Edge Plasma Research Articles

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.

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

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

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 role of shear flow collapse and enhanced turbulence spreading in edge cooling approaching the density limit

Experimental studies of the dynamics of shear flow and turbulence spreading at the edge of tokamak plasmas are reported. Scans of line-averaged density and plasma current are carried out while approaching the Greenwald density limit on the J-TEXT tokamak. In all scans, when the Greenwald fraction fG=n¯/nG=n¯/(Ip/πa2) increases, a common feature of enhanced turbulence spreading and edge cooling is found. The result suggests that turbulence spreading is a good indicator of edge cooling, indeed better than turbulent particle transport is. The normalized turbulence spreading power increases significantly when the normalized E×B shearing rate decreases. This indicates that turbulence spreading becomes prominent when the shearing rate is weaker than the turbulence scattering rate. The asymmetry between positive/negative (blobs/holes) spreading events, turbulence spreading power and shear flow are discussed. These results elucidate the important effects of interaction between shear flow and turbulence spreading on plasma edge cooling.

Cascades of Parametric Instabilities in the Tokamak Plasma Edge during Electron Cyclotron Resonance Heating.

We report observations of nonlinear two-plasmon decay instabilities (TPDIs) of a high-power microwave beam, a process similar to half-harmonic generation in optics, during electron cyclotron resonance heating in a tokamak. TPDIs are found to occur regularly in the plasma edge due to wave trapping in density fluctuations for various confinement modes, and the frequencies of both observed daughter waves agree with modeling. Emissions from a cascade of subsequent decays, which indicate a generation of ion Bernstein waves, are correlated with fast-ion generation. This emphasizes the limitations of standard linear microwave propagation models and possibly paves the way for novel microwave applications in plasmas.

Toward plasma drifts in EMC3: Implementation of gradient, divergence, and particle tracing schemes

AbstractThis paper presents a first implementation of gradient, divergence, and particle tracing schemes for the EMC3 code, a stochastic 3D plasma fluid code widely employed for edge plasma and impurity transport modeling in tokamaks and stellarators. These schemes are essential to accommodate plasma drift computations, which are currently absent in the code. Plasma drifts have been recognized to significantly influence transport of particles and energy, and their inclusion in future code upgrades will substantially enhance the code's predictive capabilities. For gradient and divergence calculations, we introduce a second‐order least‐squares gradient scheme. We confirm the second‐order convergence properties and assess the accuracy of several analytical test cases in the presence of synthetic noise. In the second part of this paper, we employ the validated gradient scheme in a fourth‐order Runge–Kutta particle tracing scheme to trace a particle through a generic drift velocity field. The impact of synthetic noise on the scheme's performance is investigated by evaluating various error metrics. We find that the implemented schemes function as intended and exhibit sufficient accuracy to enable drift computations.

Synthesizing impurity clustering in the edge plasma of tokamaks using neural networks

This work investigates the behavior of impurities in edge plasma of tokamaks using high-resolution numerical simulations based on Hasegawa–Wakatani equations. Specifically, it focuses on the behavior of inertial particles, which has not been extensively studied in the field of plasma physics. Our simulations utilize one-way coupling of a large number of inertial point particles, which model plasma impurities. We observe that with Stokes number (St), which characterizes the inertia of particles being much less than one, such light impurities closely track the fluid flow without pronounced clustering. For intermediate St values, distinct clustering appears, with larger Stokes values, i.e., heavy impurities even generating more substantial clusters. When St is significantly large, very heavy impurities tend to detach from the flow and maintain their trajectory, resulting in fewer observable clusters and corresponding to random motion. A core component of this work involves machine learning techniques. Applying three different neural networks—Autoencoder, U-Net, and Generative Adversarial Network (GAN)—to synthesize preferential concentration fields of impurities, we use vorticity as input and predict impurity number density fields. GAN outperforms the two others by aligning closely with direct numerical simulation data in terms of probability density functions of the particle distribution and energy spectra. This machine learning technique holds the potential to reduce computational costs by eliminating the need to track millions of particles modeling impurities in simulations.

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.

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

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.

Recent development of LIF diagnostics in ASIPP

In this article, recent research progress of laser induced fluorescence (LIF) diagnostics in ASIPP is reviewed. The fundamental goal of ASIPP's effort on the LIF diagnostics is to develop a working velocity distribution function (VDF) diagnostic to monitor helium ash removal in burning plasmas. Real-time monitoring of helium ash VDF requires consideration in radiation safety, measurement response time, and compatibility of tokamak operation, as well as ion/neutral VDFs with a temperature at possibly >20 eV. These considerations, almost unique to large-scale instruments or specifically to tokamak plasmas, require renewed research and development (R&D) efforts in optical design, automation, and expansion of laser functionality for the LIF diagnostics that were often not considered in conventional applications of the LIF diagnostics. To this end, ASIPP invested a series of research effort into the development of LIF techniques. Signal evaluation has been performed on a diagnostics-test device (LTS), and the obtained signal strength has been extrapolated to tokamak edge and divertor relevant environments with promising results. The extrapolations compared the available solid angle and plasma density between the test device and the design scenario where the LIF diagnostics will potentially be implemented in a tokamak edge and divertor plasma. The estimation neglects the higher density of energetic electrons in the edge and divertor regions, making it a conservative assessment. Automated post-DAQ processing of LIF signals using both “conventional” methods and an AI-augmented method were also explored. Both approaches yielded usable results, but the AI-trained method showed a faster response, which is advantageous for real-time plasma diagnostics. Basic mechanisms of LIF diagnostics were also explored. Specifically, the limitations of lock-in modulation was demonstrated to determine the limitation of time-resolved measurements using such methods. De-modulation and degradation of the LIF signal occurred as the modulation frequency exceeded 1/10th of the fluorescence frequency. This finding sets a practical limit of the modulation frequency up to which we can benefit from lock-in amplification. These published works along with other unpublished progress will be thoroughly discussed in this article to illustrate ASIPP's effort towards the implementation of LIF diagnostics in future tokamak devices and to promote the application of LIF diagnostics in other fields of research.

Electromagnetic turbulence simulation of tokamak edge plasma dynamics and divertor heat load during thermal quench

The edge plasma turbulence and transport dynamics, as well as the divertor power loads during the thermal-quench phase of tokamak disruptions, are numerically investigated with BOUT++’s flux-driven six-field electromagnetic turbulence model. Here, transient yet intense particle and energy sources are applied at the pedestal top to mimic the plasma power drive at the edge induced by a core thermal collapse, which flattens the core temperature profile. Interesting features, such as surging of divertor heat load (up to 50 times) and broadening of heat-flux width (up to four times) on the outer-divertor target plate, are observed in the simulation, in qualitative agreement with experimental observations. The dramatic changes in divertor heat load and width are due to the enhanced plasma turbulence activities inside the separatrix. Two cross-field transport mechanisms, namely, the E × B turbulent convection and the stochastic parallel advection/conduction, are identified to play important roles in this process. First, an elevated edge pressure gradient drives instabilities and subsequent turbulence in the entire pedestal region. The enhanced turbulence not only transports particles and energy radially across the separatrix via the E × B convection, which causes the initial divertor heat-load burst, but it also induces amplified magnetic fluctuation . Once themagnetic fluctuation is large enough to break the magnetic flux surface, magnetic flutter effect provides an additional radial transport channel. In the late stage of our simulation, reaches to 10−4 level that completely breaks magnetic flux surfaces such that stochastic field lines are directly connecting pedestal top plasma to the divertor target plates or first wall, further contributing to the divertor heat-flux width broadening.

Data processing and visualization tool for atomic and molecular data for collisional radiative models

The Monte Carlo kinetic code EIRENE (Sect. 2) is used for simulating the behavior of neutral species in the edge of tokamak plasma and coupled with fluid plasma codes for a self-consistent description to be compared with measured experimental conditions. The data and visualization toolbox HYDKIN (Sect. 3) has been developed as a pre-processing tool for validation of those atomic and molecular (A &M) data used in EIRENE simulations, such as cross sections and reaction rates for plasma-neutral and neutral-neutral collisions. The restructuring that is being performed to increase HYDKIN readability and usability is here presented (Sect. 4).Graphic

Numerical study of impurity effects on ion temperature gradient modes in tokamak edge plasmas based on the Euler matrix eigenvalue method

Low-Z impurity injection is frequently used for divertor detachment operations in current tokamaks; however, the impurity effects on the main plasma are yet to be fully understood. In this paper, the impurity effects on the ion temperature gradient (ITG) modes in tokamak edge plasmas are investigated based on the Euler matrix eigenvalue method. The eigen-equations with multiple ion species are established from the fundamental gyrokinetic theory, in which each ion species is treated equally. A novel and efficient gyro-kinetic code is developed for this numerical study, and the code’s availability to examine quasi-linear ITG modes is demonstrated by its comparison with existing results. At the pedestal top parameters in Experimental Advanced Superconducting Tokamak high-β p H-mode plasmas, the ITG mode behavior is investigated in pure deuterium plasmas and with impurities. Impurities can induce destabilizing or stabilizing effects on ITG modes, which are determined by the impurity density scale length. The inwardly peaked impurity density profile tends to reduce the ITG growth rate. The effect strength also increases with the impurity charge concentration. The effects of impurity species, including boron, carbon, neon and argon, are also evaluated. Numerical results show that the strength of destabilizing or stabilizing effect inverses with impurity ion charge at the same effective charge.

Nonmodal kinetic theory of the stability of the compressed–sheared plasma flows generated by the inhomogeneous microscale turbulence in the tokamak edge plasma

The nonmodal kinetic theory of the stability of the two-dimensional compressed–sheared mesoscale plasma flows, generated by the radially inhomogeneous electrostatic ion cyclotron parametric microturbulence in the pedestal plasma with a sheared poloidal flow, is developed. It bases on the investigation of the temporal evolution of the compressed–sheared modes. The integral equation, which governs the temporal evolution of the electrostatic potential of the plasma species responses on the mesoscale compressed–sheared convective flows, is derived. The exceptional advantage of the derived integral equation, which uses the wavevector-time variables, is the ability to perform the analysis of the nonmodal evolution of electrostatic potential during any finite time domain and to investigate the transient processes which occurs at any definite time scales. The approximate nonmodal solution of this equation for the kinetic drift instability in the compressed flow is given.

Towards fast surrogate models for interpolation of tokamak edge plasmas

One of the major design limitations for tokamak fusion reactors is the heat load that can be sustained by the materials at the divertor target. Developing a full understanding of how machine or operation parameters affect the conditions at the divertor requires an enormous number of simulations. A promising approach to circumvent this is to use machine learning models trained on simulation data as surrogate models. Once trained such surrogate models can make fast predictions for any scenario in the design parameter space. In future such simulation based surrogate models could be used in system codes for rapid design studies of future fusion power plants. This work presents the first steps towards the development of such surrogate models for plasma exhaust and the datasets required for their training. Machine learning models like neural networks usually require several thousand data points for training, but the exact amount of data required varies from case to case. Due to the long runtimes of simulations we aim at finding the minimal amount of training data required. A preliminary dataset based on SOLPS-ITER simulations with varying tokamak design parameters, including the major radius, magnetic field strength and neutral density is constructed. To be able to generate more training data within reasonable computation time the simulations in the dataset use fluid neutral simulations and no fluid drift effects. The dataset is used to train a simple neural network and Gradient Boosted Regression Trees and test how the performance depends on the number of training simulations.

Stochastic fluctuation and transport of tokamak edge plasmas with the resonant magnetic perturbation field

We present that a statistical method known as the complexity–entropy analysis is useful to characterize a state of plasma turbulence and flux in the resonant magnetic perturbation (RMP) edge localized mode (ELM) control experiment. The stochastic pedestal top temperature fluctuation in the RMP ELM suppression phase is distinguished from the chaotic fluctuation in the natural ELM-free phase. It is discussed that the stochastic temperature fluctuation can be originated from the narrow layer of the field penetration on the pedestal top. The forced magnetic island can emit the resonant drift wave of comparable sizes (relatively low-k) in the RMP ELM suppression phase, and it can result in the generation of stochastic higher wavenumber fluctuations coupled to tangled fields around the island. The analysis of the ion saturation current measurement around the major outer striking point on the divertor shows that it also becomes more stochastic as the stronger plasma response to the RMP field is expected.

Effects of sawtooth heat pulses on edge flows and turbulence in a tokamak plasma

Enhancements of edge zonal flows, radial electric fields, and turbulence are observed in electron cyclotron resonance heating-heated plasmas (Zhao et al 2013 Nucl. Fusion 53 083011). In this paper, the effects of sawtooth heat pulses on flows and turbulence are presented. These experiments are performed using multiple Langmuir probe arrays in the edge plasmas of the HL-2A tokamak. The edge zonal flows, radial electric fields, and turbulence are all enhanced by sawteeth. Propagation of the zonal flow and turbulence intensities is also observed. The delay time of the maximal intensity of the electric fields, zonal flows, and turbulence with respect to the sawtooth crashes is estimated as ∼1 ms and comparable to that of the sawtooth-triggered intermediate phases. Not only the zonal flows but also the radial electric fields lag behind the turbulence. Furthermore, the intensities of both the zonal flows and electric fields nearly linearly increase/decrease with the increase/decrease of the turbulence intensity. A double-source predator–prey model analysis suggests that a relatively strong turbulence source may contribute to the dominant zonal flow formation during sawtooth cycles.

A BOUT++ extension for full annular tokamak edge MHD and turbulence simulations

For tokamak edge plasma simulation, a plasma simulation framework BOUT++ employs a dual coordinate system to simulate moderate-n and high-n plasma instability with reasonable computational cost, where n is the toroidal mode number. This coordinate system however limits the computational domain to the toroidal wedge (full torus divided into N parts in the toroidal direction) for computational efficiency and the use of flute-ordering approximation in the field solver calculating the flow potential from the vorticity which may not be valid for low-n modes. Improving numerical treatment of low-n modes is however indispensable to address simulations of low-n current-driven edge localized mode (ELM), ELM control by resonant magnetic perturbations (RMPs), edge turbulence with RMPs and so on. In this work, BOUT++ is extended to simulate the interplay between n=0, low-n and high-n plasma components in a full annular tokamak edge domain through hybrid modeling of the flow potential and the vorticity. Low-n modes of flow potential are calculated in an orthogonal flux surface coordinate and high-n modes in the dual coordinate system separately in Fourier space. The proposed scheme can capture an interplay between n=1 global modes and high-n turbulence during pedestal collapse in a full annular torus domain with a circular cross section.