The power balance ion heat flux in the pedestal region on DIII-D increases and becomes increasingly anomalous (above conventional neoclassical) in experiments with higher temperature and lower density pedestals where the ion collisionality () is lowered toward values expected on ITER. Direct measurements of the main-ion temperature are shown to be essential on DIII-D when calculating the ion heat flux due to differences between the temperature of D+ and the more commonly measured impurity ions approaching the separatrix. Neoclassical transport calculations from NEO and non-linear gyrokinetic calculations using CGYRO are consistent with these observations and show that while neoclassical transport plays an important role, the turbulent ion heat flux due to ion scale electrostatic turbulence is significant and can contribute similar or larger ion heat fluxes at lower collisionality. Beam emission spectroscopy and Doppler backscattering measurements in the steep gradient region of the H-mode pedestal reveal increased broadband, long-wavelength ion scale fluctuations for the low discharges at the radius where the non-linear CGYRO simulations were run. Taken together, increased fluctuations, power balance calculations, and gyrokinetic simulations show that the above neoclassical ion heat fluxes, including the increases at lower , are likely due to weakly suppressed ion scale electrostatic turbulence. These new results are based on world first inferred ion and electron heat fluxes in the pedestal region of deuterium plasmas using direct measurements of the deuterium temperature for power balance across ion collisionalities covering an order of magnitude from high values of 1.3 down to ITER relevant .
I. INTRODUCTION
High-performance plasmas on ITER are expected to require an H-mode pedestal1 with the increased plasma pressure at the pedestal top leading to improved core performance. Robust prediction and optimization of the pedestal for next-generation devices such as ITER require theories of plasma transport that have been experimentally validated using accurate measurements of the plasma profiles, turbulent fluctuations, and the experimentally inferred particle, energy, and momentum fluxes in the pedestal region. Cross-field thermal transport in the core has been extensively studied and is relatively well understood.2 Transport is typically dominated by ion temperature gradient (ITG) modes, and it is thought that the ExB shear suppression of these modes leads to the increased gradients seen in the H-mode pedestal.3 With the suppression of the dominant instability, the profile gradients increase until additional mechanisms (or the originally suppressed instability) transport the required fluxes through the pedestal region.
A variety of mechanisms may be responsible for transporting the fluxes through the pedestal and setting the respective gradients. These include drift wave turbulence: electron temperature gradient modes (ETG), micro-tearing modes (MTM), trapped electron modes (TEM), ion temperature gradient (ITG), MHD-like kinetic ballooning modes (KBM), and neoclassical collisional transport (see Ref. 4 and references therein for more detail). These mechanisms vary in the quantities that they dominantly transport, their underlying drive and saturation mechanisms, and their spatial and temporal structure. Accurately inferring the experimental particle, ion and electron energy, momentum and impurity fluxes, and the fluctuation details are keys to helping determine the dominant underlying instabilities causing the residual transport. It is possible to make significant progress by comparing relative transport in the particle, impurity, thermal, and momentum channels with those that are expected for a range of micro-instabilities.4,5
The EPED model6 is commonly used to predict the pedestal pressure width and height. Within this model, the pedestal structure is governed by a combination of peeling ballooning modes (PBM) and kinetic ballooning modes (KBM), which set the global and local stability limits, respectively. While this model has been successfully applied to a variety of devices, fluctuation measurements on multiple machines have shown that instabilities beside the KBM are likely active in the pedestal7 and estimates of the channel-dependent fluxes through the pedestal often do not appear to match what is expected for a KBM,4 suggesting that the local stability limit is determined by instabilities other than or in combination with the KBM. Additionally, EPED does not predict the fluxes (i.e., input power) required to produce a given pedestal or how the pressure is partitioned between the density and temperature. This will further affect the core because core turbulent transport will tend to hold the temperature gradient scale length close to the non-linear stability boundary. This presents a significant challenge for predictive modeling and indicates that a more detailed transport analysis of the pedestal would complement the EPED model.
In this work, main-ion charge exchange recombination spectroscopy (MICER)8,9 is used to provide direct measurements of the hydrogenic ion temperature. As described in the Appendix, these measurements are used to more accurately infer the ion heat flux and temperature gradient in the pedestal region compared with the impurity-based measurements, allowing for better tests of neoclassical and drift-wave turbulent transport models to improve understanding of the transport processes that govern the pedestal structure.
While the total heat flux is relatively well known based on the profile of the heating sources and sinks, separating the flux into ion (Pi) and electron (Pe) contributions is challenging due to the species-dependent coupling to the sources and sinks, and the collisional power exchange between species
where ions and electrons are represented by the subscripts i and e, and are the charge, mass, density, and temperature, respectively. Near the plasma edge, the collisional exchange term can become large due to the low Te, elevated density, and relatively large volume of the outer flux surfaces. This sensitivity acts to amplify any inaccuracies in , and the exchange term may dominate the ion heat flux calculations affecting the inferred Pi and Pe as well as any derived quantities such as the thermal diffusivities (χi, χe). Typically, charge exchange recombination spectroscopy (CER) measurements of an impurity ion are used as a proxy for the temperature of the main-ions (i.e., deuterium) required for this calculation; however, near the plasma edge, the temperature measurements of the ions have been shown to diverge with the impurity temperature typically being higher9 leading to a larger inferred collisional exchange, which in some cases drives the ion heat flux to physically suspicious negative values as described in the Appendix. These challenges are overcome in this work by using the direct main-ion temperature measurements from MICER.
A key parameter that modifies plasma transport is the ion collisionality (), a measure of the importance of collisions compared with orbits. It is defined as the ratio of the effective 90° scattering collision frequency compared to the trapped particle bounce frequency and is given by where , q, R, ϵ, and vth are the effective collision frequency (sum of collision frequencies with all species), safety factor, major radius, inverse aspect ratio, and thermal velocity, respectively. The collision frequency for species 1 with species 2 is given by
where is the Coulomb logarithm, and the reduced mass ratio and relevant thermal velocity are given by and .
Neoclassical ion thermal diffusivities are expected to decrease at lower collisionalities, while micro-instabilities such as trapped electron modes (TEMs) are expected to be less stable due to lower levels of de-trapping. Plasma transport at lower collisionalities is of particular interest because larger devices such as ITER are expected to operate at collisionalities around 0.01. In this paper, pedestal thermal transport is studied across an order of magnitude range of pedestal top , with the lower values approaching those expected on ITER. ranged from 0.1 to 1.3 when including collisions with electrons and deuterium, or 0.2 to 2.6 when including additional collisions with the impurity. While changing was the focus of the experiments, this was also associated with unavoidable changes in other parameters such as the temperature and density gradients, which also modify the plasma transport.
The steep gradients and proximity to the scrape-off layer create diagnostic and theoretical challenges for studying plasma transport in the pedestal. Historical issues such as physically suspicious negative ion heat fluxes have meant that pedestal ion thermal transport analysis on DIII-D has been quite limited.10,11 As will be described in this paper, these issues have largely been resolved using the MICER measurements. Detailed modeling of a low collisionality quiescent H (QH)-mode discharge was performed using the XGC0 code which showed that the thermal transport was approximately at the neoclassical level when “extended neoclassical effects” such as the interactions with edge neutrals and orbit loss are included.12–14 Significant work in this area has been performed on ASDEX Upgrade (AUG) using impurity temperature measurements in deuterium plasmas, showing that for a range of collisionalities, the ion thermal transport was at the neoclassical level across the pedestal region.15,16 An extensive study of JET-ILW (ITER Like Wall) pedestals used gyrokinetic simulations to improve understanding of the reasons behind the loss of historical confinement levels compared with JET-C (Carbon wall).5,17 This study showed the importance of ETG, MTM, and ITG instabilities in addition to neoclassical transport in the pedestal, and in particular, how modifications to the density profile and subsequently the ratio of the density and temperature gradient scale lengths (), which are likely caused by the increased gas puffing required to prevent core impurity contamination in ILW, may lead to significant ITG transport and the reduced temperature pedestals compared with JET-C.
This paper is organized as follows: Section II describes the experiments, and Sec. III covers the interpretive experimental thermal transport analysis. Comparisons with neoclassical and drift-wave turbulent modeling are described in Sec. IV, and Sec. V discusses measurements of ion scale pedestal fluctuations. Additionally, the Appendix describes differences in the impurity and main ion temperature measurements and the associated effects on the inferred heat fluxes.
II. OVERVIEW OF THE EXPERIMENT AND MEASUREMENTS
An experiment was performed on DIII-D where the pedestal top ion collisionality was varied by changing the input power and gas puffing, effectively modifying the heating and particle sources. While the pedestal top pressure remained within 20% between discharges, by trading off between density and temperature, the collisionality varied by more than an order of magnitude. The three discharges that are examined in detail in this paper will be referred to as the low (shot #179 444, ), medium (#179 447, 0.3), and high (#179 449, 1.3) collisionality cases. The ion collisionalities increase to 0.2, 0.5, and 2.6 when including collisions with in addition to electrons and D+. Other dimensionless parameters such as and β were not matched between these shots. The discharges had an ITER similar shape (ISS),18 toroidal magnetic field in the favorable ion-drift direction for the L-H power threshold, plasma current , edge safety factor , and between 1.6 for the high collisionality case and 2.5 for low collisionality. The medium and high collisionality cases had 2.8 MW of co-Ip neutral beam injection (NBI), while the low collisionality case had 3.3 MW of co-Ip NBI and an additional 1.6 MW of electron cyclotron heating (ECH) applied at (ρ is the square root of the normalized toroidal flux). Additional heating power was required to achieve the low collisionality pedestal top conditions. All cases had good confinement despite the variation in the pedestal structure, with βN between 1.6 and 1.8, and between 1.3 and 1.6. Time histories of some key parameters, including pedestal top electron parameters and the plasma equilibrium, are shown in Fig. 1 along with the analysis time window.
Dedicated main-ion (MICER)8,9,19–21 and impurity22 charge exchange recombination spectroscopy (CER) systems on DIII-D provided simultaneous profile measurements of the D+ and ion temperature, rotation, and density using D-I () and C-VI () emission, respectively. For the edge channels, the main-ion and impurity system fibers are interleaved in a fiber clamp (see Fig. 1 in Ref. 19) allowing profile comparisons between the ion species that are free from profile alignment uncertainties. The effects of cross-sectional distortions and spatial averaging due to halo emission on the MICER measurement were corrected by iteratively inverting a forward model of the measurement.9,21 The forward model is provided by the FIDASIM code,23–25 which implements a collisional radiative model of the processes that lead to the Doppler shifted and broadened emission. The electron temperature and density profile were measured using the Thomson scattering system26 with the electron density being normalized using density measurements from interferometry.27 Details about the differences in the D+ and temperature measurements and how it can affect the transport analysis are described in the Appendix.
Following the initial edge-localized mode (ELM) crash, there is typically a rapid 5–10 ms evolution of the profiles followed by a quasi-stationary period leading up to the next ELM crash.7 This work focuses on transport in the fully formed H-mode pedestal in the quasi-stationary period by filtering the profile data to be within the last 80%–95% of the ELM cycle over a 300-ms time window () marked in gray in Fig. 1. The ELM frequency was approximately 30, 20, and 70 Hz for the low, medium, and high cases. The profiles were fit using the OMFITprofiles module28 with the bulk of the analysis being performed within OMFIT.29 The quasi-stationary electron, and D+ temperature, and electron density edge profiles for the three cases are shown in Fig. 2. These show the expected increase in temperature and reduction in density for the low collisionality case. Nominal alignment between the CER and Thomson scattering profiles was achieved by shifting the Thomson scattering data to obtain a separatrix electron temperature of approximately 80 eV, which has previously been shown to be a good approximation.20 Over the course of this analysis, several different alignments and profile fits were used with the impact on the power balance calculations reflected in the error bars shown in Fig. 3.
III. TRANSPORT ANALYSIS
Given the evolution of the density (n) and temperature profiles (T) and relevant sources/sinks (), the experimentally inferred particle () and heat fluxes [] for a species are determined using the particle and energy conservation equations
Here, V is the flow velocity and the heat flux can be split into conducted (q) and convected components [].
The important heat sources and sinks for the main ions include NBI heating, atomic physics effects such as charge exchange with edge neutrals and the ion–electron power exchange term: . For the electrons, the important sources and sinks of heat include Ohmic, ECRH, and NBI heating, radiative power loss, atomic physics effects such as ionization, and the same ion–electron collisional power exchange term (with opposite sign) .
The heat flow carried by the ions (i) or electrons (e) across a given flux surface (ρ) when the plasma is approximately stationary ( = 0), as is often the case near the end of the ELM cycle, is given by the volume integral from the magnetic axis to ρ of the sum of the contributions from the relevant sources and sinks (j): . These power flows can also be converted into fluxes .
To perform the experimentally based power balance calculation, TRANSP30 is run from OMFIT29 via the TRANSP module,31 providing Pi and Pe using the quasi-stationary plasma profiles at the end of the ELM cycle (as described in Sec. II). A single ion temperature input is used which is based on the MICER measurements. Therefore, in the power balance, the temperature is assumed to be the same as the D+ and the collisional exchange between D+ and electrons, and and electrons are included.
Before showing the results of power balance analysis for the collisionality scan (Sec. III B), a description of difficulties with the ion–electron collisional exchange term and importance of direct main-ion measurements near the plasma edge are discussed.
A. Sensitivity of the ion–electron exchange to ion species-dependent temperature
Experimental measurements of the channel-dependent heat fluxes are important for identifying the underlying collisional and micro-turbulence processes, which are active in the pedestal. For example, MTM and ETG modes are expected to dominantly transport electron heat flux. In addition, the ion heat flux has been identified as possibly playing an important role in the L-H transition,32 and is important for understanding how the power flows into the scrape-off layer, and ultimately onto plasma-facing surfaces. The ion–electron collisional energy exchange term, which depends on the temperature difference between species, plays a crucial role when calculating the channel-dependent heat fluxes, but is unimportant for the total heat flux.
As has been described earlier, due to the low electron temperature and larger volume near the separatrix, the collisional exchange term and resulting heat fluxes become increasingly sensitive to the accuracy of the temperature profiles. This sensitivity means that in some cases, the differences between the impurity and main-ion temperatures described in the Appendix can lead to large errors in the inferred ion and electron heat fluxes, as well as derived quantities such as diffusivities, when assuming the main-ion temperature is the same as the impurity measurement.
On DIII-D, measurements of the impurity ion temperature are typically larger than those of the main ions approaching the separatrix. For power balance calculations, this can lead to a significant overestimate of the ion–electron energy exchange (Pie) when using the impurity measurements, and a subsequent underestimate (overestimate) of the ion (electron) heat fluxes in the pedestal region. An example of a particularly concerning case is shown in Fig. 10(b), where the power balance calculation using the impurity ion measurement leads to a very large Pie in the pedestal region, and physically suspicious negative ion heat fluxes and large electron heat fluxes through the whole pedestal region. Performing the same power balance calculation using the new direct main-ion measurements of the D+ temperature [Fig. 10(c)] results in more reasonable ion and electron heat fluxes, which are both positive, and have similar values.
Issues such as these have hindered significant channel-dependent energy transport analysis in the pedestal region on DIII-D. As described in the Appendix, there are several reasons to suspect the impurity temperature to be a poor proxy for main-ion temperature near the plasma edge, and the main-ion temperature measurements should be used for power balance wherever available.
B. Experimentally inferred ion and electron heat fluxes
The ion, electron, and ion–electron collision exchange power flows from the interpretive TRANSP analysis of the collisionality scan shots using the main-ion measurements are shown in Fig. 3. As expected, both the ion and electron heat fluxes increase near the edge when moving to lower collisionality due to the increased input powers that were required to achieve the lower collisionality conditions (see Fig. 1). The sudden rise in the electron heat flux around for #179 444 is due to localized ECRH inside the top of the pedestal. For all three cases, the radiated power was approximately 0.5 MW at the plasma edge, and the charge exchange losses were negligible, although this term remains uncertain due to the lack of measurements of the edge neutral density. The sensitivity of this term on the neutral density is discussed later in this section.
The errorbars shown in Fig. 3 are based on several TRANSP simulations, which were run over the course of this work, each with different profile fits, and small modifications to the alignments between the electron (from Thomson scattering) and ion profiles (from MICER). Due to stronger collisional coupling between the ions and electrons, the high collisionality case is the most sensitive to profile alignment. The higher level of ion heat flux for the low collisionality case is a robust result from this analysis.
Sometimes the ion heat flux is split into conducted and convected components, which allow a heat diffusivity (χi) to be calculated and compared with analytic theory. If this is done, a high level of confidence in the inferred particle flux is required to avoid folding more uncertainty into the analysis. Due to the minimal diagnostic information available to constrain the particle sources, the particle flux remains one of the least well-constrained quantities in interpretive transport analysis. Because of this, and because the outputs of most turbulence simulations and transport models are the fluxes, in Sec. IV, we directly compare the ion heat fluxes with theoretical predictions instead of calculating the diffusivities. For completeness, the fraction of the ion heat flux that is conducted based on the TRANSP calculations is shown in Fig. 4, indicating that the heat flux is expected to be dominated by conduction. In Ref. 10, the conducted heat flux was also found to be dominant based on significant modeling efforts of the particle sources using UEDGE and SOLPS.
The edge neutral density affects both the inferred particle flux (via the particle source) and the edge ion heat flux through charge exchange losses. The edge neutral density can be modified in TRANSP by specifying the particle confinement time (τp). By decreasing this value, the density of the neutrals at the edge of the plasma increases along with charge exchange energy losses. The ion heat flux obtained using the approximately expected particle confinement time relative to the energy confinement time along with a significantly larger (1000 ms) and lower values (50, 100 ms), bounding the region of what can be reasonably expected, are shown for the low collisionality case in Fig. 5. Increasing the neutral density by a large amount (decreasing the particle confinement time by a factor of 3) leads to a modest 25% reduction in the ion heat flux. References 10 and 33 contain significantly more detailed modeling of the edge neutral density on DIII-D.
IV. COMPARISONS WITH NEOCLASSICAL AND DRIFT WAVE TURBULENT TRANSPORT
Modeling of the heat flux in the pedestal region is accomplished using the NEO34 and CGYRO codes,35,36 which calculate the neoclassical collisional transport and drift-wave-driven turbulent transport, respectively. In both cases, the same kinetic EFIT used in the TRANSP simulations is used providing general (realistic) geometry, and the experimentally inferred ExB flow shear is included. NEO34 is used to calculate the levels of ion and electron heat flux due to neoclassical collisional transport: transport due to Coulomb collisions between particles undergoing drift-orbit motion in toroidal magnetic field geometry. NEO is a Eulerian code that solves the drift-kinetic equation in a multi-ion species plasma. For modeling in the pedestal region, NEO was run with relatively high resolution: 6 energy polynomials, 27 points in the poloidal direction, and 17 polynomials in the cosine of the velocity pitch angle. Several tests using higher resolution showed that these settings were sufficient. Additionally, because of the small toroidal rotation in this region, the low rotation limit was used. Due to the computational efficiency of the code, simulations were run throughout the pedestal region. Neoclassical transport typically plays a minor role in the core, being at least an order of magnitude smaller than turbulent transport. At the plasma edge, ExB shear stabilization of turbulent transport is thought to play an important role in the L-H transition and formation of the steeper H-mode edge gradients. Consequently, neoclassical transport is expected to play a much more dominant role in H-mode edge confinement.
CGYRO is used to predict the non-linear turbulence and associated fluxes by solving the electromagnetic gyrokinetic Maxwell equations using the low- drift ordering. It uses field aligned coordinates, which are spectral in the perpendicular direction and pseudospectral in the velocity space variables.35,36 The Sugama collision operator was used in these simulations,37 and three species were included in the simulations: D+, electrons, and . The input radial electric field is based on the measurements from impurity CER including the poloidal rotation measurement. A table of several important inputs is shown in Table I. In addition to the changes in collisionality, there are several other parameter changes, which are expected to significantly modify the turbulent transport. The ion-scale non-linear CGYRO simulations use poloidal grid points, nr = 160 radial modes, toroidal modes, and binormal resolution of . These results were also verified at resolutions of and 0.1, and nr up to 256. In the velocity space, the simulations use a 192-point grid (eight energies and 24 pitch angles). Electron-scale simulations use poloidal grid points, nr = 192 radial modes, n = 48 toroidal modes, and binormal resolution .
Pulse . | q . | . | . | . | . | Te/Ti . | . | . | . | . |
---|---|---|---|---|---|---|---|---|---|---|
179 444 | 5.7 | 2.7 | 31 | 22.5 | 24 | 1.55 | 0.15 | 5.2 × 10−3 | 1.24 | 21 |
179 449 | 4.8 | 4.5 | 8.3 | 18.8 | 11.5 | 1.0 | 1.2 | 3.4 × 10−3 | 0.7 | 12 |
Pulse . | q . | . | . | . | . | Te/Ti . | . | . | . | . |
---|---|---|---|---|---|---|---|---|---|---|
179 444 | 5.7 | 2.7 | 31 | 22.5 | 24 | 1.55 | 0.15 | 5.2 × 10−3 | 1.24 | 21 |
179 449 | 4.8 | 4.5 | 8.3 | 18.8 | 11.5 | 1.0 | 1.2 | 3.4 × 10−3 | 0.7 | 12 |
As with Ref. 38, a separation of scales has been assumed for the modeling in this paper. This allows the gyrokinetic turbulence, drift kinetic neoclassical equations as well as the transport and MHD equilibrium equations to be described self-consistently and independently within a low- drift ordered framework. While this assumption may be questionable in the pedestal due to the strong variation in equilibrium quantities over several gyroradii, it has the advantage of providing a rigorous, well-defined, self-consistent formalism.37 The consequences of scale overlap on both turbulent and collisional transport require either inconsistent ad hoc approaches or the development of challenging “full-f” treatments containing the MHD equilibrium, drift kinetics, and full EM gyrokinetics along with evolution over transport timescales. The radial correlation length from the non-linear CGYRO simulations is approximately 25% of the pedestal width, so the CGYRO calculations represent the local mid-pedestal turbulent transport.
Turbulent transport levels are calculated with separate non-linear ion(i)-scale and electron(e)-scale gyrokinetic simulations. Due to the computational expense, these simulations have only been run for the high and low collisionality cases and were run at a single radius in the steep gradient region (). More comprehensive simulations across a range of radii throughout the pedestal will be the subject of future work.
Detailed comparisons between the simulated and experimental levels of both the total and ion/electron channel resolved heat fluxes are shown in Fig. 6 along with the wavenumber distribution of the ion heat fluxes from the ion-scale simulations. The simulated fluxes are split into neoclassical and turbulent components, with the turbulent fluxes further split into electrostatic (ES) electron-scale, electro-magnetic (EM) ion-scale, and electrostatic ion-scale contributions. The error bar on the top of the simulated fluxes indicates the variation in the ion-scale simulated fluxes due to modifying the input gradient scale lengths by . The errorbars on the experimental data include contributions from profile alignment shown in Fig. 3 (for Pi, Pe) uncertainty in charge exchange losses (for Pi, Ptot) such as those shown in Fig. 5 and 7.5% uncertainty based on the NBI () and ECH () powers to account for the complexities involved in calculating the absorbed powers.39
For both cases, the simulated total heat flux is close to the experimental values given the measurement and modeling challenges of the pedestal region. The simulated total heat flux is mainly due to ion-scale ES turbulence (i.e., ITG/TEM) and neoclassical transport with a small contribution from electron-scale ES (i.e., ETG) and negligible EM (i.e., MTM) contributions. The large increase in heat flux moving to the lower collisionality discharge is captured, with the increase in the simulations being dominantly due to an increased ion-scale ES turbulence, whose fraction of the simulated heat flux increases from to . Furthermore, sensitivity scans of the non-linear CGYRO fluxes show that the turbulent transport in mid-pedestal () is partially suppressed by the ExB shearing. Reducing γE from the experimental value by 40% results in a factor of 2 increases in the fluxes for the low collisionality pedestal, and by a factor of 2.5 for the high collisionality pedestal.
Results of the comparisons with channel-dependent heat fluxes, which are subject to larger experimental uncertainty, are also relatively good with Pe being well captured for both the low and higher collisionality case. For both discharges, the simulated electron heat flux is dominated by ion-scale ES turbulence with small contributions from electron-scale ES turbulence and negligible contributions from EM ion-scale turbulence. The contribution from neoclassical transport is also negligible as typically expected for the electron channel.
The ion heat flux is dominated by a mix of neoclassical and ion-scale ES turbulence, with the contribution from ion-scale ES turbulence increasing by a factor of four from the low collisionality to the high collisionality case. The ion heat flux increase moving to lower collisionality is captured and is due to a large increase in the ion-scale ES turbulence contribution in the simulations. However, in both cases, the simulated values are approximately 60% of the nominal experimental values. These results showing the importance of ion-scale ES turbulence for both the ion and electron heat fluxes are similar to simulations for JET discharges,5,17 which found that ITG can account for 17%–47% of the inter ELM heat transport, although in that work the comparisons to experiment were limited to the total heat flux. A difference compared with Refs. 5 and 17 is that the EM ion-scale contributions are negligible suggesting that MTM, which dominantly transports electron heat flux, does not play a significant role in the heat flux transport in these simulations.
Scans of the MHD ballooning parameter α have been performed using linear CGYRO to estimate the possible role of electromagnetic modes such as KBM. The modeling shows that for the high collisionality discharge, increasing the α parameter from the experimental value by changes the dominant instability (based on highest growth rate) from TEM to KBM. This proximity suggests that the pressure gradient for this pedestal may be constrained by KBM. As previously described, the transport calculated by the non-linear CGYRO shows that at this marginal KBM stability threshold the electrostatic ion-scale instabilities together with the neoclassical transport still account for a significant portion of the transported fluxes. For the low collisionality shot, the KBM limit is reached when the α parameter is increased by 40%, implying that for this case, the pressure is constrained by ion-scale ES turbulence well below the KBM threshold.
A recent study of electron-scale turbulent pedestal transport on DIII-D,38 which analyzed a discharge with comparable levels of dominantly NBI heating, found similar levels of simulated heat fluxes as the work presented here. In that study, the electron-scale ES electron heat flux (ETG) was MW at the experimental parameters, which is in close agreement with the values obtained here. The ETG instability was also found to be close to marginality and gave predictions between 0.2 and 1 MW with profile variations within the experimental uncertainties. Additionally, the level of neoclassical heat flux was MW, which is also close to the values obtained for these discharges.
A. Detailed comparisons with neoclassical ion thermal transport
As was seen in Fig. 6, at a single location in the steep gradient region, the ion heat flux is above the neoclassical level, particularly at lower collisionality. To further investigate the extent to which the ion heat flux across the whole pedestal on DIII-D is at the neoclassical level and the importance of other processes, NEO simulations were run at several radii and compared with the inferred ion heat flux from the measurements [Fig. 7(a)]. The errorbands on the experimental power balance data include contributions from profile alignment shown in Fig. 3, uncertainty in charge exchange losses shown in Fig. 5, which increase toward the edge, and 7.5% uncertainty based on the NBI power.
As expected, due to high levels of turbulent transport, the ion heat flux inside the pedestal top is significantly larger than the neoclassical level. In the pedestal region for the high and medium collisionality cases, the peak neoclassical ion heat flux is within a factor of 2 of the measured values; however, as collisionality decreases, the inferred heat flux increases significantly while the prediction remains fairly static. This is due to the reduction in the strength of the neoclassical transport (i.e., reduced effective χi) at lower being compensated by the increased temperature gradient to give similar heat fluxes (). Another way of looking at the mismatch between the fluxes is that the pedestal top experimental ion temperature is not as large as it would be if all ion thermal transport was neoclassical in the pedestal region because the ion temperature gradients are not as steep as would be expected for neoclassical transport. This suggests that while the neoclassical ion heat flux plays a significant role in these DIII-D pedestals, it is not solely responsible for the ion heat flux transport.
These results differ from several results on AUG, which have shown the ion heat flux approximately at the neoclassical level across the pedestal for a range of collisionalities.15,16 These larger than neoclassical ion heat fluxes on DIII-D are important to consider when trying to determine the dominant instabilities based on their “fingerprints.”4
At the foot of the pedestal approaching the separatrix, there are additional processes/edge effects, which have not been considered here. For example, thermal ion orbit loss, and the interaction between neutrals and thermal ions with significant orbit widths can lead to higher levels of thermal transport from the ions.12,13 These effects can be considered as additional sinks, which would decrease the experimental level of heat flux or “extended neoclassical effects,” which would increase the neoclassical heat flux depending on how they are accounted for.
Additionally, the combined ion heat fluxes simulated by the trap gyro-Landau fluid (TGLF) model40,41 and NEO are shown in Fig. 7(b). TGLF calculates the fluxes based on the linear eigenmodes and quasi-linear weights, which are based on a database of non-linear GYRO simulations. Quasi-linear models provide a theory-based output with a numerical speedup of many orders of magnitude compared with non-linear gyrokinetic simulations, making predictive transport simulations tractable.42,43 The errorbars on the TGLF data are based on variation in key parameters (ExB shearing rate, and the inverse gradient scale lengths for temperature and density) and show approximately how stiff the turbulent transport is. The large error bars, which mostly cross the experimental data inside the pedestal top, indicate stiff ion thermal transport and that the predicted temperature gradients would be close to the experimental values. The large reduction in the heat fluxes in the pedestal region is a known challenge with the sat041,44 and sat144,45 models. Work to address this issue using a new saturation rule (sat2) based on a database of CGYRO runs (as opposed to GYRO) is currently in a testing phase. Once complete, this new model will allow for more accurate transport-based predictive pedestal profiles.
V. FLUCTUATION MEASUREMENTS
In addition to comparing the experimental fluxes with theoretical predictions, measuring the spatial and temporal details of fluctuations provides an additional approach to help identify turbulent modes, which play a role in particle, energy, and momentum transport.4,46 The turbulence measurement diagnostics used here include beam emission spectroscopy (BES),47–49 multi-channel Doppler backscattering (DBS),50 and the radial interferometer polarimeter (RIP).51 Reference 7 and references therein contain a detailed summary of the wide variety of fluctuations that have been measured in the pedestal across several machines. Additionally, a recent study on DIII-D of the inter ELM evolution of the profile gradients, and ion-scale fluctuation amplitudes from DBS found significant levels of ion-scale fluctuations.52 In particular, the study found low-k () fluctuations near the foot of the pedestal () increased substantially during the ELM crash and then saturate rapidly at approximately a third the peak amplitude. On the other hand, medium-k () fluctuations in the steep gradient region () decrease during the ELM event and then increase along with the pedestal gradients as they recover.
BES provides spatial and temporal measurements of density fluctuations including those associated with turbulence47–49 by using a high-throughput optical system and sensitive detectors for high time-resolution measurements of the variation of the Doppler-shifted Balmer-alpha emission from excited neutral beam injector atoms. BES is sensitive to long-wavelength ion-scale density fluctuations () in the radial–poloidal plane. The DBS system on DIII-D is capable of measuring a range of intermediate-k wavenumbers (),50 which is a scale often associated with trapped electron modes. The DBS return signal is dominated by wavenumber-matched Bragg backscattering from turbulent structures propagating parallel or antiparallel to the propagation direction near the cutoff layer. Finally, RIP51 is used to provide direct line integrated measurements of magnetic fluctuations within the plasma and is sensitive to ().
The cross-power spectra of from two BES channels at (same location in the pedestal where the CGYRO simulations were run) for the three collisionality cases are shown in Fig. 8. As the collisionality is reduced, the cross-power increases across a wide range of frequencies (e.g., 10–100 kHz) suggesting increased normalized ion-scale fluctuation amplitudes. These increased normalized fluctuations may also be associated with increased levels of ion heat flux for the low collisionality case shown in Fig. 3, although the level of heat flux will depend on the more complicated phase relation and coherency between fluctuating quantities as well as the wavenumber range of the fluctuating potential.
The radial profile of the DBS measurements of density fluctuations is shown in Fig. 9. For the low collisionality case, fluctuations are present throughout the pedestal region and near the top of the pedestal and steep gradient region, where the non-linear CGYRO simulations predicted significant levels of ion-scale electrostatic turbulence. The fluctuations for the lower collisionality case are significantly larger than those from the higher collisionality in this region; however, moving further out in radius toward the foot of the pedestal the density fluctuations for the medium and higher collisionality cases become comparable or larger at the outermost regions suggesting a possible change in the dominant transport mechanisms. For more in-depth analysis of DBS data and profile gradients throughout the ELM cycle, see Ref. 52.
Magnetic fluctuations with several properties associated with micro-tearing modes (MTM) have been observed previously in DIII-D plasmas using the RIP diagnostic51 and Mirnov probes.53 RIP measurements were also available for these shots and show broadband fluctuations in the 200–500 kHz range for all three cases. However, the amplitude of these magnetic fluctuations is very close to the noise floor and shows no obvious variation between the three cases, suggesting that for these cases, MTM may be present, but may not be dominant or significantly contribute toward the increased heat flux for the low collisionality case. This is consistent with observations in Ref. 51 where MTM-like fluctuations peaked at an intermediate and become much weaker at lower . These higher frequency modes are also seen in the BES data and are at a similar level for all three shots.
In summary, multiple turbulence diagnostics show the presence of ion scale fluctuations in the pedestal region for the three discharges studied here, and there is evidence that the fluctuation amplitudes in the steep gradient region increase for the lower collisionality case. While the level of heat flux depends on the phase relation between fluctuating quantities, these increased fluctuations are suggestive of increased transport and may be associated with larger than neoclassical ion heat fluxes, which were shown in Sec. IV.
VI. CONCLUSIONS
The ion and electron heat fluxes in the pedestal region of DIII-D have been inferred using direct measurements of the deuterium temperature across a range of collisionalities between low ITER relevant values of 0.1 and up to 1.3. Main-ion temperature measurements are essential when calculating the ion heat flux to reveal above neoclassical ion thermal transport due to differences between the temperature of D+ and the more commonly measured impurity ions approaching the separatrix. These new observations are consistent with low- drift ordered transport calculations from NEO and non-linear CGYRO that show, while neoclassical transport plays an important role, the turbulent ion heat flux due to ion-scale electrostatic turbulence can be significant and can contribute similar or larger levels of ion heat fluxes, particularly at lower collisionality.
Fluctuation measurements in the steep gradient region from beam emission spectroscopy and Doppler backscattering reveal broadband, long-wavelength ion-scale fluctuations for both the low and higher discharges. As decreases, the fluctuations increase at the radius where the non-linear CGYRO simulations also predict significant increases in the levels of ion-scale electrostatic turbulence-driven transport. Taken together, the power balance calculations, neoclassical and gyrokinetic simulations, and increased levels of fluctuations show that the ion heat flux in the DIII-D pedestal is above the neoclassical level and becomes increasingly so moving toward higher temperature pedestals with characteristics such as lower , largely due to weakly suppressed ion scale turbulence.
Looking toward ITER, pedestals are expected to have significantly larger pedestal top ion temperatures and mid-pedestal gradients, which will increase the drive for ITG type modes. The lower collisionality pedestal top conditions may also lead to reduced de-trapping stabilization for TEM type modes, and lower levels of neoclassical transport. When combined with the expected reduction in the levels of ExB shear turbulence suppression due to reduced rotation54 and small normalized gyroradius,55 this means that ion-scale electrostatic modes are likely to play an important role in ITER pedestals.
ACKNOWLEDGMENTS
The work was supported by the U.S. Department of Energy under DE-FC02–04ER54698, DE-AC02–09CH11466, DE-SC0019352, DE-FG02–08ER54999, DE-FG02–95ER54309, and DE-SC0019302. Part of the data analysis was performed using the OMFIT integrated modeling framework.29 The authors would like to thank Orso Meneghini and Sterling Smith for their support with OMFIT. This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.
AUTHOR DECLARATIONS
Conflict of Interest
The authors have no conflicts of interest to disclose.
DATA AVAILABILITY
The data that support the findings of this study are available from the corresponding author upon reasonable request.
APPENDIX: IMPURITY AND MAIN-ION TEMPERATURE DIFFERENCES
MICER and impurity CER can give different temperature profiles for D+ and as shown in Fig. 10 and described below. This can lead to significant differences in the inferred thermal transport. These differences are explored in more detail using temperature profiles in the pedestal region for the D+, , and electrons for a higher density DIII-D ITER baseline shot #164 988 (Fig. 10). These profiles are at a time following the L-H transition but before the first ELM and provide a good illustration of differences often seen between the impurity and main-ion temperature measurements approaching the separatrix. Note that this is not one of the shots from the collisionality scan described in the paper, but is shown because it provides a good illustration of the differences that can arise between ion species temperature measurements, and the effects that this can have on the ion heat flux calculations (described more in Sec. III A). Additionally, this extends previous discussions of this shot in Refs. 56 and 57.
An important term in the calculation of the experimental ion and electron heat fluxes is the collisional power exchange between the ions and electrons , which can become dominant in the pedestal region due to the lower electron temperature and larger volume. This makes Pie sensitive to the accuracy of . In the absence of direct main-ion measurements, as has historically been the case, the D+ temperature is often assumed to be the same as the impurity temperature. The justification for this is based on the rapid equilibration time between the impurities and main-ions. The thermal equilibration time between species α and a background species β is given by58
where m(g), T(eV), and Z are the mass, temperature, and charge state of the respective species, is the density, and is the Coulomb logarithm. Because of the dependence, the equilibration time between an impurity with appreciable Z such as and D+ is rapid. This evaluates to tens of microsecond approaching the DIII-D plasma edge, which is fast compared with the radial transport timescale (), leading to the expectation that the two species should have similar temperatures (as described in the Appendix of Ref. 59). However, as has been reported previously on DIII-D, direct measurements of the main-ion temperature have shown that near the edge, it is possible for the impurity and main-ion temperature measurements to diverge considerably. This can be seen clearly in Fig. 10(a) (compare blue and cyan curves). The differences can usually be split into an offset from the top of the pedestal inward, and divergence from the pedestal top outward where the impurity temperature is higher. As will be described, the difference from the pedestal top inward appears to be due to Zeeman and fine structure broadening causing the impurity temperature to appear larger than its true temperature, while the divergence further out is less well understood.
Splitting of spectral lines due to atomic fine structure and the Zeeman effect leads to additional broadening of the observed spectral emission, which can result in higher apparent temperatures than the underlying temperature of the species being measured.60 The effect on the measurement is significantly larger than for D+. For typical DIII-D parameters, the correction for the measurement is approximately 65 eV at the plasma edge and up to 150 eV in the core, while it is for D+ for typically accessible DIII-D parameters. To accurately calculate the correction, the l sub-level populations of the excited state are required; however, for typical high-temperature plasmas, a measurement of this information is not available. Consequently, the correction is often estimated by assuming the l sub-level states are statistically populated,60 which may not be true if the population mechanism is non-thermal as is the case for the active charge-exchange process. This uncertainty is part of the reason corrections for these effects have not historically been applied to the measurement on DIII-D. The direct D+ measurements provide one way to test the accuracy of the correction for the impurities because the correction is not significant for the D+ measurement. Applying the correction reduces the measurement and greatly improves the agreement between the D+ and from the pedestal top inward [compare blue and green curves in Fig. 10(a)], largely resolving discrepancies that were first noted for Fig. 5(b) of Ref. 57.
The differences in the ion species temperatures approaching the separatrix are not always consistent and are not fully understood. The signal-to-noise ratio for these outer radii can make the measurement challenging and time slice subtraction is often crucial. Some important Physics effects, which are being considered, include cooling of the D+ (but not ) via charge exchange with colder edge neutrals, the existence of multiple charge states for carbon—the electron temperature drops below the last ionization energy for carbon, which is 490 eV, and the possibility that the impurity measurement is being dominated by higher energy thermal particles from the pedestal top that have significant orbit widths and lower collision frequencies. Some of these possibilities will be explored in a more systematic study of the impurity and main-ion temperature measurements in future work. It is worth noting that in the core, temperatures of the impurities and ions can be expected to be different due to different coupling to the heating sources and slower equilibration times due to the higher temperatures.
One of the key advances of the MICER diagnostic on DIII-D has been direct measurements of the D+ temperature. Details of issues, such as negative ion heat fluxes, which can occur in the power balance calculation when using the impurity temperature profiles, are shown in Figs. 10(b) and 10(c) are discussed in Sec. III A and are repeated below for convenience.
On DIII-D, measurements of the impurity ion temperature are typically larger than those of the main-ions approaching the separatrix. For power balance calculations, this can lead to a significant overestimate of the ion–electron energy exchange (Pie) when using the impurity measurements, and a subsequent underestimate (overestimate) of the ion (electron) heat fluxes in the pedestal region. An example of a particularly concerning case is shown in Fig. 10(b), where the power balance calculation using the impurity ion measurement leads to a very large Pie in the pedestal region, and physically suspicious negative ion heat fluxes and large electron heat fluxes through the whole pedestal region. Performing the same power balance calculation using the new direct main-ion measurements of the D+ temperature [Fig. 10(c)] results in more reasonable ion and electron heat fluxes, which are both positive, and have similar values.