Last Closed Flux Surface Research Articles

First experimental confirmation of island SOL geometry effects in a high radiation regime on W7-X

Abstract This work characterizes the detachment behavior and radiation characteristics of the low
iota configuration in the Wendelstein 7-X (W7-X) stellarator. The island scrape-off layer (SOL) of the
low iota has a poloidal mode number of 6 islands surrounding the last closed flux surface (LCFS).
The island geometry of the low iota configuration is significantly different to that of the standard
magnetic field configuration, whose detachment characteristics have already been described in previous
work[2, 3, 4]. Experimental results show that the radiation pattern in the low iota configuration
is starkly different to that of the standard magnetic field configuration, with radiation concentrated
at the island SOL O-points, rather than the X-points. Additionally, this O-point localized radiation
pattern is associated with unstable detachment, with both radiation oscillations in experiments and the
lack of a self-consistent plasma solution at high radiated power fraction in EMC3-Eirene simulations.
EMC3-Eirene simulations are used to understand the radiation distribution. It was found that the O-
point localized radiation arises first from local impurity accumulation near the parallel flow stagnation,
which is located close to the geometrical center of the island (”O-point”). The local cooling in this
region leads to plasma condensation in the islands in closest magnetic connection to the divertor target
plates. The heat source to this region of the island, which is thermally isolated from the upstream heat
source in terms of parallel transport, must arise via perpendicular heat transport. This heat source is
expected to be large for the low iota configuration due to its very small internal island field line pitch.
This work highlights the importance (complementary to previous work, e. g. [5, 6]) of the internal
island field line pitch not only on the radiation pattern, but also the detachment performance of the
island divertor.

Access to an ELM-suppressed X-point radiator regime in TCV snowflake minus configurations

TCV’s operating regime with an X-point radiator (XPR) has been broadened by changing the magnetic geometry. XPRs have properties that could make them an attractive power exhaust solution for fusion reactors. These include the conversion of a high fraction of exhaust power into radiation. TCV had previously accessed the XPR regime only with difficulties, as predicted for plasmas where radiative losses are dominated by carbon impurities, that are ubiquitous in TCV. Guided by this theoretical model of the XPR, recent experiments employed TCV’s configurational versatility to demonstrate that XPR access can be facilitated by introducing a second X-point in the vicinity of the separatrix. This configuration, which has a snowflake-minus topology, features a particularly long magnetic connection length from the region just above the X-point to the outer midplane together with a wide geometrical interface with the private flux region that reaches high neutral pressure. Transitioning to this configuration in a high-power H-mode leads to a shift in the radiating region across the separatrix from the divertor to a volume above the X-point, i.e. within the last closed flux surface (LCFS). This displacement of the radiating region is co-incident with the disappearance of edge localised modes (ELMs), while retaining H-mode confinement, a behaviour only, to date, observed in devices with metallic walls. In contrast to observations in these other devices, on TCV, the primary strike points in these configurations remain attached. Detailed measurements of the plasma kinetic parameters inside and outside of the separatrix now challenge the models for access and stability of the XPR and ELMs alike.

The formation of an radial edge electric field due to finite ion orbit width effects is the possible root cause of the H-mode edge

Abstract Full orbit-following simulations of thermal ions show that finite ion-orbit width effects create charge separation near the last closed flux surface (LCFS) which generates a localized radial electric field. Experimentally, edge electric fields are observed in H-mode plasmas and they are necessary for the edge turbulence suppression via the E × B flow shear mechanism. Confined trapped (and to a lesser extent co-passing) ions near the plasma edge form a positive charge distribution outside the LCFS, while thermal electrons are tied more tightly to field lines owing to their small mass and are poorly confined outside the LCFS, hence charge neutrality is violated outside the LCFS. A large number of reported observations from spherical and conventional tokamaks support the results from the simulations although the simulations were not performed fully self consistently. The results suggest ways to lower the H-mode power threshold and optimize the H-mode plasma edge.

Realization of a gas puff imaging system on the Wendelstein 7-X stellarator.

A system for studying the spatiotemporal dynamics of fluctuations in the boundary of the W7-X plasma using the "Gas-Puff Imaging" (GPI) technique has been designed, constructed, installed, and operated. This GPI system addresses a number of challenges specific to long-pulse superconducting devices, such as W7-X, including the long distance between the plasma and the vacuum vessel wall, the long distance between the plasma and diagnostic ports, the range of last closed flux surface (LCFS) locations for different magnetic configurations in W7-X, and management of heat loads on the system's plasma-facing components. The system features a pair of "converging-diverging" nozzles for partially collimating the gas puffed locally ≈135mm radially outboard of the plasma boundary, a pop-up turning mirror for viewing the gas puff emission from the side (which also acts as a shutter for the re-entrant vacuum window), and a high-throughput optical system that collects visible emission resulting from the interaction between the puffed gas and the plasma and directs it along a water-cooled re-entrant tube directly onto the 8 × 16 pixel detector array of the fast camera. The DEGAS 2 neutral code was used to simulate the Hα (656nm) and HeI (587nm) line emission expected from well-characterized gas-puffs of H2 and He and excited within typical edge plasma profiles in W7-X, thereby predicting line brightnesses used to reduce the risks associated with system sensitivity and placement of the field of view. Operation of GPI on W7-X shows excellent signal-to-noise ratios (>100 at 2 Mframes/s) over the field of view for minimally perturbing gas puffs. The GPI system provides detailed measurements of the two-dimensional (radial and poloidal) dynamics of plasma fluctuations in the W7-X edge and scrape-off layer and in and around the magnetic islands outside the LCFS that make up the island divertor configuration employed on W7-X.

Optimization of lithium vapor box divertor evaporator location on NSTX-U using SOLPS-ITER

Commercial fusion reactors will be faced with extremely high divertor target heat fluxes that will require mitigation. Simulations of detachment in an NSTX-U scenario projected to have 92 MW m−2 unmitigated peak target heat flux are presented, which reaches sub-10 MW m−2 target heat flux using a highly dissipating lithium vapor box divertor design. The lithium vapor box is a detached divertor design which employs lithium vapor evaporation and condensation to contain lithium below the X-point. Previous SOLPS modeling has indicated a lithium vapor box can reduce the heat flux down to 10 MW m−2 via simultaneous evaporation from the Private Flux Region (PFR) and the Common Flux Region (CFR) sides of the vapor box. It is found here that PFR evaporation has improved access to the separatrix leading to significantly more efficient power dissipation than CFR evaporation. Simulations of target evaporation with an evaporation distribution that is self-consistent with the temperature of a Capillary Porous System with Fast flowing liquid lithium could reach nLi / ne∼ 0.025–0.030 at the Last Closed Flux Surface (LCFS) depending on the liquid metal flow speeds and lithium sputtering yield, while PFR-side evaporation can reach acceptable heat fluxes with nLi / ne∼ 0.038 at the LCFS. However, PFR evaporator performance can be improved if the target is allowed to be hot enough such that it reflects lithium, reaching nLi / ne∼ 0.028 and reducing required lithium evaporation. Ultimately PFR evaporation and target evaporation are found to have similar ability to produce acceptable heat flux solutions with minimal upstream concentration.

Self‐consistent transport simulation of boron dust particle injection in the peripheral plasma in Large Helical Device

AbstractThe trajectories and the ablation positions of boron dust particles dropped from an impurity powder dropper in the peripheral plasma in the Large Helical Device (LHD) were calculated using a three‐dimensional edge plasma simulation code (EMC3‐EIRENE) and a dust transport simulation code (DUSTT). The simulation shows that the trajectory of the boron dust particles is deflected at the upper divertor leg due to the effect of the hydrogen plasma flow, and the ablation positions of the dust particles in an ergodic layer change toward the outboard side of the torus for higher plasma densities. The effect of the boron ion flow in the divertor leg on the deflection is investigated by coupling the two codes self‐consistently. The simulation predicts that the boron ions in the divertor leg, which are produced by sputtering on the divertor plates, which do not affect the change in the ablation positions. It also shows that the ablation positions move toward the inboard side and approach the Last Closed Flux Surface (LCFS) in case of increased boron dust drop rates, which is caused by the lowered plasma flow in the upper divertor leg due to the lowered electron temperature by radiation cooling by the dropped dust particles.

Predict the last closed-flux surface evolution without physical simulation

One of the main challenges in developing effective control strategies for the magnetic control system in tokamaks has been the difficulty in obtaining the last closed-flux surface (LCFS) evolution results from control commands. We have developed a data-driven model that combines a predictive model and a surrogate model for physics simulation programs. This model is capable of predicting the LCFS without relying on physical simulation codes. Addressing the data characteristics of LCFS, we have proposed a specialized discretization approach to achieve dimensionality reduction. Furthermore, we have excluding the control references, the model can be seamlessly integrated into the control system, providing real-time LCFS prediction. Following comprehensive testing and multifaceted evaluation, our model has demonstrated highly satisfactory results of 95% or above, meeting practical requirements.

Characterization of impurity distribution and composition on the shutter plate for an optical diagnosis in EAST tokamak using laser-induced breakdown spectroscopy

The quantification of impurities in tokamak devices is of great significance as it allows for a better understanding of the plasma performance and the lifetime of plasma-facing components (PFCs). This study focuses on the characterization of the impurity distribution and composition on the surface of a shutter plate for an optical diagnosis in the Experimental Advanced Superconducting Tokamak (EAST) by Laser-Induced Breakdown Spectroscopy (LIBS). The primary impurity elements, including copper (Cu), tungsten (W), molybdenum (Mo), lithium (Li), and Sodium(Na), were identified by analyzing the LIBS spectra obtained from the surface of the shutter plate. The spatial distribution of these impurities on both sides of the plate was investigated. The analysis results indicate an increase in impurity content on the outer surface of the shutter plate as proximity to Last Closed Flux Surface (LCFS), followed by a near-linear decrease with the distance from the LCFS. The results of the inner ring on the inner side facing the glass window show fewer metal impurities than the outer rings on the edge for the inner side of the plate. Moreover, the thickness of the deposition layer was determined by estimating the Average Ablation Rate (AAR) through the measurement by confocal microscopy. In addition, Calibration-Free LIBS method were performed to determine the relative content of impurities. The results of this study provide valuable references for studying the migration and transportation of impurities.

How turbulent transport broadens the heat flux width: local SOL production or edge turbulence spreading?

This paper uses data from limited HL-2A Ohmic-plasma to answer the question of how turbulent transport broadens the heat flux width. A key issue in this study is the determination of the origin of scrape-off layer (SOL) turbulence. We develop the concept of the energy production ratio Ra , which compares the flux of turbulence energy across the last closed flux surface (LCFS) to the net, integrated energy production in the SOL. The flux of turbulence energy (i.e. spreading) is measured directly, using Langmuir probes. Experimental data is used to evaluate Ra . Results show that usually 1$?> Ra>1 , indicating that SOL turbulence is energized primarily by edge turbulence spreading. The exceptions—cases where Ra<1 —are those with relatively stronger E×B shear near the LCFS. The latter inhibits both turbulence spreading and local SOL production, but has greater effects on spreading. High blob fraction in the turbulence correlates with large values of Ra . The implications for heat flux width physics are discussed.

Improved flux-surface parameterization through constrained nonlinear optimization

Parameterization of magnetic flux-surfaces is often used for magnetohydrodynamic stability analysis and microturbulence modeling in tokamaks. Shape parameters for such local parameterization of a (numerical) equilibrium are traditionally computed analytically using geometrically derived quantities. However, often the shape is approximated by the average of values for different sections of the flux-surface contour or a truncated series, which does not guarantee an optimal fit. Here, instead nonlinear least squares optimization is used to compute these parameters, with a weighted sum of squared error cost function that is robust to outliers. This method results in a lower total absolute error for both the parameterization of the flux-surface contour and the poloidal magnetic field density than current methods for several parameterizations based on the well-known “Miller geometry.” Furthermore, rapid convergence of shape parameters is achieved, no approximate geometric measurements of the contour are needed, and the method is applicable to any analytical shape parameterization. Validation with local, linear gyrokinetic simulations using these optimized shape parameters showed reduced root mean square errors in both the growth rate and frequency spectra when compared with simulations based on numerical equilibria. In particular, the popular Turnbull–Miller parameterization benefits from this approach, extending its usability closer toward the last-closed flux-surface for cases with minor up-down asymmetry.

Particle orbit description of cyclotron-driven current-carrying energetic electrons in the EXL-50 spherical torus

In EXL-50 plasma currents over 100 kA are non-inductively generated and maintained solely by electron cyclotron heating (ECH) power with an efficiency of ∼1 A W−1. These currents are carried by energetic electrons (EEs) in the energy range from several tens of keV up to several hundreds of keV which also account for almost all pressure in plasma. This EE component can be viewed as a large number collection of various periodic orbits of energetic particles. Based on this picture we have developed a method for particle orbit description of the EE component in a typical plasma at = 121 kA as analysis target. We use a fluid description as a bridge to describe successfully the EE component as a collection of various passing and trapped orbits in the approximation of monochromatic particle energy with good matching to the flux loop signals. The description has revealed characteristics of passing and trapped particles. Passing particles carry almost all toroidal current, while they account for only 20 of total particle number of the EE component. While net current carried by trapped particles is a very small fraction, they account for a major fraction in number and carry a large positive current outside the last closed flux surface (LCFS) and a large negative current inside. As a result, trapped particles redistribute the current from inside of the LCFS to outside both radially and vertically, generating a large vertically elongated cross section in current as well as number density profiles. There is a ridge-like structure along the LCFS in the current density profile, with no such structure in the number density profile. The results suggest that forward passing particles are more advantageous in confinement than backward passing particles. This advantage increases with particle energy and contributes to the current generation observed in EXL-50 experiments.

A machine-learning-based tool for last closed-flux surface reconstruction on tokamaks

Tokamaks allow to confine fusion plasma with magnetic fields. The prediction/reconstruction of the last closed-flux surface (LCFS) is one of the primary challenges in the control of the magnetic configuration. The evolution in time of the LCFS is determined by the interaction between the actuator coils and the internal tokamak plasma. This task requires real-time capable tools to deal with high-dimensional data and high resolution at same time, where the interaction between a wide range of input actuator coils with internal plasma state responses adds an additional layer of complexity. In this work, we present the application of a novel state-of-the-art machine learning model to LCFS reconstruction in an experimental advanced superconducting tokamak (EAST) that learns automatically from the experimental data of EAST. This architecture allows not only offline simulation and testing of a particular control strategy but can also be embedded in a real-time control system for online magnetic equilibrium reconstruction and prediction. In real-time modeling tests, our approach achieves very high accuracies, with an average similarity of over 99% in the LCFS reconstruction of the entire discharge process.

Comparison of MHD stability properties between QH-mode and ELMy H-mode plasmas by considering plasma rotation and ion diamagnetic drift effects

Magnetohydrodynamic (MHD) stability at tokamak edge pedestal in a quiescent H-mode (QH-mode) and type-I ELMy H-mode plasmas in DIII-D experiment was analyzed by considering plasma rotation and ion diamagnetic drift effects. QH-mode plasma is marginally stable to kink/peeling mode (K/PM), but ELMy H-mode one is almost unstable to peeling-ballooning mode (PBM). It was identified that there are three physics features responsible for the difference in the MHD stability properties between QH-mode plasma and ELMy H-mode one. These are the distance of pedestal foot from the last closed flux surface (LCFS), the amount of the ion diamagnetic drift frequency at pedestal, and impact of coupled rotation and ion diamagnetic drift effects. These features were confirmed through the numerical experiments that the stability properties of the QH-mode plasma can be changed to that of the ELMy H-mode one by shifting the plasma profiles inward in the radial direction and halving the ion diamagnetic drift frequency. The reasons of the change in the stability properties are thought as that K/PM is stabilized due to the inward shift of the bootstrap current profile, and PBM is destabilized due to the reduction of the coupled rotation and ion diamagnetic drift stabilizing effect. Importance of these features was validated through numerical experiments with experimental data of other QH-mode plasmas in DIII-D. All the results show that MHD stability properties of QH-mode plasma can be obtained in case that pedestal foot is close to LCFS, ion diamagnetic drift frequency is large due to high ion temperature, and strong rotation shear exists near pedestal.

Characterizing the flow and turbulence structure near the last closed flux surface in L-mode plasmas of ASDEX Upgrade

Since high density operation is advantageous for building an efficient fusion reactor, understanding the density limit in tokamaks has been seen as one of the most important issues. This paper reports a series of measurements around the last-closed flux surface (LCFS) in L-mode plasmas by using a thermal helium beam diagnostic. Fluctuation analysis has been employed to characterize the poloidal flow and the turbulence structure. A reversal of the poloidal flow in the scrape-off layer and concomitant cooling of the outer divertor plasma are observed as the density is raised. While, in the confined region, the change in the density barely affects the poloidal flow, a higher density shifts the fluctuation power spectral densities toward lower frequencies and wave numbers. The eddy tilting of this region is consistent with what is expected from the magnetic shear effect. A radially coherent low frequency mode appears in the case of the highest density investigated in this study (n¯e/ne,GW = 0.51), and higher frequencies near the LCFS are modulated by this mode.

Development of two dimensional full wave spectral code for the ICRF heating and current drive research including scrape-off layer in tokamaks

It is important for an ICRF full wave code to simulate the SOL (Scrape Off Layer) plasma as well as the core inside of the LCFS (Last Closed Flux Surface) for the precise prediction of the coupling between the antenna and the core plasma in tokamaks. To this end, a two dimensional full wave code based on a Fourier spectral algorithm has been developed. The spectral algorithm and procedures are described and the simulation results for the minority heating in KSTAR are reported including electric field, power absorption and power flux.

Experimental study of the characteristics of energetic electrons outside LCFS in EXL-50 spherical torus

Significant number of confined energetic electrons have been observed outside of the LCFS (last-closed flux surface) of EXL-50’s solenoid-free electron cyclotron resonance heating (ECRH) sustained plasmas. Several measurement technologies have been applied to verify the key characteristics of energetic electrons for the first time. Experiments reveal that the presence of high-temperature, low-density electrons can carry relatively large quantities of the stored energy. The boundary between the thermal plasma and the energetic fluid is clearly separated and the distance between the two boundaries can reach tens of centimeters (around the size of the minor radius of the thermal plasma). This implies that the Grad-Shafranov equilibrium is not adequate to describe the equilibrium of EXL-50 plasma and a multi-fluid model is required. Particle simulations of full orbits show that energetic electrons can be well confined outside the LCFS. This is consistent with the experimental observations.

Finite elements method based ICRF waves heating simulation integrating with SOL plasma for EAST tokamak

Abstract Ion cyclotron range of frequency (ICRF) waves heating simulation is often carried out in the core plasma region. However, the inclusion of scrape-off layer (SOL) plasma in the simulation model may lead to new physical phenomenon and needs to be studied. In this paper, we apply finite elements method (FEM) based on the approach of [Vallejos 2019], to simulate ICRF waves heating in account of the realistic SOL plasma for EAST tokamak. In the presence of density pedestal near last closed flux surface (LCFS), a kind of cavity mode is observed for the case of low parallel wave number. Near ion-ion hybrid resonance (IIR) layer in SOL region, mode conversion from fast waves to slow waves takes place. ICRF waves coupling characteristics are roughly consistent with the prediction of the dispersion relation except for some small deviations, which may be caused by fast waves reflection in the high field side. Approximate on axis heating of minority H is observed and power deposition zone broadens with parallel wave number increasing. Waves energy dissipation in SOL plasma is less than 7% and localized near IIR region. Furthermore, the comparison between D(H) and D(He-3) minority heating scenarios is also carried out. The results and conclusions in this paper can provide theoretical reference to ICRF heating experiments and may supply a new insight in ICRF waves form in the plasma edge.

Optical Boundary Reconstruction With Visible Camera in the EXL-50 Spherical Tokamak

Plasma position and shape parameters are essential for equilibrium control and physics analysis in a tokamak. Such information is often obtained via optical boundary analysis. In this study, a new analysis of the visible image histogram of a high-speed high-resolution camera is presented which can effectively distinguish between the foreground information (showing the plasma of interest) and the background information (showing the inside views of the vacuum vessel wall and flanges, and so on). Using this method, we can obtain a reasonable approximation to the plasma boundary close to the last closed flux surface (LCFS) where plasma brightness contrast is greatest. The reliability and accuracy of this method are checked by comparing it favorably with other algorithms for different plasma shapes. The method is successfully tested also when the outboard plasma boundary oscillates in time with a magnitude of 10%.

Simultaneous measurements of plasma parameters and blob characteristics at the far-SOL region using a hybrid probe in KSTAR

We developed a hybrid probe comprised of an electrical probe and optical probe to investigate the properties of the far scrape-off layer (SOL) plasma and the blob in Korea Superconducting Tokamak Advanced Research (KSTAR). The hybrid probe is attached to a horizontal manipulator, and the radial profiles of plasma parameters such as electron temperature, ion flux, and the Dα signals are measured with time resolution (100 μs) by varying the radial position (0.15–0.4 m away from the last closed flux surface (LCFS)). In ELMy H-mode discharge, the blob radial velocity is obtained from the time delay between the start of the peak Dα signal and the peak electrical probe current and the corresponding radial position. The obtained blob radial velocity is in good agreement with the radial velocity of the filament obtained using the two radially separated electric probes at the far-SOL in the KSTAR. The profiles of the blob radial velocity for five discharges are obtained depending on the radial position in similar experimental parameters. The blob radial velocity is estimated as 44.1–250 m/s and 25.4–135 m/s at the radial position of 0.15 m (near the LCFS) and 0.4 m (near the outer wall), respectively. It is observed that the blobs are propagated to the outer wall with various radial velocities, and the radial velocity slows down as they get closer to the outer wall. The hybrid probe measurement found that the blob properties are about 2 to 10 times larger than the background plasma, and these show the same trend with the blob radial velocity. The hybrid probe is expected to contribute to the analysis and understanding of far-SOL plasma research in fusion reactors.

Modeling of SOL helical current filaments induced by biased electrode on J-TEXT

It has been demonstrated in J-TEXT experiments that a biased electrode or electrode biasing (EB) in the scrape-off layer (SOL) can drive SOL helical current filaments (HCFs). The bright helical radiation belts of carbon impurities in the SOL indicate that SOL current flows along the magnetic field lines. Based on the experimental phenomenon, three SOL current models (model A, B, C) have been set-up in order to understand the spatial structure of SOL current and the perturbed magnetic field it generates. Model A is a simplified calculation of HCFs in the cylindrical geometry, and takes into account the presence of cross-field current by a linear decay of current along magnetic field lines. Model B take into account the actual toroidal geometry and the complex path of HCFs connected from the electrode to the limiters. By including the radial dependence of the resistivity into model B, model C is developed and describes the SOL current more perfectly than the other two models. Furthermore, the model C shows that SOL helical current can produces stronger boundary resonant magnetic perturbations (RMPs) at the last closed flux surface (LCFS) due to the consistent helixity of SOL current filaments and the boundary rational surface, which may be a new way to generate RMPs to control the edge-localized modes (ELMs). The equivalent inductance and resistance of HCFs at different edge safety factor q a are measured by applying a square wave voltage. The results show that the inductance and resistance of the HCFs are related to q a and the radial position of the biased electrode r EB, in a qualitatively consistent manner as that predicted by model C.