H-mode Transition Research Articles

Criterion for long sustained highly peaked ion temperature in diverted configuration of KSTAR tokamak

In the context of KSTAR plasma research, the discovery of the fast ion regulated enhanced mode is noteworthy due to its remarkable ability to maintain ion temperatures exceeding up to 10 keV for a few tens of seconds, avoid impurity accumulation, and keep low loop voltages. This new plasma operating scenario is achieved in a diverted configuration plasma by avoiding the H-mode transitions with sufficient additional power for the transition. Keeping the density low is the primary method for the avoidance. Additionally, adjustments to other parameters (plasma shape, neutral beam injection, and toroidal magnetic field) associated with the H-mode threshold power are applied to inhibit the transition process. This paper includes an experimental analysis and discussion of these findings.

Impact of β n and spectrum of n = 1 applied fields on fast ion losses in DIII-D

The effect of n = 1 magnetic perturbations (MPs) on prompt fast ion losses in DIII-D has been investigated using the light ion beam probe technique. The effect of normalized beta, β n , and the plasma response to the MPs is studied for several MP spectra. Magnetics data show a strong dependence of plasma response to β n that depends on the phase difference in perturbation coils, . For most phases, the response increases with β n , however, the response is suppressed for phases between 180∘ and 240∘. Experimental data from scintillator based fast ion loss detectors shows that relative fluctuation of lost ions (20%–30% of the steady signal) does not diminish across the L- to H-mode transition for , despite the 34% decrease in radial response field and 50% decrease in poloidal response field. Simulations of the DIII-D discharges using M3D-C1 and ASCOT5 find that prompt losses from neutral beam injection in each investigated case hit the first wall at several concentrated locations: the vessel floor, midplane diagnostic ports, vessel ceiling, and inner wall. Simulated losses from co-injection neutral beams are born outside the last closed flux surface, corresponding to radial orbit displacements of 3–6 cm due to the MPs.

Turbulence and E × B flow correlations across the L-H transition in DIII-D deuterium and hydrogen plasmas.

The isotope dependence of the low- to high confinement-mode (L- to H-mode) transition power threshold PLH presents significant challenges for the initial (non-nuclear) hydrogen operations phase of the international thermonuclear experimental reactor (ITER). Here, we examine the isotope dependence of turbulence and E × B flow correlation properties in the L-mode edge plasma, leading up to the L-H transition. At marginal auxiliary power (near PLH), turbulence is initially suppressed periodically during limit cycle oscillations (LCO) that precede the transition to sustained H-mode confinement. We present evidence that the long-range (toroidal) correlation of the E × B edge plasma flow across the LCO phase is much weaker in hydrogen than in deuterium in the DIII-D tokamak, congruent with the higher threshold power PLH required to access LCO and H-mode in hydrogen. Concomitantly, the time required to initially quench edge turbulence via localized edge E × B flow shear is significantly longer in hydrogen (1-1.5 ms) than in deuterium (approx. 100 µs). No toroidal long-range correlation of the turbulence amplitude is observed, in agreement with expectations based on the relatively short poloidal turbulence correlation length. Radial edge turbulence and flow correlation lengths are longer in deuterium than in hydrogen plasmas as one would expect from 'naïve' gyro-Bohm isotope transport scaling, despite the substantially higher thermal flux across the last closed flux surface in hydrogen before the L-H transition. This article is part of a discussion meeting issue 'H-mode transition and pedestal studies in fusion plasmas'.

Turbulence characteristics and flow dynamics impacts on the H-mode transition in favourable magnetic geometry with lower power threshold.

The L-H transition power threshold (PLH) in favourable magnetic geometry (ion ∇B drift pointing towards X-point) is much lower than in the unfavourable magnetic geometry (ion ∇B drift pointing away from X-point) on multiple tokamaks. In a systematic experiment on DIII-D, the ion ∇B drift direction was changed continuously from the unfavourable to favourable configuration during plasma discharges. During such process, the input neutral beam power was kept constant at a value that was above PLH for favourable configuration, but lower than PLH for unfavourable configuration. Toroidal field and plasma current were also kept constant and there was little change in the edge electron density ne and electron temperature Te profiles. The density fluctuation amplitude was reduced approaching the transition, while a large increase of turbulence Reynolds stress and flow shear were simultaneously observed. The turbulence decorrelation rate was found to increase as the ion ∇B drift direction was moving towards the favourable configuration, but the flow shear also increased and exceeded the turbulence decorrelation rate. These measurements demonstrate an important correlation between turbulence and turbulence-driven flow and a lowering of PLH, provide insights into the underlyingphysics behind the hidden parameters and inform a more complete physics-based model of the L-H transition power threshold. This article is part of a discussion meeting issue 'H-mode transition and pedestal studies in fusion plasmas'.

H-mode transition in the TJ-II stellarator plasmas.

Since the first H-mode transitions were observed in TJ-II plasmas in 2008, an extensive experimental effort has been done aiming at better physics understanding of confinement transitions. In this article, an overview of the main findings related to the L-H transition in TJ-II is presented including how the radial electric field is driven, what are the possible mechanisms for turbulence suppression and what are the related temporal and spatial scales that can impact the transition. The trigger of the L-H transition in TJ-II plasmas is found to be more correlated with the development of fluctuating [Formula: see text] flows than with steady-state [Formula: see text] effects, pointing to the role played by zonal flows in mediating the transition. Experimental evidence supporting the predator-prey relationship between turbulence and flows as the basis for the L-H transition, found for the first time in TJ-II, reinforces this conclusion. Besides, the reduction in the turbulent transport at the transition is detected at the barrier region but also in a wider radial range with weak or even zero [Formula: see text] flow shear, which points to other mechanisms beyond the turbulence suppression by local sheared flows. This article is part of a discussion meeting issue 'H-mode transition and pedestal studies in fusion plasmas'.

H-mode transition and pedestal studies.

The high confinement mode (H-mode) is the widely adopted standard operation scenario for the path to fusion in toroidal confinement devices. Since its discovery in 1982, the H-mode and access to the H-mode (the low to high and high to low transitions) remain two of the most actively researched areas in magnetically confined fusion programmes across the world. Significant progress has been made in the understanding of the intricate H-mode phase dynamics in recent years, from improvement in experimental diagnostic capability, theoretical development and modelling. The 'H-mode transition and pedestal studies' Special Issue provides a timely overview of recent progress in the study of H-modes covering experimental studies, further theoretical inquiry and computational modelling. This article is part of a discussion meeting issue 'H-mode transition and pedestal studies in fusion plasmas'.

H-mode dithering phase studies on ST40.

The dithering H-mode phase, characterized by oscillations, is generally observed at input power values close to the L-H transition power threshold and low plasma collisionalities (low electron density and/or high plasma temperature). Measurements to characterize the dithering phase are presented for the low aspect ratio, high magnetic field tokamak, ST40. The dithering phase oscillation frequency is observed between 400 and 800 Hz and demonstrates an inverse relationship with core plasma density. Dithering phase H-modes are documented across a nonlinear, low-density power threshold operational space, with signature low- and high-density branches. The minimum power threshold for dithering H-mode access is measured at a core, line average electron density of 4.7(±0.5) × 1019 m-3, close to a predicted value of 4.1(±0.4) × 1019 m-3 from multi-machine studies. ASTRA calculated values of power coupled to the ion species, at the dithering H-mode transition, exhibit a similar nonlinear dependence on density. This analysis points to the important contribution of the ion thermal channel to the L-H phase transition. The low-frequency plasma density and D-alpha dithers appear to be accompanied by sudden bursts of magnetohydrodynamic (MHD) activity. A simple model is tested to demonstrate a possible scenario of self-regulation among turbulence, zonal flows, pressure (density) gradient and MHD activities. This article is part of a discussion meeting issue 'H-mode transition and pedestal studies in fusion plasmas'.

Characteristics of constrained turbulent transport in flux-driven toroidal plasmas.

We study the dynamics of turbulence transport subject to a constraint on the profile formation and relaxation, dominated by the ion temperature gradient modes, within the framework of adiabatic electron response using a flux-driven global gyro-kinetic toroidal code, GKNET. We observe exponentially constrained profiles, with two different scale lengths, that are spatially constant in each region in higher input power regimes. The profiles are smoothly connected in the knee region located at [Formula: see text] of the minor radius, outside which the gradient is steepened and shows a weak confinement improvement. Based on the probability density function analysis of heat flux eddies, the power law demonstrates a dependence on the eddy size S, as [Formula: see text], which distinguishes events into diffusive and non-diffusive parts including the validation of quasi-linear hypotheses. Radially localized avalanches and global bursts, which exhibit different spatial scales, play central roles in giving rise to constrained profiles on an equal footing. It is also found that the [Formula: see text] shear layers are initiated by the global bursts, which evolve downward on a slow time scale across the knee region and play a role in adjusting the profile by increasing the gradient. This article is part of a discussion meeting issue 'H-mode transition and pedestal studies in fusion plasmas'.

An overview of dynamical methods for studying transitions between states in sheared plasma flows.

The self-organization of structures in a tokamak plasma as it undergoes an [Formula: see text]-mode transition shows properties similar to simpler shear flow configurations. We will describe recent dynamical studies of plasma shear flows, including the idea of tracking the edge of chaos that separates two bistable states, computing the nonlinear minimal seed that can lead to turbulence, finding the attractor solution on the edge and seeing how starting from this solution we can understand the stability of relative period orbits that permeate the turbulent basin of attraction. We present a modus operandi developed for these simple configurations that can be adapted to understand the [Formula: see text]-mode transition. This article is part of a discussion meeting issue 'H-mode transition and pedestal studies in fusion plasmas'.

Comparing pedestal structure in JET-ILW H-mode plasmas with a model for stiff ETG turbulent heat transport.

A predictive model for the electron temperature profile of the H-mode pedestal is described, and its results are compared with the pedestal structure of JET-ILW plasmas. The model is based on a scaling for the gyro-Bohm normalized, turbulent electron heat flux [Formula: see text] resulting from electron temperature gradient (ETG) turbulence, derived from results of nonlinear gyrokinetic (GK) calculations for the steep gradient region. By using the local temperature gradient scale length [Formula: see text] in the normalization, the dependence of [Formula: see text] on the normalized gradients [Formula: see text] and [Formula: see text] can be represented by a unified scaling with the parameter [Formula: see text], to which the linear stability of ETG turbulence is sensitive when the density gradient is sufficiently steep. For a prescribed density profile, the value of [Formula: see text] determined from this scaling, required to maintain a constant electron heat flux [Formula: see text] across the pedestal, is used to calculate the temperature profile. Reasonable agreement with measurements is found for different cases, the model providing an explanation of the relative widths and shifts of the [Formula: see text] and [Formula: see text] profiles, as well as highlighting the importance of the separatrix boundary conditions. Other cases showing disagreement indicate conditions where other branches of turbulence might dominate. This article is part of a discussion meeting issue 'H-mode transition and pedestal studies in fusion plasmas'.

Bifurcation behaviour of resonant magnetic perturbation control of edge localized modes in tokamaks: nonlinear simulation results.

In this article, some novel results of two fluid nonlinear simulations on the control of edge localized modes (ELMs) in tokamaks by resonant magnetic perturbations (RMPs) are presented. Many experiments around the world have demonstrated that RMPs are effective in possibly mitigating or even completely suppressing strong (type I) ELMs that would seriously degrade confinement and could cause other heat-flux problems in both present (e.g. JET) and planned future tokamaks (ITER). Our simulations demonstrate that non-axisymmetric RMPs with toroidal mode numbers [Formula: see text] and suitable field-strengths (kAturns) at the plasma wall imply significant bifurcations in their ability to mitigate or even suppress type-I ELMs, qualitatively similar to RMP effects on ELMs reported in experiments. This article is part of a discussion meeting issue 'H-mode transition and pedestal studies in fusion plasmas'.

A stochastic model of edge-localized modes in magnetically confined plasmas.

Magnetically confined plasmas are far from equilibrium and pose considerable challenges in statistical analysis. We discuss a non-perturbative statistical method, namely a time-dependent probability density function (PDF) approach that is potentially useful for analysing time-varying, large, or non-Gaussian fluctuations and bursty events associated with instabilities in the low-to-high confinement transition and the H-mode. Specifically, we present a stochastic Langevin model of edge-localized modes (ELMs) by including stochastic noise terms in a previous ODE ELM model. We calculate exact time-dependent PDFs by numerically solving the Fokker-Planck equation and characterize time-varying statistical properties of ELMs for different energy fluxes and noise amplitudes. The stochastic noise is shown to introduce phase-mixing and plays a significant role in mitigating extreme bursts of large ELMs. Furthermore, based on time-dependent PDFs, we provide a path-dependent information geometric theory of the ELM dynamics and demonstrate its utility in capturing self-regulatory relaxation oscillations, bursts and a sudden change in the system. This article is part of a discussion meeting issue 'H-mode transition and pedestal studies in fusion plasmas'.

Overview of L- to H-mode transition experiments at ASDEX Upgrade

This paper presents an overview of results from L–H transition experiments that were performed at ASDEX Upgrade (AUG) with the aim of identifying the underlying mechanisms leading to H-mode confinement. With a broad variety of experiments and new diagnostic techniques, as well as modeling efforts, AUG has contributed substantially to improving our understanding of the L–H transition over the past years. In this review, the important roles of the ion heat channel and the edge radial electric field (E r ) in the L–H transition physics are brought into context with known dependencies of the H-mode power threshold (), such as the impact of wall material, magnetic perturbations, and the magnetic configuration. Furthermore, experimental and theoretical results obtained at AUG on the L-mode edge turbulence are connected to the mean-field E r and its related shear flow. This led to a deeper understanding of the I-phase plasma regime, has resolved the so-called isotope effect of , and led to the development of a semi-analytical model that can describe AUG’s experimental observations of the L–H transition together with the L- and H-mode density limits.

Local measurements of the pedestal magnetic field profile throughout the ELM cycle on DIII-D

New high speed localized measurements of the pedestal magnetic field during the edge localized mode (ELM) cycle of a DIII-D High confinement mode (H-mode) discharge indicate a temporally and spatial complex redistribution of the edge current density profile, jedge. The measurement technique extracts the magnetic field magnitude, B, via the spectral separation of Stark-split neutral beam radiation in the pedestal. Single spatial channel measurements from a novel spatial heterodyne spectrometer are validated in discharges with core current profile changes. The technique measures Stark-splitting changes that imply B changes as small as 1 mT with high time resolution (50 μs). At normalized poloidal flux ψn=1.0, B appears saturated in the inter-ELM period and then rapidly decreases in <200 μs by ∼1%, before edge recycling emission begins to increase. Radially inboard of jedge, B increases at the ELM crash. The behavior is consistent with a rapid collapse of jedge at the ELM crash and subsequent pedestal recovery. In some discharges, at ψn<0.96, changes in B are observed throughout the ELM cycle. In others, B recovers and is relatively stable until a few ms leading up to the next crash. Measurements of B during the H-mode transition show a large increase at ψn=1 with little change at ψn=0.9, consistent with the formation of the edge bootstrap current density peak. The ψn=0.9 spectrum is complicated by predicted changes to the Stark component intensities with density at the L–H transition.

Characterization of pedestal burst instabilities during I-mode to H-mode transition in the EAST tokamak

Quasi-periodic pedestal burst instabilities (PBIs), featuring alternative turbulence suppression and bursts, have been clearly identified by various edge diagnostics during I-mode to H-mode transition in the EAST Tokamak. The radial distribution of the phase perturbation caused by PBI shows that PBI is localized in the pedestal. Prior to each PBI, a significant increase of density gradient close to the pedestal top can be clearly distinguished, then the turbulence burst is generated, accompanied by the relaxation of the density profile, and then induces an outward particle flux. The relative density perturbation caused by PBIs is about 6%–8%. Statistic analyses show that the pedestal normalized density gradient R/L n triggering the first PBI has a threshold value, mostly in the range of 22–24, suggesting that a PBI triggering instability could be driven by the density gradient. And R/L n triggering the last PBI is about 30–40 and seems to increase with the loss power and the chord-averaged density. In addition, the frequency of PBI is likely to be inversely proportional to the chord-averaged density and the loss power. These results suggest that PBIs and the density gradient prompt increase prior to PBIs can be considered as the precursor for controlling I–H transition.

I-mode pedestal relaxation events in the Alcator C-Mod and ASDEX Upgrade tokamaks

In some conditions, I-mode plasmas can feature pedestal relaxation events (PREs) that transiently enhance the energy reaching the divertor target plates. To shed light on their appearance, characteristics and energy reaching the divertor targets, a comparative study between two tokamaks — Alcator C-Mod and ASDEX Upgrade — is carried out. It is found that PREs appear only in a subset of I-mode discharges, mainly when the plasma is close to the H-mode transition. Also, a growing oscillating precursor before the PRE onset is observed in the region close to the separatrix in both devices, and a discussion on a possible triggering mechanism is outlined. The PRE relative energy loss from the confined region is found to increase with decreasing pedestal top collisionality . Similarly, also the relative electron temperature drop at the pedestal top, which is related to the conductive energy loss, rises with decreasing . Based on these relations, the PRE relative energy loss in future devices such as DEMO and ARC is estimated. Finally, the divertor peak energy fluence due to the PRE is measured on each device. Those values are then compared to the model introduced in Eich et al (2017 Nucl. Mater. Energy 12 84–90) for type-I edge localized modes. The model is shown to provide an upper boundary for PRE energy fluence data, while a lower boundary is found by dividing the model by three. These two boundaries are used to make projections of the PRE divertor energy fluence to DEMO and ARC.

Preemptive RMP-driven ELM crash suppression automated by a real-time machine-learning classifier in KSTAR

Suppression or mitigation of edge-localized mode (ELM) crashes is necessary for ITER. The strategy to suppress all the ELM crashes by the resonant magnetic perturbation (RMP) should be applied as soon as the first low-to-high confinement (L–H) transition occurs. A control algorithm based on real-time machine learning (ML) enables such an approach: it classifies the H-mode transition and the ELMy phase in real-time and automatically applies the preemptive RMP. This paper reports the algorithm design, which is now implemented in the KSTAR plasma-control system, and the corresponding experimental demonstration of typical high-δ KSTAR H-mode plasmas. As a result, all initial ELM crashes are suppressed with an acceptable safety factor at the edge (q 95) and with RMP field adjustment. Moreover, the ML-driven ELM crash suppression discharges remain stable without further degradation due to the regularization of the plasma pedestal.

Power characteristics of multiple inductively coupled RF discharges inside a metallic chamber

The characteristics of an innovative configuration of multiple radiofrequency (RF) coils immersed in a large metallic chamber are presented. Water-cooled copper coils were mounted within the slits of double-walled glass tubes, which were immersed into a stainless-steel chamber. The coils were connected in parallel to a gamma-type matching network, powered by an RF generator operating at industrial frequency. Adjustable leads enabled optimisation of the line impedances and thus uniformly distributed RF power across the four coils. Transitions from E- to H-mode and vice versa were measured for all coils at various oxygen pressures between 5 and 25 Pa. A uniform plasma was sustained in H-mode at the absorbed power threshold, which increased monotonously with increasing pressure in the metallic chamber. All coils exhibit the same E- to H-mode transition hysteresis and need the same amount of power for transitioning from E- to H-mode. The setup enables maintaining uniform plasma in virtually any number of coils at high power without the risk of arcing and without the dead volume typical for a classical configuration with coils mounted outside the metallic chamber.

Theoretical Study of the Impedance Matching of the Ferrite Tuner System for ICRF Heating

A theoretical study on a ferrite stub tuner antenna system for ion cyclotron resonance frequency (ICRF) heating is discussed in this paper. High amounts of radio frequency power can be reflected at the antenna as a result of impedance mismatches arising from large changes in the plasma resistance during L- to H-mode transitions or edge localized modes. A fast-response ferrite stub tuner network has been proposed to mitigate these reflections by rapidly varying the impedance to match the rapid load changes on the ICRF antenna. This study numerically shows the influence relationship of the normalized mechanical length and the ratio of the ferrite part of two ferrite stubs on the regulating range of a biasing magnetic field of two stubs. A prematching stub can be used to reduce the standing-wave voltage on the ferrite tuners. The analysis of the ideal position and length of the prestub as well as the distance between the ferrite network and prestub are presented. Numerical simulations demonstrate that selecting ideal values for mechanical length and the ratio of the ferrite part of two ferrite stubs plays an important role in the impedance matching performance of the triple ferrite system during a large variation in plasma resistance.

Self-consistent cross-field transport model for core and edge plasma transport

A two-equation model to self-consistently determine cross-field fluxes in the edge and scrape-off layer (SOL) region of diverted plasma is used to complete 2D mean-field edge transport description of plasma wall interaction. Inspired by the Reynolds average Navier–Stokes simulations for neutral fluids, this model is based on the local evolution of the turbulent kinetic energy κ and its dissipation rate ɛ. These two equations are algebraically derived for RANS modeling and are very slightly modified and adapted to describe self-consistent plasma turbulent transport. The general features of the model are discussed and bridged to the well-known predator–prey and quasilinear models commonly used to investigate plasma transport. Specific closures are proposed based on the interchange turbulence. Results of the 1D model are confronted to experimental evidence by analyzing the computed SOL width and comparing the results to the existing scaling law for L-mode plasmas. Introducing a dependence on the shear of large scale flows, typically the zonal flows, 1D simulations can exhibit an H-mode like transition when increasing the input power, generating an increased stored energy thanks to an interface barrier located at the separatrix. Further 2D plasma–wall interaction simulations for WEST are analyzed that show a good match with the experimental profiles, as well as a ballooned transport driving turbulent transport in the divertor SOL and nearly no transport in the private flux region. The SOL width of WEST is also recovered. These results show the remarkable capability of the κ–ɛ model to capture key aspects of the physics of turbulent transport throughout the plasma knowing that a unique scalar free parameter is available to tune cross field transport in the whole 2D cross section of the plasma.