Plasma Transport Research Articles

Effects of plasma nonuniformity on zero frequency zonal structure generation by drift Alfvén wave instabilities in toroidal plasmas

Abstract The effects of plasma nonuniformity on zero frequency zonal structure (ZFZS) excitation by drift Alfvén wave (DAW) instabilities in toroidal plasmas are investigated using nonlinear gyrokinetic theory. The governing equations describing nonlinear interactions among ZFZSs and DAWs are derived, with the contribution of DAW self-beating and radial modulation accounted for on the same footing, and the physics picture contributing to both channels clarified. The obtained equations are then used to derive the nonlinear dispersion relation, which is then applied to investigate ZFZS generation in several scenarios. In particular, it is found that the condition for zonal flow excitation by the kinetic ballooning mode (KBM) could be sensitive to plasma parameters and a more detailed investigation is needed to understand KBM nonlinear saturation, crucial for bulk plasma transport in future reactors.

Numerical study of turbulent eddy self-interaction in tokamaks with low magnetic shear. Part I: Linear simulations

Abstract This study examines the impact of low and zero magnetic shear, along with rational values of safety factor, on linear mode behavior in tokamak plasmas. We focus on how magnetic field line topology and parallel domain length influence linear mode structures and growth rates as magnetic shear decreases. Our results
show that as magnetic shear is reduced to low values, linear modes can transition between different branches, significantly affecting their characteristics. At zero magnetic shear, accurate modeling requires precisely capturing magnetic topology, as small deviations near rational surfaces can greatly impact growth rates. These findings are extended to nonlinear simulations in a companion paper (Volčokas, 2024), revealing that long turbulent eddies and magnetic field line topology play a crucial role in turbulence self-interaction and plasma transport.

Numerical simulation of flame propagation characteristics of NH3/Air flames assisted by non-equilibrium plasma discharge

Nanosecond non-equilibrium plasma-assisted combustion technology emerges as a reliable novel approach to enhance the flame propagation speed of NH3. In this study, we developed a zero-dimensional + one-dimensional (0-D+1-D) non-equilibrium plasma-assisted combustion model to investigate the impact of nanosecond pulse discharge on the freely propagating flame speed of NH3/Air mixture. The results reveal that due to the plasma discharge, abundant intermediate species (N2H4, N2H3, NO, H2O2) are formed at the inlet and are subsequently transported downstream, facilitating flame propagation. As a result, the speed of the 1-D freely propagating flame increases, and the flame front is closer to the inlet compared to the non-plasma condition. The transport effect of H2 is also evident, with high concentrations of H2 from the inlet providing the basis for reactions at the flame front that promote combustion. Furthermore, after the initial mixture flows into the flame front, a slight increase in heat release is observed, but this increase occurs within a very limited distance. Notably, in the case of plasma, a stronger heat release is evident at the flame front. Moreover, with plasma, the peaks of OH, H, O, NH2, and HO2 are higher and earlier than those of the non-plasma case due to the transport and kinetic effects of plasma. Pathway flux analyses reflect significant changes in the production and consumption paths of the three components OH, H, and O, which are most important for consuming NH3 due to plasma addition. The higher OH mass fraction promotes the chain reactions that consume NH3, effectively enhancing the flame propagation speed. Novelty and significance statementThis study introduces a novel 0-D+1-D nanosecond non-equilibrium plasma-assisted combustion model to examine the impact of nanosecond pulse discharge on NH3/Air flame propagation. It uniquely analyzes the interaction between species at the inlet and flame front, highlighting the transport effects of plasma-generated intermediates (N2H4, N2H3, NO, H2O2, H2) that enhance flame speed, with a detailed pathway analysis of key species (O, OH, H).

Lower‐Hybrid Wave‐Induced Plasma Mixing Related to Kelvin‐Helmholtz Vortices During Southward IMF

AbstractWe examine characteristics of the boundaries of 11 Kelvin‐Helmholtz vortex crossings observed by MMS on 23 September 2017 under southward IMF conditions. At both the leading and trailing edges, boundary regions of mixed plasma are observed together with lower‐hybrid wave activity. We found that thicker boundary regions feature a higher number of sub‐ion scale current sheets, of which only one shows clear reconnection signatures. Moreover, the lower‐hybrid waves along the vortex spine region are identified as an effective mechanism for plasma transport with an estimated diffusion coefficient of s. Comparisons with 3D simulations performed under the same conditions as the MMS event suggest that the extension of the boundary regions as well as the number of current sheets are related to different evolutionary stages of the vortices. Such observations can be explained by changes in the upstream magnetic field conditions.

Dependence of divertor asymmetries on the toroidal magnetic field

A study of the effect of toroidal magnetic field (Bt) on the divertor asymmetries is carried out with a plasma transport code under BOUT++ framework with the magnetic equilibria from EAST and C-Mod. For the simulation cases with drifts, the density is larger at the inner divertor target, while the temperature and heat flux are larger at the outer divertor target. The ratio of the total particle flux at the outer target to that of the inner target increases with increasing Bt, while the ratio of the total heat flux at the outer target to that of the inner target decreases with increasing Bt. The in–out divertor asymmetries of both total particle and heat fluxes get weaker with increasing Bt. Further analysis shows that the edge radial transport induced by drifts is much weaker for the simulation case with higher Bt, indicating that drift-driven divertor asymmetries may be less important for future tokamaks with high Bt.

The effect of CD4 injection on WD molecule sputtering at the divertor target in EAST

Tungsten (W) is one of the preferred plasma-facing materials for future fusion reactors because of the advantages of high melting point, low physical sputtering rate and low fuel retention. The lifetime and service performance of W materials are limited by erosion processes. In recent years, tungsten deuteride molecular (WD) sputtering has been discovered in tokamak. Studying WD sputtering helps to better understand the erosion of tungsten materials in tokamak. EAST adopts the method of injecting impurity gas in the divertor to alleviate the particle flux and heat flux bombarding the tungsten divertor, and CD4 is one of the impurities used. CD4 injection experiments on EAST show that after CD4 is injected from the upper outer (UO) divertor target, despite that the electron temperature (Te) around the strike point on the UO divertor target drops to about 8 eV, strong WD sputtering occurs in the far scrape-off layer (SOL) region. The divertor probe data shows that after CD4 injection, the particle flux from the upstream plasma onto the divertor split into two bands, creating a new particle flux strike point in the far SOL region. The energy of incident particles at the original strike point is significantly reduced, while the energy of incident particles at the far SOL region is enhanced. The edge electron density profile at mid-plane indicates that CD4 injection causes an increase of density in the SOL, which could improve the coupling of Lower-Hybrid Wave (LHW) with the edge plasma as evidenced by the decreasing reflected power of LHW. The increase in absorbed power of LHW could change the particle and energy transport in the edge plasma, thus plays an important role in the enhanced WD sputtering in the far SOL region after CD4 injection.

Surrogate model of turbulent transport in fusion plasmas using machine learning

Abstract The advent of machine learning (ML) has revolutionized the research of plasma confinement, offering new avenues for exploration. It enables the construction of models that effectively streamline the simulation process. While previous first-principles simulations have provided physics-based transport information, they have been inadequate fast for real-time applications or plasma control. In order to address this challenge, we introduce SExFC, a surrogate model based on the Gyro-Landau Extended Fluid Code (ExFC). An approach of physics-based database construction is detailed, as well the validity is illustrated. Through harnessing the power of ML, SExFC offers the capability to deliver rapid and precise predictions, facilitating real-time applications and enhancing plasma control. The proposed model integrates the recurrent neural network (RNN) algorithm, specifically leveraging the Gated Recurrent Unit (GRU) for iterative prediction of flux evolutions based on radial profiles. Therefore, the SExFC model has the potential to enable rapid and physics-based predictions that can be seamlessly integrated into future real-time plasma control systems.

Effects of discharge parameters on plasma acceleration and transmission characteristics of a coaxial gun operated in gas-prefilled mode

The effects of discharge parameters on the discharge process and plasma transport characteristics of a coaxial gun in the gas-prefilled mode are studied. The plasma optical intensity and ejection velocity are measured by photodiodes, the optical emission spectrum is taken by a spectroscopic system, and the plasma evolution in the transport process is captured by a high-speed camera. The plasma acceleration characteristics under different discharge parameters show that the velocity and electron density of the ejection plasma are mainly determined by the pre-filled pressure and discharge current, which is consistent with the snowplow model. The kinetic energy of ejection plasma can be significantly increased by reducing the outer loop inductance, which is conducive to increasing the energy utilization efficiency. The time-varying images of plasma radiation and the plasma density at different transport locations illuminate the transmission characteristics of coaxial gun discharge plasma. The results show that the snowplow effect continues to play a role in the plasma transport process, and the plasma accumulation is induced by the combination of shock wave compression. The current-driven magneto hydrodynamics instability occurs during the transport process, and the luminous signal of the plasma current sheet oscillates periodically. In addition, the plasma impact effect is obvious and the gas retarding effect is enhanced with the increase in the gas pressure. These results give us a more comprehensive view of the coaxial gun discharge process and plasma transport and provide a certain reference for optimizing the parameters selection and physical design of coaxial gun discharge plasma characteristics.

Model-predictive kinetic control with data-driven models on EAST

Abstract In this work, model-predictive control (MPC) was combined for the first time with singular perturbation theory, and an original plasma kinetic control method based on extremely simple data-driven models and a two-time-scale MPC algorithm has been developed. A comprehensive review is presented in this paper. Slow and fast semi-empirical models are identified from data, by considering the fast kinetic plasma dynamics as a singular perturbation of a quasi-static equilibrium, which itself is governed, on the slow time scale, by the flux diffusion equation. This control technique takes advantage of the large ratio between the time scales involved in magnetic and kinetic plasma transport. It is applied here to the simultaneous control of the safety factor profile, q(x), and of several kinetic variables, such as the poloidal beta parameter, βp, and the internal inductance parameter, li, on the EAST tokamak. In the experiments, the available control actuators were lower hybrid current drive (LHCD) and co-current neutral beam injection (NBI) from different sources. Ion cyclotron resonant heating (ICRH) and electron cyclotron resonant heating (ECRH) are used as additional actuators in control simulations. In the controller design, an observer provides, in real time, an estimate of the system states and of the mismatch between measured and predicted outputs, which ensures robustness to model errors and offset-free control. A number of control applications are described in the paper, either in nonlinear simulations with EAST-like parameters or in real experiments on EAST. Various controller configurations were tested, with up to three controlled variables chosen among q0 = q(x=0), q1 = q(x=0.5), βp and li. Both the extensive nonlinear simulations and the experiments described in this paper have demonstrated the relevance of combining model-predictive control, data-driven models and singular perturbation methods for plasma kinetic control.

Biological evaluation of sophoridine by interaction with plasma transport protein and protective effects in cardiomyocytes

Numerous studies have demonstrated the protective benefits of sophoridine, a bioactive alkaloid, on cell damage. However, its primary biological properties such as interaction with plasma protein, which serves as the primary drug carrier, and its cardioprotective properties are still unknown. In the present study, we aimed to analyze the binding characteristics of sophoridine with alpha-2-macroglobulin (α2M) by spectroscopic and theoretical studies. Then, the cardioprotective effects of sophoridine on myocardial ischemia/reperfusion (MI/R) injury in vitro were investigated using H9c2 cardiomyocytes. The results reveal that one molecule of sophoridine favorably binds to one molecule of α2M dominantly through interaction with hydrophobic amino acid residues (VAL758, PHE735, PHE735, and TRP739). Also, sophoridine leads to partial changes in the structure of this carrier protein in the vicinity of TRP739 residue. Cellular assays exhibit that sophoridine recovered cell viability, membrane leakage, and apoptosis induced by MI/R injury. It was detected that sophoridine could mitigate the oxidative stress and intrinsic apoptosis pathway through regulation of Bax, Bcl-2, and caspase. ELISA analysis also exhibits that sophoridine upregulates phosphorylation of Akt and PI3K in H9c2 cells. Our findings suggest that sophoridine could show favorable plasma protein interaction and promising cardioprotection against MI/R injury mediated by the upregulation of PI3K/AKT signaling pathway.

Poloidal magnetic field reconstruction by laser-driven ion-beam trace probe in spherical tokamak

The poloidal magnetic field ( plays a critical role in plasma equilibrium, confinement and transport of magnetic confinement devices. Multiple diagnostic methods are needed to complement each other to obtain a more accurate profile. Recently, the laser-driven ion-beam trace probe (LITP) has been proposed as a promising tool for diagnosing and radial electric field ( ) profiles in tokamaks [Yang X Y et al 2014 Rev. Sci. Instrum. 85 11E429]. The spherical tokamak (ST) is a promising compact device with high plasma beta and naturally large elongation. However, when applying LITP to diagnosing in STs, the larger invalidates the linear reconstruction relationship for conventional tokamaks, necessitating the development of a nonlinear reconstruction principle tailored to STs. This novel approach employs an iterative reconstruction method based on Newton’s method to solve the nonlinear equation. Subsequently, a simulation model to reconstruct the profile of STs is developed and the experimental setup of LITP is designed for EXL-50, a middle-sized ST. Simulation results of the reconstruction show that the relative errors of reconstruction are mostly below 5%. Moreover, even with 5 mm measurement error on beam traces or 1 cm flux surface shape error, the average relative error of reconstruction remains below 15%, initially demonstrating the robustness of LITP in diagnosing profiles in STs.

Charged-particle transport in high energy density plasmas

This Special Topic Collection grew out of two gatherings of researchers active in the high energy density (HED) physics community: a mini-conference on charged-particle transport in HED plasma held during the 64th annual meeting of the American Physical Society's Division of Plasma Physics (Spokane, WA, November 2022) and a dedicated charged-particle transport coefficient code comparison workshop (Livermore, CA, July 2023). These gatherings provided opportunities for theoretical, computational, and experimental researchers to discuss the state of the field, including current capabilities and methods, needs of hydrodynamic simulations, and frontiers for future research. This special issue collects a total of 13 research and review articles on charged-particle transport in HED plasmas.

Electron Pitch Angle Distributions in Magnetotail Tailward Flows

AbstractElectron pitch angle distributions (PADs) are crucial to revealing electron acceleration and heating in geospace. The electron PADs in the Earth's magnetotail have been widely studied by statistical or case analysis. However, the statistical features of electron PADs in tailward flows are still unclear. We survey data from the Magnetospheric Multiscale (MMS) satellite to statistically investigate electron PADs in tailward flows in the Earth's magnetotail for the first time. We find that for most (66.3%) tailward flows, electrons with energy from 0.1 to 30 keV are mainly field‐aligned. The PADs of suprathermal (>2 keV) electrons in a part of tailward flows (26.3%) are mostly isotropic. Additionally, the perpendicular‐dominated PADs of suprathermal electrons only exist in a few (7.4%) tailward flows. According to the different dominant PADs of suprathermal electrons, the tailward flows are classified into three types: field‐aligned‐dominated type, isotropic‐dominated type and perpendicular‐dominated type flows. The dependence of electron PADs on plasma environmental parameters is investigated in these three types of flows. For field‐aligned‐dominated type flows, the field‐aligned anisotropy decreases toward the central plasma sheet (CPS) and with the increase of the energy. In addition, it is found that the field‐aligned anisotropy in the field‐aligned‐dominated tailward flows reduces noticeably when the |Vix| exceeds 800 km/s. In isotropic‐dominated type flows, the field‐aligned anisotropy of electrons with energy ≥10 keV also shows a slight decreasing trend toward the CPS. For perpendicular‐dominated type flows, the perpendicular anisotropy exhibits two non‐monotonic processes, initially increasing and then decreasing with the increase of distance from the CPS; while becomes more evident for higher energy electrons. Our statistical results indicate that in tailward flows, electron anisotropy depends on the distance from the CPS, energy and plasma flow velocity. Tailward flows are associated with the transport of plasma toward the distant tail, and the statistical analysis of electron PADs in these flows can improve our understanding of the related electron dynamics in the magnetotail.

ETHOS: An automated framework to generate multi-fidelity constitutive data tables and propagate uncertainties to hydrodynamic simulations

Accurate constitutive data, such as equations of state and plasma transport coefficients, are necessary for reliable hydrodynamic simulations of plasma systems such as fusion targets, planets, and stars. Here, we develop a framework for automatically generating transport-coefficient tables using a parameterized model that incorporates data from both high-fidelity sources (e.g., density functional theory calculations and reference experiments) and lower-fidelity sources (e.g., average-atom and analytic models). The framework incorporates uncertainties from these multi-fidelity sources, generating ensembles of optimally diverse tables that are suitable for uncertainty quantification of hydrodynamic simulations. We illustrate the utility of the framework with magnetohydrodynamic simulations of magnetically launched flyer plates, which are used to measure material properties in pulsed-power experiments. We explore how changes in the uncertainties assigned to the multi-fidelity data sources propagate to changes in simulation outputs and find that our simulations are most sensitive to uncertainties near the melting transition. The presented framework enables computationally efficient uncertainty quantification that readily incorporates new high-fidelity measurements or calculations and identifies plasma regimes where additional data will have high impact.

Multifaceted Analysis of Bempedoic Acid Binding to Subdomain IIA of Human Serum Albumin

The molecular association between bempedoic acid (BAC) and the major blood plasma transporter, human serum albumin (HSA), was investigated using molecular docking, molecular dynamics (MD) simulation, isothermal titration calorimetry (ITC), atomic force microscopy (AFM), and spectroscopic techniques. During the docking and MD simulation investigations, it was observed that BAC interacted with subdomain IIA (Site I) of HSA through hydrogen bonds and hydrophobic interactions. This interaction ensured the stability of the complex throughout the duration of 100 ns. The observed enhancement in the fluorescence intensity of HSA after BAC inclusion and the swelling of HSA generated by BAC in the AFM data also suggested the formation of a complex between BAC and HSA. The BAC demonstrated a moderate affinity towards HSA, with a binding constant (Ka) of 1.21 ± 0.05 × 105 M−1 at 300 K. Notable modifications in the secondary and tertiary structures of the protein, as well as changes in the protein's Tyr/Trp surroundings, were observed using circular dichroism and three-dimensional fluorescence spectra when the protein was attached to BAC. Insightful information regarding molecular interactions that regulate the stability of the BAC-HSA complex is provided by these investigations.

Nup210 Promotes Colorectal Cancer Progression by Regulating Nuclear Plasma Transport

The nuclear pore complex (NPC) regulates nucleoplasmic transport, transcription, and genomic integrity in eukaryotic cells. However, little is known about how NPC works in cancer. In this study, we investigated the role of the nuclear pore protein 210 (Nucleoporin 210, Nup210) in colorectal cancer (CRC). Bioinformatics analysis revealed that the expression of Nup210 was increased in CRC and was associated with poor patient prognosis, but it was not a statistically significant independent prognostic factor. Moreover, knockdown of Nup210 in CRC cells inhibited the proliferation, invasion, and metastasis of CRC cells in vivo and in vitro. Additionally, nuclear size and nuclear plasma material transport capacity decreased along with the number and density of NPCs on the surface of CRC cells when Nup210 expression was inhibited. Furthermore, Nup210 required nuclear localization sequences (NLS) to localize to the nuclear membrane surface and interact with importin-α/β, which in turn affected the transit of nuclear plasma material. Importazole, a small molecule inhibitor of importin, along with therapy that targets the Nup210 protein is anticipated to be a novel strategy for CRC treatment. Their combination may be able to more effectively lower CRC tumor load. In conclusion, Nup210 modulates cellular nucleoplasmic transport capability and cell surface NPC density via NLS, thus promoting CRC progression. This discovery validates the molecular function of NPC in the development of CRC and provides a theoretical foundation for NPC-regulated nuclear import targeting as a therapeutic strategy for CRC.

Neuroprotective effect against amyloidogenic transthyretin aggregates - Induced cytotoxicity on human neuroblastoma cell by phenolic-rich Centella asiatica extract

Transthyretin (ATTR) amyloidosis is a progressive and life-threatening neurodegenerative disease caused by aggregation of the plasma transport protein, transthyretin, for which treatment is rare and cure unavailable. Centella asiatica is a small edible herb with a long history of neurological application in ethnomedicine. This work investigated whether hydrophilic extract of C. asiatica (CAB) could suppress the toxic effects of transthyretin amyloid aggregate (TTRa) in cell model derived from the same in vivo target. TTRa was prepared via thermal-induced aggregation. Chemical cross-linking and Tricine-SDS-PAGE, Thioflavin-T fluorescence, and TEM analyses confirmed that TTRa matched the profile of TTRL55P nonfibrillar amyloid aggregates. PrestoBlue cell viability assay revealed that exposure of IMR-32 human neuroblastoma cells to TTRa (2–8 μM) resulted in significant cytotoxicity. Conversely, exposure of IMR-32 cells to CAB did not adversely affect their viability. In addition, when IMR-32 cells were co-treated with TTRa and varied concentrations of CAB, the toxic effect of TTRa was significantly (p < 0.01) inhibited dose-dependently. The extract was found to possess potent radical scavenging effects, and quantitative RP-HPLC analysis showed that asiaticoside and phenolics were its main components. The cytoprotective effect against TTRa, antioxidant property, and good safety profile collectively suggest that CAB could be applied in the development of nutraceuticals or therapeutics against transthyretin amyloidosis.

Solar Flare Effects in the Martian Ionosphere and Magnetosphere: 3‐D Time‐Dependent MHD‐MGITM Simulation and Comparison With MAVEN and MGS

AbstractA comprehensive modeling study has been conducted to investigate space weather effects at Mars during the 10 September 2017 solar flare, utilizing an integrated framework that combines the global magnetohydrodynamic (MHD) model and Mars Global Ionosphere‐Thermosphere Model (MGITM). This is the first time the thermosphere‐ionosphere‐magnetosphere system is self‐consistently simulated under realistic, time‐varying conditions. Our simulations align well with observations from the Mars Atmosphere and Volatile EvolutioN (MAVEN). Recognizing that complexities due to highly disturbed upstream conditions and rotating crustal fields obscure solar flare effects in orbit‐to‐orbit comparisons, we perform controlled simulations of nonflare and flare cases and exploit their contrast to quantify spatiotemporal variations in flare impact. Our results highlight pronounced and rapid dayside ionospheric perturbations, contrasting with weaker and delayed nightside responses. Notably, in the topside ionosphere, and C densities increase primarily on the dayside below 300 km altitude, peaking with an increase of 20%–30%. The density shows a more significant increase of up to 50%, extending into the magnetosphere and nightside via plasma transport, increasing its total loss rate by 14%. We observe distinct altitude‐dependent patterns in dayside electron density enhancements in percent, characterized by a weakening with altitude and a rapid decay below 150 km in line with the flare development, and a gradual intensification between 150–300 km due to plasma transport and flare‐induced atmospheric upwelling. Earlier Mars Global Surveyor observations were limited to the low‐altitude pattern due to atmospheric expansion and missed the higher altitude variations observed by MAVEN.

Saturation of fishbone instability through zonal flows driven by energetic particle transport in tokamak plasmas

Saturation of fishbone instability through zonal flows driven by energetic particle transport in tokamak plasmas

Non-linear MHD modelling of transients in tokamaks: a review of recent advances with the JOREK code

Abstract Transient MHD events like edge localized modes (ELMs) or disruptions are a concern for magnetic confinement fusion power plants. Research with the MHD code JOREK towards understanding control of such instabilities is reviewed here. Experimental validation for unmitigated vertical displacement events (VDEs) progressed. The mechanism of vertical force mitigation by impurity injection was identified. Two-way eddy current coupling to CARIDDI was completed. Shattered pellet injection (SPI) was simulated in JET, KSTAR and ASDEX Upgrade (AUG) and ITER. Benign runaway electron (RE) beam termination in JET and ITER was studied. Coupling of kinetic REs to the MHD is ongoing and a virtual RE synchrotron radiation diagnostic was developed. Regarding pedestal physics, regimes devoid of large ELMs in AUG were simulated and predictive JT60-SA simulations are ongoing. For ELM suppression by resonant magnetic perturbations (RMPs), AUG, ITER and EAST simulations were performed. A free boundary RMP model was validated against experiments. Evidence for penetrated magnetic islands at the pedestal top based on AUG experiments and simulations was found. Simulations of the naturally ELM-free quiescent H-mode (QH) in AUG and HL-3 show external kink mode formation prevents pedestal build-up towards an ELM within windows of the edge safety factor. With kinetic neutral particles, high field side high density (HFSHD) formation in ITER was simulated and with kinetic impurities, tungsten transport in AUG RMP plasmas was studied. To capture turbulent transport, electro-static full-f PiC models for ion temperature gradient (ITG) and trapped electron modes (TEM) were established and benchmarked. Application to RMP plasmas shows enhanced turbulence in comparison to unperturbed states. Energetic particle (EP) interactions with MHD were studied. Flux-pumping that prevents the safety factor on axis from dropping below unity was simulated. First non-linear stellarator applications include current relaxation in l=2 stellarators, while verification for advanced stellarators progresses.