Core Transport Barriers Research Articles

Core transport barriers induced by fast ions in global gyrokinetic GENE simulations

A novel type of internal transport barrier called F-ATB (fast ion-induced anomalous transport barrier) has been recently observed in state-of-the-art global gyrokinetic simulations on a properly optimized ASDEX Upgrade experiment and presented in Di Siena et al (2021 Phys. Rev. Lett. 127 025002). Unlike the transport barriers previously reported in the literature, the trigger mechanism for the F-ATB has been shown to be a wave-particle resonant interaction between supra-thermal particles—generated via ion cyclotron resonance heating—and ion scale plasma turbulence. This resonant mechanism strongly depends on the particular shape of the fast ion temperature and density profiles. Therefore, to further improve our theoretical understanding of this transport barrier, we present results exploring the parameter space and physical conditions for the F-ATB generation by performing a systematic study with global GENE simulations. Particular emphasis is given to the transport barrier width and its localization by scanning over different energetic particle temperature profiles. The latter are varied in amplitude, half-width, and radial localization of an ad-hoc Gaussian-like energetic particle logarithmic temperature gradient profile. For the reference parameters at hand, a threshold in the ratio between the fast ion and electron temperature and the amplitude of the fast ion logarithmic temperature gradient is identified to trigger the transport barrier effectively. The role of q = 1 rational surface to the transport barrier formation is investigated as well by retaining electromagnetic effects and its impact found to be negligible for this particular barrier formation mechanism.

Role of sheared E × B flow in self-organized, improved confinement states in magnetized plasmas

A major scientific success story of magnetic fusion research in the past several decades has been the theoretical development and experimental testing of the process of turbulence decorrelation and stabilization by sheared E × B flow, which shows that E × B shear effects are ubiquitous in magnetized plasmas. This concept of turbulence decorrelation and stabilization has the universality needed to explain the H-mode edge transport barriers seen in limiter and divertor tokamaks, stellarators, and mirror machines; the broader edge transport barrier seen in VH-mode plasmas; and the core transport barriers formed in tokamaks. Similar effects are seen in linear devices. These examples of confinement improvement are of considerable physical interest; it is not often that a system self-organizes to reduce transport when an additional source of free energy is applied to it. The transport decrease associated with E × B velocity shear is also of great practical benefit to fusion research, since it contributed to substantially increased fusion yield in all DT magnetic fusion experiments conducted to date. The fundamental physics involved in transport reduction is the effect of E × B shear on the growth, radial extent, and phase correlation of turbulent eddies in the plasma. The same basic transport reduction process can be operational in various portions of the plasma because there are a number of ways to change the radial electric field Er. An important secondary theme in this area is the synergistic effect of E × B velocity shear and magnetic shear. Although the E × B velocity shear appears to have an effect on broader classes of microturbulence, magnetic shear can mitigate some potentially harmful effects of E × B velocity shear and facilitate turbulence stabilization. Our present understanding in this area is the result of a multi-decade, intertwined effort in theory, modeling, and diagnostic development combined with continuing experimental investigations. These experiments have clearly demonstrated that increased E × B shear causes reductions in turbulence and transport. The experimental results are generally consistent with the basic theoretical models although considerable work remains to be done before we have a fully predictive theory of transport in magnetized plasmas including E × B shear effects.

Helical equilibrium magnetohydrodynamic flow effects on the stability properties of low-n ideal external-infernal modes in weak shear tokamak configurations

The impact of equilibrium helical flows on the stability properties of low shear tokamak plasmas is assessed. The corrections due to such helical flow to the equilibrium profiles (mass density, pressure, Shafranov shift, magnetic fluxes) are computed by minimising order by order the generalised Grad–Shafranov equation. By applying the same minimisation procedure, a set of three coupled equations, suitable for the study of magnetohydrodynamic perturbations localised within core or edge transport barriers is derived in circular tokamak geometry. We apply these equations to modelling the impact of strong poloidal flow shear in the edge region caused by a radial electric field on the stability of edge infernal modes retaining vacuum effects. Due to the poloidal flow shearing, the effect of plasma rotation is not simply a Doppler shift of the eigenfrequency. Stabilisation is found even for weak flow amplitude.

OEDGE modeling for the planned tungsten ring experiment on DIII-D

The OEDGE code is used to model tungsten erosion and transport for experiments with toroidal rings of high-Z metal tiles in the DIII-D tokamak. Such modeling is needed for both experimental and diagnostic design to have estimates of the expected core and edge tungsten density and to understand the various factors contributing to the uncertainties in these calculations. OEDGE simulations are performed using the planned experimental magnetic geometries and plasma conditions typical of both L-mode and inter-ELM H-mode discharges in DIII-D. OEDGE plasma reconstruction based on specific representative discharges for similar geometries is used to determine the plasma conditions applied to tungsten plasma impurity simulations. A new model for tungsten erosion in OEDGE was developed which imports charge-state resolved carbon impurity fluxes and impact energies from a separate OEDGE run which models the carbon production, transport and deposition for the same plasma conditions as the tungsten simulations. These values are then used to calculate the gross tungsten physical sputtering due to carbon plasma impurities which is then added to any sputtering by deuterium ions; tungsten self-sputtering is also included. The code results are found to be dependent on the following factors: divertor geometry and closure, the choice of cross-field anomalous transport coefficients, divertor plasma conditions (affecting both tungsten source strength and transport), the choice of tungsten atomic physics data used in the model (in particular ionization rate for W-atoms), and the model of the carbon flux and energy used for calculating the tungsten source due to sputtering. Core tungsten density is found to be of order 1015m−3 (excluding effects of any core transport barrier and with significant variability depending on the other factors mentioned) with density decaying into the scrape off layer. For the typical core density in the plasma conditions examined of 2 to 4 ×1019m−3, this represents a concentration on the order of 5 × 10−5.

Turbulence in edge and core transport barriers: new experimental results and modeling

In this paper, recent progressive studies on experimental analysis and theoretical models for turbulence phenomena around the transport barriers in high-performance magnetic confined fusion plasma are reviewed. The linkage of radial electric fields and turbulence, the importance of radial electric field curvature, and observations of spatiotemporal turbulence structures are described with related theoretical models.

The role of zonal flows and predator–prey oscillations in triggering the formation of edge and core transport barriers

We present direct evidence of low frequency, radially sheared, turbulence-driven flows (zonal flows (ZFs)) triggering edge transport barrier formation preceding the L- to H-mode transition via periodic turbulence suppression in limit-cycle oscillations (LCOs), consistent with predator–prey dynamics. The final transition to edge-localized mode-free H-mode occurs after the equilibrium E × B flow shear increases due to ion pressure profile evolution. ZFs are also observed to initiate formation of an electron internal transport barrier (ITB) at the q = 2 rational surface via local suppression of electron-scale turbulence. Multi-channel Doppler backscattering (DBS) has revealed the radial structure of the ZF-induced shear layer and the E × B shearing rate, ωE×B, in both barrier types. During edge barrier formation, the shearing rate lags the turbulence envelope during the LCO by 90°, transitioning to anti-correlation (180°) when the equilibrium shear dominates the turbulence-driven flow shear due to the increasing edge pressure gradient. The time-dependent flow shear and the turbulence envelope are anti-correlated (180° out of phase) in the electron ITB. LCOs with time-reversed evolution dynamics (transitioning from an equilibrium-flow dominated to a ZF-dominated state) have also been observed during the H–L back-transition and are potentially of interest for controlled ramp-down of the plasma stored energy and pressure (normalized to the poloidal magnetic field) in ITER.

Radial resolution enhancement of the NSTX Thomson scattering diagnostic

Current magnetic confinement plasma physics research has increased the demand for radial resolution in profile diagnostics, in particular in the edge and pedestal regions. On NSTX, an upgrade of the existing multi-point Thomson scattering diagnostic has been implemented in order to respond to the research program needs. Twelve new radial channels have been added bringing the total number of positions to 42. Four previously un-instrumented fiber bundles were put in service. Eight existing "active" fiber bundles were divided in two sub-bundles each in order to increase spatial resolution. Twelve radial channels now cover the pedestal region with a resolution near one centimeter. Fifteen radial channels cover the core and internal transport barrier regions. Two additional channels were added, one near the inner edge and one in the outer scrape-off layer. The intersection of the focused viewing optics field of view with a finite-width laser beam results in major-radius cross talk between adjacent fiber sub-bundles. A discussion and calculation of the cross talk will be presented.

Access to sustained high-beta with internal transport barrier and negative central magnetic shear in DIII-D

High values of normalized β (βN∼4) and safety factor (qmin∼2) have been sustained simultaneously for ∼2s in DIII-D [J.L. Luxon, Nucl. Fusion 42, 64 (2002)], suggesting a possible path to high fusion performance, steady-state tokamak scenarios with a large fraction of bootstrap current. The combination of internal transport barrier and negative central magnetic shear at high β results in high confinement (H89P>2.5) and large bootstrap current fraction (fBS>60%) with good alignment. Previously, stability limits in plasmas with core transport barriers have been observed at moderate values of βN (<3) because of the pressure peaking which normally develops from improved core confinement. In recent DIII-D experiments, the internal transport barrier is clearly observed in the electron density and in the ion temperature and rotation profiles at ρ∼0.5 but not in the electron temperature profile, which is very broad. The misalignment of Ti and Te gradients may help to avoid a large local pressure gradient. Furthermore, at low internal inductance ∼0.6, the current density gradients are close to the vessel and the ideal kink modes are strongly wall-coupled. Simultaneous feedback control of both external and internal sets of n=1 magnetic coils was used to maintain optimal error field correction and resistive wall mode stabilization, allowing operation above the free-boundary β limit. Large particle orbits at high safety factor in the core help to broaden both the pressure and the beam-driven current profiles, favorable for steady-state operation. At plasma current flat top and β∼5%, a noninductive current fraction of ∼100% has been observed. Stability modeling shows the possibility for operation up to the ideal-wall limit at β∼6%.

Density and temperature profile modifications with electron cyclotron power injection in quiescent double barrier discharges on DIII-D

Quiescent double barrier (QDB) conditions often form when an internal transport barrier is created with high-power neutral-beam injection into a quiescent H-mode (QH) plasma. These QH-modes offer an attractive, high-performance operating scenario for burning plasma experiments due to their quasi-stationarity and lack of edge localized modes. Our initial experiments and modelling using ECH/ECCD in QDB shots were designed to control the current profile and, indeed, we have observed a strong dependence on the q-profile when EC-power is used inside the core transport barrier region. While strong electron heating is observed with EC power injection, we also observe a drop in the other core parameters, namely ion temperature and rotation, electron density and impurity concentration. At onset and termination of the EC pulse, dynamically changing conditions are induced that provide a rapid evolution of Te/Ti profiles accessible with 0.3 < (Te/Ti)axis < 0.8 observed in QDB discharges. We are exploring the correlation and effects of observed density profile changes with respect to these time-dependent variations in the temperature ratio. Increases in the measured ion thermal and particle diffusivities inside the barrier region during an ECH pulse correlate with electron heating and a rise in the core Te/Ti ratio as the ion temperature and density profiles flatten with this change in transport. The change in transport is consistent with a destabilization of ITG turbulence as inferred from the reduction of the stability threshold due to the change in Te/Ti.

Role of E × B Shear and Magnetic Shear in the Formation of Transport Barriers in DIII-D

Development of the E × B shear stabilization model to explain the formation of transport barriers in magnetic confinement devices is a major achievement of fusion research. This concept has the universality needed to explain the H-mode edge transport barriers seen in limiter and divertor tokamaks, stellarators, and mirror machines; the broader edge transport barrier seen in VH-mode plasmas; and the core transport barriers formed in tokamaks with low or negative magnetic shear. These examples of confinement improvement are of considerable physical interest; it is not often that a system self-organizes to reduce transport when an additional source of free energy is applied to it. The transport decrease associated with E × B velocity shear is also of great practical benefit to fusion research. The fundamental physics involved in transport reduction is the effect of E × B shear on the growth, radial extent, and phase correlation of turbulent eddies in the plasma. The same basic transport reduction process can be operational in various portions of the plasma because there are a number of ways to change the radial electric field Er. An important theme in this area is the synergistic effect of E × B velocity shear and magnetic shear. Although the E × B velocity shear appears to have an effect on broader classes of microturbulence, magnetic shear can mitigate some potentially harmful effects of E × B velocity shear and facilitate turbulence stabilization. The experimental results on DIII-D and other devices are generally consistent with the basic theoretical models.

Long distance coupling of lower hybrid waves in JET plasmas with edge and core transport barriers

Efficient coupling of lower hybrid (LH) waves in conditions close to those foreseen in ITER has been obtained in advanced scenario plasmas in the JET tokamak. Up to 3 MW of lower hybrid current drive (LHCD) power has been coupled at a distance between the separatrix and the launcher of 11 cm, in the presence of edge localized mode activity. The key to the improved LH wave coupling is local control of the Scrape-Off-Layer (SOL) density through gas injection in the region magnetically connected to the launcher. This increases the electron density in front of the launcher so as to improve the coupling of the LH waves, i.e. reduce the reflected power in the launcher. The average power reflection coefficient was 5.7% with gas injection, at 11 cm distance between the separatrix and the launcher. A change in the gas injection design has made the gas puffing more efficient, making the use of D2 injection possible as an alternative to CD4. At similar injected electrons/s rates, D2 gives higher electron density in the SOL than CD4, resulting in better LH coupling with D2. The possibility of using D2 instead of the earlier used CD4 is an encouraging result in view of ITER operation, as CD4 may not be compatible in ITER due to the problem of tritium retention in deposited carbon layers.

Predicting core and edge transport barriers in tokamaks using the GLF23 drift-wave transport model

The density and temperature profiles are predicted in core and edge transport barriers in the DIII-D tokamak [J. L. Luxon and L. G. Davis, Fusion Technol. 8, 441 (1985)] using the GLF23 drift-wave model. The GLF23 model has been retuned to yield a better fit to the linear gyrokinetic growth rates for reversed magnetic shear and H-mode pedestal parameters. The turbulent saturation levels are determined using nonlinear gyrokinetic simulations. Using a large profile database, it is found that the retuned and original GLF23 models yield comparable results for discharges with monotonic safety factor profiles and no discernable internal transport barriers (ITBs). Examples of using retuned GLF23 model to predict the temperature profiles in simulations of several DIII-D strongly reversed magnetic shear ITB discharges are provided. Particle transport simulations show that the model is successful in predicting the density profile in discharges without ITBs but that some additional background particle diffusivity is needed in order to reproduce the measured density profiles within the barrier region of ITB plasmas where the ion temperature gradient and trapped electron mode transport have been quenched by rotational shear stabilization.

Double transport barrier experiments on Alcator C-Mod

Double transport barrier modes (simultaneous core and edge transport barrier) have been observed with off-axis ion cyclotron range of frequencies (ICRF) heating in the Alcator C-Mod tokamak [I. H. Hutchinson et al., Phys. Plasmas 1, 1511 (1994)]. An internal transport barrier (ITB) is routinely produced in enhanced DαH-mode (EDA) discharges where the minority ion cyclotron resonance layer is at r/a∼|0.5| during the current flat top phase of the discharge. The density profile becomes peaked without the presence of a particle source in the plasma core and continues to peak until the increased core impurity radiation arrests the improved energy confinement, ultimately leading to a barrier collapse. With the addition of moderate (0.6 MW) central ICRF heating, the double barrier mode was maintained for as long as the ICRF power was applied. Modeling shows that the internal thermal barrier was maintained throughout the discharge. The presence of sawteeth throughout most of the ITB discharge allows sawtooth-induced heat pulse analysis to be performed. This analysis indicates that there is an abrupt radial discontinuity in the heat pulse time to peak profile when an ITB is present. Furthermore, this discontinuity appears to move into the core plasma from the edge region in about 0.2 s, several confinement times. The deduced thermal diffusivity, χhp, indicates that a barrier exists in the electron thermal transport, the barrier is limited to a narrow radial region, and the transport is unaffected outside this narrow radial extent.

Progress towards increased understanding and control of internal transport barriers in DIII-D

Substantial progress has been made towards bothunderstanding and control of internal transport barriers (ITBs) onDIII-D, resulting in the discovery of a new sustained high performanceoperating mode termed the quiescent double barrier (QDB) regime. TheQDB regime combines core transport barriers with a quiescent ELM-freeH mode edge (termed QH mode), giving rise to separate (double) coreand edge transport barriers. The core and edge barriers are mutuallycompatible and do not merge, resulting in broad core profiles with anedge pedestal. The QH mode edge is characterized by ELM-free behaviourwith continuous multiharmonic MHD activity in the pedestal region andhas provided density and radiated power control for longer than 3.5 s (25τE)with divertor pumping. QDB plasmas are long pulse high performancecandidates, having maintained a βNH89 product of 7 for five energyconfinement times (Ti⩽16 keV, βN⩽2.9, H89⩽2.4, τE⩽150 ms, DDneutron rate Sn⩽4×1015 s-1). The QDB regime has only been obtainedin counter-NBI discharges (injection antiparallel to the plasma current)with divertor pumping. Other results include successful expansion ofthe ITB radius using (separately) both impurity injection andcounter-NBI, and the formation of ITBs in the electron thermal channelusing both ECH and strong negative central shear (NCS) at highpower. These results are interpreted within a theoretical framework inwhich turbulence suppression is the key to ITB formation and control,and a decrease in core turbulence is observed in all cases of ITBformation.

The quiescent double barrier regime in the DIII-D tokamak

Experiments on the DIII-D tokamak have identified a new sustained high-performance operating mode, termed the quiescent double barrier (QDB) regime. The QDB regime combines internal transport barriers (ITBs) with a quiescent, edge localized mode (ELM)-free H-mode edge, termed QH-mode, giving rise to separate core and edge transport barriers. These double barriers have been maintained for {>}3.5 s (~25τE), demonstrating a long-pulse, quasi-steady-state capability. The combination of core ITBs and edge H-mode temperature pedestals results in high-performance plasmas; a βNH89 product of 7 has been maintained for 10τE, other peak (non-simultaneous) parameters include Ti⩽17 keV, βN⩽2.9% m T MA-1, H89⩽2.6, β⩽3.8%, τE⩽ 160 ms, and DD neutron rate Sn⩽5.5×1015 s-1. These results address a major issue with tokamak plasmas: how to sustain long-pulse, high-performance H-mode plasmas without ELMs, yet retaining the density and impurity control hitherto provided by ELMs. In these QDB plasmas ELMs are replaced by continuous benign MHD activity in the edge, which enhances particle transport. A signature of operation with a QH-mode edge appears to be very large radial electric fields in the edge and scrape-off layer (SOL). In the core, simulations and modelling replicate many of the features of the observed transport and fluctuation behaviour, including the ion temperature profile and turbulence correlation lengths. Slow high-Z impurity accumulation (τ⩾500 ms) is observed in the centre of many QDB plasmas, and is the subject of ongoing analysis. To date the QDB regime has only been obtained in plasmas with counter-NBI (injection anti-parallel to the plasma current), and with divertor cryopumping to control the density.

Quiescent double barrier regime in the DIII-D tokamak.

A new sustained high-performance regime, combining discrete edge and core transport barriers, has been discovered in the DIII-D tokamak. Edge localized modes (ELMs) are replaced by a steady oscillation that increases edge particle transport, thereby allowing particle control with no ELM-induced pulsed divertor heat load. The core barrier resembles those usually seen with a low (L) mode edge, without the degradation often associated with ELMs. The barriers are separated by a narrow region of high transport associated with a zero crossing in the E x B shearing rate.

MHD instabilities occurring near/at the transportbarrier

In configurations with transport barriers the improved edge andcore confinement leads to a large pressure gradient and largeedge bootstrap current density which often drivemagnetohydrodynamic (MHD) instabilities terminating thedischarge or reducing the discharge performance. The edge andthe core transport barriers deteriorate or are completely lost.In this paper, recent experimental and theoreticaldevelopments concerning MHD instabilities occurring near/at theedge and the core transport barriers are summarized emphasizingthe dominant instabilities and the comparison with theory.

Observation of simultaneous internal transport barriers in all fourtransport channels and correlation with turbulence behaviour in NCSdischarges on DIII-D

Very steep internal transport barriers (ITBs) have been observed in allfour transport channels on DIII-D. These ITBs are among the mosthighly localized (width⩽5 cm), simultaneous core transport barriersobserved on any machine to date, and have only been observed in dischargeswith a negative central magnetic shear (NCS discharges), at power levelsabove ~8 MW. Profile gradients and scale lengths at the location ofthe core (ρ~0.3-0.4) transport barriers are similar to thoseobserved at the plasma edge during H-mode, while profiles inside thetransport barriers are flat. The spatial location of the transport barrierscoincides in all four transport channels, although the temporal evolutionof the profiles is different; very steep gradients in the electron densityand temperature profiles form after such gradients are first observed inthe ion temperature and angular momentum profiles. Turbulence measurementsduring the evolution of the core particle transport barrier show nodecrease in low-wavenumber (0-6 cm-1) turbulence levels in theplasma centre, including within the steep gradient ITB region. Severalpossible interpretations for this observation are presented.

Comparative studies of core and edge transport barrier dynamics of DIII-D and TFTR tokamak plasmas

The plasma dynamics of enhanced confinement regimes in the TFTR core and the DIII-D core and edge are compared in order to identify a common physics basis. Despite differences in transition timescale and location, as well as the sign of the radial electric field Er, observations suggest that E × B shear effects on turbulence induced transport play a dominant role in governing barrier dynamics in all cases. Fast confinement bifurcations are observed in the TFTR core enhanced reverse shear (ERS) regime and in the edge DIII-D H mode. Both show spontaneous Er shear layer formation prior to the confinement change and a negative Er well that persists as steep gradients form. These dynamics differ from those of DIII-D negative central shear (NCS) plasmas. There, slow transitions are observed when the applied torque from unidirectional beam injection is small, while faster development and more dramatic confinement improvements occur at higher applied torques. Unlike the H mode and ERS cases, the NCS core generally has a positive Er hill and no strong Er shear precursor. However, similarity experiments performed on TFTR indicate that ERS, L mode and NCS-like regimes can all be accessed in a continuous fashion by varying the E × B shear through changes in the applied torque at constant power. As in the DIII-D NCS case, core confinement in TFTR reverse shear plasmas improves slowly as co-rotation begins to dominate the determination of Er, no strong Er shear layer develops prior to that improvement, and the plasma possesses a positive Er hill. Reductions in transport with Er gradients of either sign are consistent with the picture of E × B shear suppression and decorrelation of turbulence. At fixed input power, intermediate levels of confinement improvement are achieved by varying the E × B shear with changes in the applied neutral beam torque. The data suggest that control over the plasma pressure profile in a reactor may be possible if an external source of E × B shear, such as might be applied with RF techniques, is used to modify the shear which otherwise occurs.

Core reflectometer density profile measurements on DIII-D

Measurements of core (normalized flux coordinate ρ⩽0.3–0.4) electron density profiles have been obtained on the DIII-D tokamak via a reflectometer system operating in the ordinary polarization (O mode). This system was developed and implemented for two primary reasons: first, there is a pressing need for core density profile measurements on DIII-D in plasmas with core transport barriers and centrally peaked profiles, and second, the measurements reported here further extend the demonstrated range of conditions in which reflectometry can provide reliable density profile measurements. As a test of the ability of reflectometry to measure such core profiles an existing DIII-D broadband frequency swept (FMCW) reflectometer system was converted to use O-mode propagation. This test system covers 50–75 GHz, corresponding to densities of 3.1–7.0×1019 m−3. Using this system, core access has been investigated in medium density discharges. Results demonstrate that adequate signals, and hence, accurate profiles, can in fact be obtained to the plasma center in discharges with centrally peaked profiles.