Elements of H-mode pedestal structure

This paper reviews current understanding of key physics elements that control the H-mode pedestal structure, which exists at the boundary of magnetically confined plasmas. The structure of interest is the width, height and gradient of temperature, density and pressure profiles in the pedestal. Emphasis is placed on understanding obtained from combined experimental, theoretical and simulation work and on results observed on multiple machines. Pedestal profiles are determined by the self-consistent interaction of sources, transport and magnetohydrodynamic limits. The heat source is primarily from heat deposited in the core and flowing to the pedestal. This source is computed from modeling of experimental data and is generally well understood. Neutrals at the periphery of the plasma provide the dominant particle source in current machines. This source has a complex spatial structure, is very difficult to measure and is poorly understood. For typical H-mode operation, the achievable pedestal pressure is limited by repetitive, transient magnetohydrodynamic instabilities. First principles models of peeling–ballooning modes are generally able to explain the observed limits. In some regimes, instability occurs below the predicted limits and these remain unexplained. Several mechanisms have been identified as plausible sources of heat transport. These include neoclassical processes for ion heat transport and several turbulent processes, driven by the steep pedestal gradients, as sources of electron and ion heat transport. Reduced models have successfully predicted the pedestal or density at the pedestal top. Firming up understanding of heat and particle transport remains a primary challenge for developing more complete predictive pedestal models.


Introduction
Very shortly after the discovery of the high confinement or Hmode regime in ASDEX [1], measurements showed the existence of a 'transport barrier' at the plasma edge [2]. Likewise, measurements on PDX showed much steeper gradients of edge electron temperature T e and density n e in H-mode than in low confinement or L-mode [3]. These results showed that the narrow region of the edge transport barrier enabled much of the increase in stored energy of the H-mode relative to the Lmode. This barrier was eventually called the 'H-mode pedestal' due to its shape and appearance of 'supporting' core profiles.
The importance of the H-mode pedestal for the achievement of fusion power burst onto the research scene after models, based on the gyrokinetic equation, provided good predictions of core transport. These models showed that the fusion performance of ITER was highly sensitive to the ion temperature at the top of the pedestal T ped i [4,5]. Some projections of T ped i for ITER were pessimistic and suggested difficulty for ITER to achieve its mission. These concerns launched an international effort in theory, experiment and simulation to develop predictive capability for the H-mode pedestal.
The purpose of this paper is to show that these efforts have succeeded in developing an understanding of many of the physics elements which contribute to pedestal structure. (As used here, 'pedestal structure' refers primarily to the width, height and gradients of density, temperature and pressure profiles.) This understanding has produced successful models for predicting limits to the pedestal pressure and for predicting pressure on the pedestal top. Moreover, models are showing improved capability to predict transport of energy in the pedestal.
As in any magnetic confinement system, the pedestal profiles are determined by sources, transport and magnetohydrodynamic (MHD) limits. Thus, the organization of the paper will be aligned with those topics.
First, though, section 2 describes basic characteristics of the H-mode pedestal, as observed on multiple machines. A knowledge of what the pedestal 'looks like' is important for formulating ideas for the underlying physics. Section 3 discusses how sources and sinks for the pedestal are determined and how they are used to evaluate transport coefficients. A consistent picture of transport is generally observed over multiple machines and forms a basis for evaluating some transport models. The pedestal transport is sufficiently low that the pedestal pressure typically increases until limited by brief and repetitive MHD instabilities, discussed in section 4. These limits are mostly well understood and provide a basis for predicting the maximum pedestal pressure expected for given operating conditions. Section 5 describes experimental and theoretical work to identify measured fluctuations in the pedestal. We also examine simulations of power transported by various turbulent mechanisms. Reduced pedestal models are discussed in section 6. These have provided predictions for pedestal pressure and pedestal density. We wrap up in section 7 which gives a summary of major results and suggestions for further research needed to develop predictive pedestal models.
Due to the necessity to limit scope of the paper, many important H-mode topics are not discussed. As noted in section 2, we specialize the discussion to discharges with a specific MHD instability, typically observed in H-mode operation. Thus, we ignore many other regimes, particular those which avoid or mitigate MHD activity. In addition, we will not discuss in any depth the physics of the radial electric field, rotation, non-linear evolution of MHD instabilities, poloidal asymmetries of profiles and other quantities, impurities, etc. Discussion of the transition from the L-mode to the H-mode is also outside the scope of this paper.

Characteristics of the H-mode pedestal
Careful measurements of characteristics of the H-mode pedestal are needed for us to develop an understanding of pedestal physics. What are these characteristics? They include the height and width of its profiles (including temperature, density, pressure, radial electric field E r and bootstrap current), the hard limits imposed on the achievable pedestal pressure by magnetohydrodynamic instabilities called edge localized modes (ELMs) and the temporal evolution of its profiles during recovery from an ELM event. These characterizations have often involved a back and forth between theory and experiment.
Theory has provided ideas for important measurements and experiment has provided the data needed for tests of theoretical ideas. This synergistic experiment-theory process has enabled progress in our understanding of pedestal physics, as documented in several reviews, including Hubbard [6], Fujita [7], Leonard [8], Maggi [9] and Urano [10]. Our current understanding of important pedestal characteristics is summarized in the following sub-sections.

Pedestal structure
Early research showed the existence of ELMs, observed in ASDEX as bursts on magnetic coils and in soft x-ray (SXR) signals [1] and observed in PDX as spikes in Deuterium Balmer alpha emission D α [3]. These bursts, indicating that plasma was leaving the confinement volume, were accompanied by reductions of temperature and density in outer portions of the plasma, providing early evidence for MHD limits imposed on the pedestal.
Research on many machines in the intervening years has provided a consistent picture that the pedestal is a narrow region, located just inside the separatrix, which contains very large gradients of temperature, density and pressure ( figure 1(a)). This region also contains a negative-going 'well' in the radial electric field E r ( figure 1(b)). This quantity reaches its minimum in the steep gradient of the pedestal and then rises to more positive values on either side of the minimum.
The E r well with its large gradients produces a large rotational shearing rate ω E×B , which is the leading candidate to enable the H-mode regime. An example of the Hahm-Burrell E × B shearing rate [11] is shown in figure 1(b). The underlying theoretical hypothesis is that this shear reduces or eliminates turbulence in the pedestal, thus reducing turbulent-driven transport and enabling the formation of the observed gradients. Substantial theoretical work supports this hypothesis, as proposed by Biglari et al [12] and reviewed by Terry [13]. In addition, a large body of experimental work shows a strong spatial and temporal correlation between the increase of gradients at the transition to H-mode, the formation of the E r well and the suppression of long wavelength turbulence, as reviewed in [14][15][16][17][18][19][20].
The large gradient in the pedestal pressure drives a large current density peak J in the pedestal due to the bootstrap effect [21]. Figures 1(a) and (c) show the co-existence of the large pressure gradient and current density due to this effect. Sufficiently large values of J can drive kink or peeling modes, which can lead to the onset of ELMs. As discussed in section 4, a more complete theory for the ELM threshold combines the physics of kink/peeling modes, driven by the pedestal current density, with ballooning modes, driven by the pedestal pressure gradient ∇P. The bootstrap current also strongly modifies the magnetic shear in the pedestal (figure 1(c)) and thus can affect the physics of instabilities which are sensitive to this shear.

Classification of ELMs.
However, we will now discuss the classification of ELMs in order to clarify some of the discussion. Discussion of the physics of ELMs is deferred to section 4.
ELMs are traditionally classified by how they were originally observed [22], not by their triggering mechanisms. Type I and Type III ELMs are the most typical ELMs and are observed in various plasma configurations and operating conditions. ELMs are usually distinguished by their response to heating. Type I ELM frequency increases with increasing heating power while Type III ELM frequency decreases. The pedestal pressure height and the plasma confinement are usually lower with Type III than Type I ELMs. Type IV ELMs are similar to Type III ELMs but are generally observed in low collisionality pedestals rather than in high collisionality pedestals, where Type III are observed [23].
Type II ELMs are very small and observed only in highly shaped (elongation, triangularity and close to double null (DN) configuration) plasmas. The 'grassy' ELMs observed in JT-60U have some similarities with Type II ELMs [24]. Finally, small Type V ELMs are observed in NSTX high performance high density discharges when the shape of a connected DN plasma (with Type I ELMs) is changed to a single null (SN) configuration [25].
Of course, there are exceptions to all statements here. For example, a period of ELMs or limit cycle oscillations of the pedestal is sometimes seen immediately after the L-H transition. There are also regimes, such as the enhanced D-alpha H-mode (EDA) [26] or quiescent H-mode [27] in which ELMs do not occur; rather, other instabilities provide transport in the pedestal to limit its evolution. For purposes of this paper, the emphasis is on the physics of the Type I ELMing H-mode regime. This regime is sometimes referred to as the 'ELMy H-mode'. We note that this regime may contain a mixture of ELM types in that 'small' ELMs sometimes occur between 'large' Type I ELMs and the classification of the small events is not always clear. We also note that the size of ELMs ('small' vs 'large') is usually obtained from the relative sizes of ELM spikes in D α signals. This method of inferring ELM size is convenient but not quantitative regarding losses of particles or energy from an ELM.
The rationale for studying the ELMy H-mode regime is that it is the most widely accessible and studied regime. Moreover, much of the understanding of the ELMy H-mode regime is expected to be of use for other H-mode regimes.

Temporal evolution of pedestal gradients
Turbulence, driven by gradients of temperature, density or pressure, is considered a primary candidate for driving transport in the pedestal [28]. Thus, many experiments have measured the behavior of these gradients during the evolution of the pedestal. Basic observations will be discussed here and potential linkages of gradients and pedestal fluctuations will be discussed in section 5. Te data (red crosses) in a DIII-D discharge. Pedestal height and width are obtained as fit parameters [29] and are shown by horizontal and vertical dashed lines, respectively. Reproduced courtesy of IAEA. Figure from [30]. Copyright (2009) IAEA.
After the L-H transition, the pedestal structure typically forms very rapidly and values of temperature, density and pressure on top of the pedestal increase for periods of a few milliseconds (ms) to hundreds of ms or more, depending on the control parameters such as heating power or fueling rate. For ELMing H-modes, this evolution is halted when the ELMing phase begins; each ELM rapidly reduces pedestal values after which the values recover. During the ELMing phase, the period between ELMs and the amplitude of ELMs is variable with fixed control parameters. In addition, variation of heating or fueling typically leads to variations of ELM frequency and amplitude.
For a specific measurement, evaluation of the pedestal height is often done by using a diagnostic chord that is close to but inboard of the steep gradient region. When multiple chords are available to resolve a pedestal profile, a common analysis technique is to fit the data with a tanh function [31] with a possible additional term [29] to accommodate transition of the pedestal to the core. This technique, illustrated in figure 2, generally works well to provide a good metric for pedestal height. A two-line fit, called a bilinear fit is also used to obtain the pedestal height [32]. With data of sufficient spatial resolution and signal strength, these techniques can also provide a metric for pedestal width as well as the pedestal gradient.
Pedestal diagnostics with high spatial and temporal resolution have provided a clear picture of the evolution of pedestal profiles within an ELM cycle. As a prelude to the following discussion, we note that statements about density, temperature or pressure profiles are generally based on measurements of the electrons. Many measurements of impurity ion temperature T i and density are also available. These measurements typically show similar trends to the electron measurements. The discussion also focuses on discharges for which the ELM period is sufficiently long that the pedestal evolution between ELMs can be measured.
A range of behaviors is observed with a good generalization being the following. Very early in the ELM cycle (i.e. after the end of the ELM), there is an initial very rapid rate of increase in gradients, lasting a few ms. This rapid rise is then followed by a slower rate of rise of gradients or even a saturation (i.e. steady state), lasting until the next ELM. A second generalization is that when measurements of both ∇T e and ∇n e are available, the ∇T e recovery is usually seen to last longer than that of ∇n e . We caution the reader that these generalizations should not be taken as absolutes; you might see data which shows variations from the trends noted here. Nevertheless, these trends are widely observed.
An example of the typical trends for gradient recovery after an ELM is shown in figure 3. This figure depicts gradient recovery, obtained with very high time resolution measurements in ASDEX Upgrade [33]. These data show that the magnitudes of ∇n e , ∇T i and the gradient of He 2+ impurities increase and then reach approximate saturation within 3-4 ms after an ELM crash. In contrast, ∇T e achieves saturation later in the recovery from the ELM. We expect that the evolution of gradients is controlled by sources, sinks and transport. Thus, the behavior of ∇T e suggests that the T e profile is controlled by different physics than the other profiles, a point to be examined later.

Temporal evolution of pedestal width
Models have been developed to examine the time-dependent pedestal structure under the assumption that E × B shear enables development of the pedestal [43][44][45]. These models predict that the pedestal has a 'spatio-temporal' character, meaning that width of the pedestal increases with time. Thus, examination of the temporal behavior of pedestal widths may provide deeper understanding into the physics of the pedestal.
A number of machines have measured expansion in the width of one or more profiles in the period between ELMs. These machines include DIII-D [36,46], MAST [47], NSTX [40], JET [41,48] and Alcator C-Mod [49]. These measurements were primarily of n wid e , T wid e and p wid e , the widths of the (e) Shunt current I div increases (decreases) with decrease (increase) of gradients after ELM crash. Vertical dotted line denotes onset of ELM (from I div ). Reproduced from [33]. © IOP Publishing Ltd. All rights reserved. electron density, temperature and pressure profiles; in NSTX, width of the total pressure profile P wid TOT was measured. A slight digression: we will use the terms 'ELM cycle' or 'inter-ELM cycle' to refer to the time between ELMs. Depending on the study, the definition for the start of the cycle may be either the onset or the end of the ELM instability. The exact definition does not affect our interest, which is the time sequence of different signals during recovery from an ELM. (Also, in studies of the ELM crash itself, 'ELM cycle' might mean the time from the onset to the end of the ELM instability). Figure 4 shows typical observations of barrier expansion as obtained from MAST [47]. These data, which show profiles in the early, middle and late parts of an inter-ELM cycle, show an increase in n wid e and p wid e throughout the ELM cycle. These increases occur with the maxima of ∇n e and ∇p e remaining approximately constant. Thus, with the widths expanding at constant gradient, the pedestal heights for n e and p e are also increasing in the cycle. In contrast, T wid e and ∇T e increase slightly from the early to middle parts of the ELM cycle and then remain about constant (figure 4(c)). This is more evidence for physics differences between the T e and n e profiles. Reproduced from [47]. © IOP Publishing Ltd. All rights reserved.
Having shown these data, we take another slight digression. In some pedestal studies, pedestal profiles, particularly of p e , have persisted with saturated gradients for some time before an ELM crash has occurred [35]. From these observations, it has been argued that there must be some physics, not contained in standard models for the ELM instability, which actually triggers the ELM. However, the MAST data in figure 4 (plus other data not shown here) demonstrate that due to barrier (width) expansion, it is possible for a profile to continue evolving during the ELM cycle even though its gradient has saturated. In a pedestal such as this, the MHD stability threshold for ELM onset is changing throughout the ELM cycle. Thus, pedestal height as well as gradients should be examined to determine if a pedestal reaches full saturation during an ELM cycle.
In contrast to barrier expansion, JET has reported a reduction of p wid e with gas puffing with both a graphite wall [48] and with the ITER-like wall (JET-ILW) [41]. The reported studies in JET-ILW have comprehensive data from scans of power, gas as well as current. The p wid e reduction was measured at high power and is associated with a clamping of T wid e part way through the ELM recovery cycle. These observations show that the inter-ELM evolution of the pedestal in JET-ILW does not follow a specific pattern but can vary in a complex way depending on plasma conditions. We note that the common observation of barrier expansion is qualitatively consistent with pedestal models which predict this evolution due to the physics of E × B shear suppression of turbulence. However, we are not aware of experimental studies which have also examined the evolution of the pedestal E r profile and fluctuations to examine these models more deeply. Nevertheless, the differences of width expansion between profiles may reflect different physics processes at work in the pedestal.

Dimensionless identity experiments
Dimensionless identity experiments are wind tunnel tests for tokamaks. The underlying concept for these studies is that plasma transport is controlled by a set of dimensionless parameters that reflect the underlying physics [50,51]. Thus, if we have a correct understanding of the physics, we should be able to project profiles in one machine to another machine by operating the two devices at the same appropriate dimensionless parameters. Such experiments are called 'dimensionless identity' or 'similarity' experiments. This technique enables comparisons of devices with different sizes, magnetic fields and plasma currents. Such experiments have proved valuable for obtaining insight into pedestal physics.
These experiments have been performed by matching plasma equilibrium shapes and adjusting heating and fueling to obtain the desired dimensionless parameters at the top of the pedestal. If this matching were obtained, then agreement between the machines of scaled pedestal profiles would have indicated that plasma physics was controlling profiles in both machines. Differences in profiles would have suggested that other physics, such as related to neutrals, might be operative.
The matched plasma parameters were ρ * , β, q and ν * . The normalized toroidal gyroradius ρ * ∼ T 1/2 /(aB T ) is the ratio of gyroradius to machine size where T is temperature, a is plasma minor radius and B T is toroidal magnetic field. The normalized plasma pressure β ∼ (nT)/B T 2 ) is the ratio of plasma stored energy to energy in the toroidal magnetic field where n is density. The safety factor q ∼ (aB T )/I p is typically evaluated at the 95% flux surface where I p is plasma current. The normalized collisionality ν * ∼ (anq)/T 2 is the ratio of the collision frequency to bounce frequency. Typically, the plasma parameters n and T were matched for the electrons without an attempt to make sure ions also exhibited dimensionless identity.
Experiments have been performed between Alcator C-Mod and DIII-D [52], DIII-D and JET [53][54][55] and JET and C-Mod [56]. In these studies, the results showed that when properly scaled pedestal top T e measurements were in agreement, the scaled pedestal T e profiles overlaid within reasonable error bars. The simplest interpretation of these results is that the pedestal profiles were governed by plasma physics and that other physics, such as atomic physics, was negligible. These results Comparison of averaged ne and Te pedestal profiles (top and bottom panels, respectively) versus normalized poloidal flux for C-Mod (red circles) and DIII-D (blue squares). DIII-D data are scaled by machine size. Reprinted from [52], with the permission of AIP Publishing. also indicated that for given dimensionless parameters, the T e width scaled with machine size.
In the experiment between C-Mod and DIII-D, pedestal profiles from single Thomson Scattering laser pulses showed some scatter, which was attributed to observed pedestal fluctuations. With several profiles averaged to smooth out these effects, the scaled n e and T e profiles overlapped within error bars. Scaling was done by adjusting the DIII-D to C-Mod parameters. The agreement, which is shown in figure 5, thus suggests that plasma physics alone controlled these profiles.
However, for the latter two experiments (DIII-D/JET and C-Mod/JET), differences were measured in the n e profiles. Figure 6 shows that the n e profile for JET was shifted outwards with respect to C-Mod. For both machines, Thomson scattering was used to measure both the T e and n e profiles. Thus, the observed shift cannot be ascribed to a systematic measurement issue and is a real effect. A possible explanation of these differences was that atomic physics due to neutral fueling was affecting the density profiles.
In a series of pedestal identity experiments performed between two large machines of similar size, JET and JT-60U, additional power was required in JT-60U in order to obtain proper scaled pedestal pressures in the two machines [57]. The relatively large toroidal field ripple of ∼1.2% in JT-60U was proposed as a possible explanation for the differences between the machines. This hypothesis was verified by experiments in which JT-60U used ferritic inserts to substantially reduce its toroidal field ripple [58].
Overall, the dimensionless experiments indicate that plasma physics plays a fundamental role in controlling pedestal structure. Nevertheless, there are other factors, such as fueling and toroidal asymmetries, which might also play a role.

Scaling of pedestal width
ITER needs a sufficiently high ion temperature on its pedestal in order to meet its mission (see section 4.2.1 in [59]). In order to obtain a prediction for the ITER T i , pedestal studies have had a focus on obtaining a scaling for the pedestal width. Why the width? Emphasis on the width builds on evidence that MHD theory (discussed in section 4) can be used to predict the pedestal pressure gradient. Therefore, given a predictive model for the pedestal pressure width, it would be possible to predict the pedestal pressure height [6,8,59,60]. With an assumption for the pedestal density, researchers could then predict the pedestal T i .
Theory has developed and experiment has evaluated a wide range of models for the pedestal width [6][7][8][9][10]. These models typically assume that the pedestal is formed in a region where E × B shear suppresses turbulence. A common condition for this suppression is that the E × B shearing rate is larger than the growth rate of the most unstable linear mode in the pedestal. Various models follow from a range of assumptions about the relevant turbulence and source of the E × B shear.
Models based on E × B shear suppression of long wavelength turbulence provide a special concern for ITER. These models predict that the width scales as a positive power of the normalized ion gyroradius ρ * . Since ITER will have a significantly smaller ρ * than existing machines [54], these models predict that ITER would have a smaller normalized pedestal width (∆/a) than current machines, leading to concerns that ITER would not have a sufficiently large T ped i . Much experimental and theoretical work has ultimately developed a width scaling which has shown wide success and predictive power. We do not have space or time to discuss all of the research that has been done. Rather, in the following discussion, we will focus primarily on studies of scaling with ρ ped θ , β ped θ and ρ * . The normalized poloidal beta β ped θ ∼ (nT)/(B ped θ ) 2 is the ratio of plasma pressure on the pedestal top to the energy evaluated for the pedestal top poloidal magnetic field B ped θ . The ion poloidal gyroradius at the pedestal top is the ion temperature evaluated on the pedestal top.
Prior to the discussion, some issues related to definitions will be clarified. One of these issues is the definition of 'pedestal width'. During early pedestal research, a single width was assumed to apply to many profiles of interest. However, improved measurements have shown that this assumption is incorrect. Rather, different widths between n e and T e profiles and larger widths for T i than for n e or T e are commonly observed. Thus, discussions of 'pedestal width' should define how the term is used.
Another issue follows from the fact that measurements of pedestal electron profiles are typically more readily available than measurements of ion profiles. Therefore, the pedestal width studies have often substituted electron parameters for ion parameters in quantities of interest, such as β ped θ , ρ ped θ or ρ * . We note that JT-60U had very good measurements of pedestal profiles of T i and its width and these data were used in many pedestal studies done on the machine [61].

DIII-D empirical scaling.
Scaling studies of pedestal width over a large data set on DIII-D by Osborne [62] provided early evidence for a scaling with β ped θ , the poloidal beta at the pedestal top. A statistical analysis showed that p wid e , used as measure of pedestal width ∆, was correlated only with T ped e , n ped e , I p (plasma current) and related quantities. Regression fits of the data showed that the scalings ∆ ∝ (β ped θ ) 0.5 and ∆ ∝ (ρ ped θ ) 0.6 had comparable statistical significance. The colinearity between ρ ped θ and poloidal beta β ped θ was broken with a divertor pumping experiment which showed that the scaling with β ped θ was clearly the best description of the data [62,63]. In later power and shape scans in DIII-D, the total pedestal pressure P wid TOT scaled with (β ped ϕ ) 0.5 , with β ped ϕ being the pedestal toroidal beta; scaling with β ped θ was not specifically examined [64].   [23]. For Type I ELMing discharges, p wid e also scaled approximately as (β ped θ ) 0.5 .

ASDEX Upgrade/DIII-D width scaling studies.
Coordinated power and fueling scans were performed in ASDEX Upgrade and DIII-D to study pedestal scaling [66]. For the DIII-D data, both T wid e and n wid e scaled approximately as (β ped θ ) 0.5 . For ASDEX Upgrade, a scaling of T wid e with (β ped θ ) 0.5 was potentially consistent with the data but could not be firmly stated. In short, the two machines showed similar trends for T wid e . The machines showed a clear contrast in the n wid e , which displayed no dependence on β ped θ in ASDEX Upgrade whereas n wid e ∝ (β ped θ ) 0.5 in DIII-D. These results support a picture previously noted: the pedestal T e and n e profiles show evidence of responding to different physics.

JET/DIII-D scan of gyroradius.
The JET/DIII-D dimensionless identity experiment, discussed in section 2.4, was also used to measure pedestal width scaling with the normalized gyroradius ρ * . This experiment combined data from both machines to vary ρ * by a factor of four [55]. Throughout the scans on both machines, the plasma shape, q 95 and the pedestal top values of β θ and normalized collisionality ν * were held constant. The pedestal matching was performed with the electron profiles, the ion ρ * was calculated with the assumption that T i = T e and T wid e was used as the metric for pedestal width. As shown in figure 8, T wid e /a was constant at 2.5% ± 0.5% over the factor of four range of ρ * . These results suggest that there is a little or no dependence of the pedestal width on ρ * .
In contrast to the T wid e scaling, n wid e in the JET/DIII-D experiment showed a weak positive variation with ρ * . In addition, the scaled electron density profiles from the two machines did not match at all points in the scan. Moreover, there was a systematic trend of the midpoint of the n e pedestal to move outwards relative to the midpoint of the T e pedestal as ρ * increased. A simple model for neutral fueling was able to capture some of these trends, but the observations could not be fully explained. These observations foreshadowed subsequent work on the 'density shift', discussed in section 2.6.

Width scalings in terms of pedestal beta poloidal.
Focus on width scalings in terms of β ped θ continued as Snyder proposed a scaling of ∆ = c(β ped θ ) 0.5 [67,68]. This scaling was based on a model for kinetic ballooning modes (KBM) limiting the pedestal pressure gradient. In this formulation, pedestal width is defined as ∆ = 0.5(n wid e + T wid e ) and is measured in terms of normalized poloidal magnetic flux ψ N . With c = 0.076 obtained from a fit to a DIII-D data set, this scaling provided a good fit to the experimental widths, which had a range of ∼2.5. The widths showed no significant dependencies on other parameters.
For a combined pedestal database from DIII-D, ASDEX Upgrade and JET, shown in figure 9, the data are consistent with ∆ = c(β ped θ ) 0.5 , where ∆ is the average of T wid e and n wid e . With ∆ expressed in terms of ψ N , the coefficient c is in the range 0.07-0.10 [55].
Pedestal width data (average of T wid e and n wid e ) from ELMing H-modes in C-Mod are consistent with a (β ped θ ) 0.5 scaling with the constant c in the range 0.083-0.095, depending on the type of binning performed in the analysis [69]. Analysis of this data set finds weak or no dependence of pedestal width on B T , ρ * , ν * , or elongation κ.
Some agreement with and some deviations from these results have been observed in spherical tokamaks. MAST data show that T wid e ∝ (β ped θ ) 0.5 [23]. However, in a fit of 0.5(n wid e + T wid e ) = c(β ped θ ) 0.5 , c = 0.13 and 0.19 for Type I ELMing connected DN and SN discharges, respectively. These numbers are significantly larger than the values of 0.07-0.10 observed in the conventional aspect ratio tokamaks, just discussed. Later analysis of a larger MAST data set obtained similar results [70] with c = 0.146 and 0.145 for Type I ELMing DN and SN discharges, respectively.
The newer analysis for MAST also shows that p wid e = c(β ped θ ) 0.5 provides a good fit to the data with c = 0.11 -0.12 [70], as demonstrated in figure 10. This result is obtained for both DN and SN diverted discharges. The MAST pedestal database also shows that p wid e ∼ 0.8 × (n wid e + T wid e )/2. Thus, both the older and newer results from MAST show that the assumption p wid e = (n wid e + T wid e )/2 has limitations. The measured pedestal width in the spherical torus NSTX scales as (β ped θ ) 1.05 [71], showing a much stronger dependence on β ped θ than the other measurements discussed here. In brief, pedestal width scaling with (β ped θ ) 0.5 generally provides a good description of the data in several tokamaks, particularly for pedestal width taken as T wid e or 0.5(n wid e + T wid e ). In contrast, the dependence of pedestal width on ρ * or ρ ped θ is weak at best. In section 6.1, we will discuss a theoretical model for the width scaling ∆ = c(β ped θ ) 0.5 , where c ∼ 0.1.

Density shift
Early experiments in JET with its ITER like wall (JET-ILW [73]) found a reduction of global confinement in an ITER baseline scenario, as compared to JET with a carbon wall (JET-C) [74,75]. The confinement reduction is correlated with high gas fueling, used in many JET discharges [76]. Similarly, gas fueling is correlated with reductions of confinement in ASDEX Upgrade [77]. Extensive studies in JET-ILW and ASDEX Upgrade show this confinement reduction correlates with a reduction of pedestal top pressure [76][77][78]. Extensive research has also linked the pedestal pressure reduction to an outward shift of the pedestal n e profile with respect to the pedestal T e profile [79,80]. This shift is accompanied by an increase of the ratio n sep e /n ped e , where n sep e is n e evaluated at the separatrix [72]. These changes in pedestal structure may be causing changes in pedestal stability and/or pedestal transport, which could result in reduced pedestal pressure. Here, our goal is to summarize observations with regard to the density shift. For detailed analysis of physics mechanisms for reduction of pedestal height, the interested reader is referred to work by Dunne et al [77], Stefanikova et al [81,82] and Frassinetti et al [72,80,83].
2.6.1. Relative shift with gas fueling. Main ion fueling with gas has caused the n e profile to shift outwards relative to the T e profile in several machines. These devices include ASDEX Upgrade [77], JET [72,[80][81][82][83], TCV [84] and DIII-D [55,85,86]. The measurement of this shift, called 'relative shift' [82], is defined as n pos Thomson scattering systems, simultaneously measuring T e and n e , are used to make these measurements. This procedure eliminates errors in alignment of the n e and T e profiles. Examples of profiles showing the relative shift due to gas fueling in JET are shown in figure 11 and discussed in the next paragraph. Profiles showing the shift can also be found for ASDEX Upgrade [77], TCV [84] and DIII-D [86]. Figure 11 demonstrates this effect for cases of low and high gas fueling in similar JET discharges. Increased gas lowers the pedestal T e profile (figure 11(a)). There is no corresponding shift in the location of maximum ∇T e (figure 11(d)). In contrast, increased gas causes an increase of the magnitude of n e (figure 11(b)) and an outward shift of the location of the maximum of ∇n e (figure 11(e)). Increased gas leads to lowering of pedestal top p e (figure 11(c)) but little change in the location of maximum ∇p e (figure 11(f)).

Relative shift with heating power.
Heating power is a parameter that can affect the relative shift, as seen for example in JET [81][82][83] and DIII-D [85]. Figure 12 shows an example from JET. The relative shift is plotted against power crossing the separatrix (P sep ) for three levels of fueling (low, medium, high), as denoted by three colors. The relative shift increases with increasing P sep for all levels of fueling. In addition, for a given P sep , the relative shift increases from the lowest gas level to the two higher levels. These results show that the relative shift depends on both power and fueling level. (The observation of little change in relative shift for the two high gas levels is discussed further in [81]).
2.6.3. Effect of divertor configuration on relative shift. Divertor configuration can have an effect on the relative shift. For example, gas scans at two levels of power were performed for two divertor configurations in DIII-D. One configuration had low closure and the other, high closure [85], where closure is the ability of a divertor to confine neutrals to the divertor region. Better confinement of neutrals in the divertor is obtained with increased closure.
For the more open divertor, the shift parameter remained small throughout the scans of both power and fueling level. In contrast, the relative shift increased with both fueling level and heating power for the more closed divertor with better trapping of neutrals. Analysis with OEDGE shows that more ionization occurred in the SOL for the closed divertor and more ionization occurred inside the separatrix for the open divertor case [87]. These two trends may have contributed to an outward shift of the n e profile with increased divertor closure.
This supposition is consistent with results from another DIII-D experiment in which a gas scan to high levels of fueling was performed at high power in DIII-D. A systematic outwards shift of the n e profile with increased fueling was not observed [88]. Rather, the peak of ∇n e generally shifted slightly inwards from the reference case with no fueling [88]. The reader may be asking if the divertor had an open or closed configuration. These discharges used the open divertor configuration [89] discussed in the previous paragraph. This was the configuration for which little density shift was observed.
In JET, changes of divertor configuration also have effects on the pedestal density [83]. For a given fueling level, discharges with the outer strike point (OSP) on a horizontal target have higher values of n ped e than discharges with the OSP in the corner of the divertor chamber (figure 10(b) of [83]). A possible explanation for this effect is that the corner configuration has better pumping efficiency than the horizontal configuration, and more fueling is necessary to reach a given n ped e with the corner than with the horizontal configuration [83]. It is not clear if this effect is the same as that observed in DIII-D. Nevertheless, divertor configuration has effects on the n e pedestal for both devices.

Effect of impurity radiation on relative shift.
Impurity radiation has been used to decrease the relative shift in ASDEX Upgrade [77]. For sufficiently high heating power and gas fueling, a localized region of high density, called the highfield-side high-density front (HFSHD), forms in the scrape-off layer (SOL) on the high field side of the plasma. Associated with the HFSHD is an outward shift of n pos e relative to T pos e and an increase of n sep e . Radiation from seeded nitrogen reduces the power crossing the separatrix, thereby reducing the ionization that forms the HFSHD, which results in a reduction of the relative shift. In JET-ILW, the HFSHD has also been observed, but clear correlations of n pos e with the HFSHD have not been established [80].

Ratio of separatrix to pedestal density.
Systematic trends of the separatrix electron density n sep e and the density ratio n sep e /n ped e occur as the relative shift n pos e − T pos e changes. One of these trends is that n sep e increases as the relative shift increases (ASDEX Upgrade [77], JET [80,81]). A related trend is that the ratio of separatrix to pedestal density n sep e /n ped e increases as the relative shift increases (JET [72,82]). Figure 13 illustrates this behavior in a JET data set that has an order of magnitude range in fueling rate and a factor of three change in heating rate. The value of n sep e /n ped e increases as the relative shift increases.
When nitrogen seeding reduces the density of the HFSHD in ASDEX Upgrade, n sep e decreases and the n e profile shifts inwards [77]. In DIII-D, increase of n sep e /n ped e is correlated with increased n sep e for fueling scans in both closed and open divertor configurations [87]. For a given n ped e , n sep e is higher for the closed divertor configuration.

Modeling of fueling and density profile.
Modeling is being employed to understand the interaction of fueling and the pedestal density profile characteristics. This modeling strives to produce accurate treatments of 2D neutral fueling, which typically has large poloidal and radial variations in the pedestal. Such modeling is providing insights into issues such as the effect of divetor closure on the density pedestal shape and the role of fueling in the density shift.
Modeling with both OEDGE [85,87,91] and SOLPS [87,90,92] has been used to study the effect of divertor closure on fueling in DIII-D. These studies show that the more closed divertor confines neutrals better in the divertor region than does the more open divertor. As a consequence, discharges have higher fueling in the pedestal region with an open divertor than with a closed divertor.
SOLPS shows that for the same value of n sep e the fueling rate inside the separatrix between the X-point and the outer midplane is ≈four times lower for the closed than for the open configuration [90]. For a case of low n sep e , figure 14 shows that the poloidally averaged radial profiles of ionization rate for both deuterium and carbon are much lower for the closed divertor (USN) than the open divertor (LSN). With the lower ionization source in the pedestal, the discharge with the closed divertor would be expected to have a lower pedestal density than for the more open divertor. This result is observed in experiments which compare the density profiles of the two divertor configurations [85].
The JINTRAC [93] code suite, using EDGE2D-EIRENE [94][95][96] for the scrape-off layer transport and for the neutral transport, has modeled the effect of fueling rate on the pedestal density profile in JET [72]. The modeling was done by obtaining transport coefficients for pedestal temperature and density profiles plus a critical pressure gradient for ELM onset for a base case with low gas fueling. The modeling was then performed with these coefficients for a number of gas fueling rates.
This approach has matched the trends of n sep e /n ped e and n pos e to increase with fueling rate [72]. Figure 15 shows that the increase of fueling level leads to an increase in the ionization rate outside the separatrix with a corresponding decrease inside the separatrix, as modeled by JINTRAC. These changes in ionization profile are consistent with increased fueling causing an increase of n sep e and n sep e /n ped e . A continuing challenge for edge modeling, including the sophisticated analyses discussed here, is that physics-based models of particle transport in the pedestal do not exist. These transport coefficients are typically chosen in a way to give reasonable agreement with experiment. Thus, we consider the importance of modeling to be establishing possible qualitative trends in the experiments.

Effect of density shift on pedestal pressure.
How could the density shift lead to a reduction of pedestal pressure? We will not discuss this in detail but will briefly note some possibilities which are under study.
Reduced MHD stability due to the shift may be causing the reduced pedestal pressure. For ASDEX Upgrade, the predictive pedestal modeling showed that an inward shift of the density pedestal produced a higher pedestal pressure [77]. This result was due to the inward shift of the pedestal pressure profile causing improved MHD stability (against Type I ELMs) [97,98].
Reduced MHD stability may also be contributing to reduced pedestal pressure in JET-ILW as compared to JET-C discharges. Modeling shows that factors including the increased relative shift as well as change in Z eff and reduced global normalized beta β n act to reduce p ped e in some JET-ILW discharges [82]. Other factors may be important. For instance, modeling shows that increased p wid e acts to increase p ped e . However, the net effect of all factors causes a reduction of p ped e . Changes in the pedestal structure due to increasing separation between the temperature and density profiles (ions and electrons) may be leading to increased turbulence to drive electron and/or ion heat transport. Such processes might well cause a reduction of pedestal pressure. Theoretical simulations have shown that these processes are capable of driving large amounts of heat in JET-ILW discharges [72,100]. These mechanisms for transport will be discussed in more detail in section 5.

Summary
A large and international research effort during the last few decades has produced a picture a basic pedestal phenomenology. The pedestal is a narrow region of large gradients of temperature, density, pressure, radial electric field and current just inside the separatrix.
In typical operation, periodic MHD instabilities transiently destroy the pedestal and its gradients. The recovery of pedestal gradients from an ELM event typically show two phases with the first phase being a rapid increase of a few milliseconds duration followed by a period of more slowly increasing gradients, ultimately reaching near steady-state. During recovery from an ELM, the widths of some profiles, particularly for density and pressure, often increase with time.
Details of edge fueling can have significant effects on the pedestal profile. High gas fueling can shift the profile outwards relative to the temperature profile, increase n sep e and increase n sep e /n ped e . A pedestal width scaling which describes a large range of data is ∆ ∼ (β ped θ ) 1/2 , where ∆ is T wid e or 0.5(n wid e + T wid e ).
Scaling of width with ρ * is found to be weak at best. As an aside, we note that these scaling results have been established without specific consideration of the density shift. It is certainly plausible that large shifts might have an effect on the scaling as compared to smaller shifts.

Sources, sinks, transport
Sources of heat and particles provide the energy and fuel required to form the pedestal. A good experimental understanding of the sources and their sinks is required so that pedestal transport can be adequately characterized. This characterization is required for tests of theoretical models that make quantitative predictions of pedestal transport. In this section, we discuss current understanding of these sources and sinks and briefly review experimental understanding of transport in the pedestal.

Evaluation of pedestal sources, sinks and transport
3.1.1. Evaluation of heat source. Heat transported from the core is the primary heat source for the pedestal. Core transport codes are typically used to compute this source. Such codes use models to compute heating from ohmic dissipation, neutral beam injection and various forms of injected waves. These codes also compute sources or sinks for processes such as electron-ion collisions, radiation, charge exchange, ionization or recombination. Heat transported in the ion and electron channels is computed from the remaining heat after balancing all sources and sinks. Figure 16 shows a calculation of sources and sinks for power balance in a JET discharge [99]. Experimental profiles used as inputs for interpretive transport analysis by the TRANSP code [101] are displayed in figure 16(a). The resulting TRANSP power balances for ions and electrons are shown versus the normalized toroidal flux coordinate ρ tor in panels (b) and (c), respectively. Curves for heating (P heat,i , P heat,e ), equilibration (P ie , P ei ) and sinks (P CX , P rad , P 0,ion ) show radial integrals of heat gained or lost by a specific process inside each ρ tor value. The transport terms (P trans,i , P trans,e ), with each being the sum of conducted and convected power, show power flowing across a surface ρ tor . These latter terms provide the primary heat source for the pedestal.
Because the heat flowing into the pedestal depends upon processes occurring from the magnetic axis all the way to the pedestal, there is potential for errors in the modeled ion and electron heat flowing in the pedestal due to imperfections in the models or the data. A well known problem is that of plasmas with large ion-electron equilibration. In such a case, significant errors in the computed ratio of the electron to ion heat can occur even for small systematic errors in the data such as temperature measurements. Another systematic issue is that there are small but important uncertainties in mapping measurements of ion and electron profiles onto one another in the pedestal, due to uncertainties in the separatrix location with respect to measurements. , ne (solid green), n i (dashed green), T i (blue) and toroidal rotation at angular frequency (magenta); (b) Power balance for ions: P heat,i (red) is absorbed heating power, P ie (magenta) is equilibration power to electrons, P trans,i (blue) is transported power (from conduction and convection) and P CX (green) is sink due to charge exchange with neutrals; (c) Power balance for electrons: P heat,e (red) is absorbed heating power, P ei (magenta) is equilibration power to ions, Ptrans,e (blue) is transported power (from conduction and convection), P P rad (cyan) is sink from radiation (due to electron impact excitation) and P 0,ion (green) is sink from ionization of neutrals. Reproduced from [99]. © CCFE.
Problems such as those noted here can result in incorrect inferences about the importance of ion versus electron heat transport in the pedestal. We will discuss differences of T i in DIII-D as measured for impurity ions versus main ions in section 3.2.3. These differences produce different ratios of ion to electron heat transport in the pedestal.
3.1.2. Measurement of particle source. The particle source in the pedestal (ionization source) originates primarily from recycling edge neutrals. Neutral density and the ionization source are often inferred from spectroscopic measurements of hydrogenic emission lines. Recent measurements include 2D measurements of D α and D γ in the divertor of ASDEX Upgrade [103], 2D measurements of D α in the outer midplane of NSTX-U [104] and 1D measurements of L α of the inner and outer edge plasmas in DIII-D [105]. Such measurements can be used to compute neutral density or ionization rate if T e and n e data are available at the location of the measurements. In addition, neutral particle analyzers in ASDEX Upgrade provide direct measurements of neutral density [106].
These measurements are highly valuable and needed to help understand the particle source, which remains poorly understood. For these or any measurements related to ionization source to provide a global picture of fueling in a tokamak, they must be used in combination with appropriate modeling, such as discussed in the next section.

Coupled edge plasma-neutral codes for particle
source. At present, coupled 2D edge plasma transport and neutral transport codes provide the only approach to obtain the total pedestal particle source. For this approach, a 2D plasma transport code computes plasma density and temperature profiles in the SOL and in the pedestal. The neutral transport code launches neutrals into the SOL plasma and computes their transport in the plasma to obtain profiles of neutral density and ionization rate [107].
Such calculations use available experimental data to constrain the allowable solutions. These data might include temperature and density in the plasma, SOL as well as at divertor plates. Useful data might also come from measurements of D α or L α emission lines and/or of heat and particle fluxes at material surfaces. For several reasons, there are large uncertainties in current knowledge of the pedestal particle source: the source is coupled to complex and not fully understood SOL and divertor physics, the problem is 2D and possibly 3D, some important quantities are not measured over a large spatial domain or not measured at all, etc. When available, measurements of internal quantities related to the ionization rate, such as D α or L α emission lines, are highly valuable in constraining solutions of these modeling calculations.
Edge modeling typically shows that the ionization rate and neutral density profiles span from the SOL across the separatrix and have significant fall-off in the pedestal. In addition, there are parameters that have a strong poloidal variation, typically peaking in the divertor region. These features are demonstrated in figure 17 for an ASDEX-Upgrade discharge [102] for which EMC3-EIRENE [94,108] was used to compute the ionization rate in a 2D model. Bock et al [102] also used EMC3-EIRENE to perform 3D simulations in order to examine differences in the ionization source due to toroidal asymmetries caused by machine structures. This study showed that 3D structures produced effects on ionization rate and other parameters which were not localized to the structures; rather, the effects were global and had effects far from the 3D perturbations.
Machines with high field and or large size, operating at sufficiently high densities, are expected to have 'opaque' SOLs, meaning neutrals will be attenuated on the open field lines and not provide significant fueling in the pedestal. Such conditions have already been obtained in the C-Mod tokamak as shown by SOLPS modeling of high density discharges [109]. The simulations show that the neutral penetration depth into the pedestal is very small compared to the density pedestal width. In addition, rather than peaking in the divertor, the poloidal distribution of neutrals peaks near the midplane. These results indicate that neutral and ionization profiles in present day machines may be qualitatively very different than those expected in many future machines.
3.1.4. Reduced models for particle source. Core transport codes do not model the plasma past the separatrix and therefore use reduced models to obtain the particle source. These codes typically have a simple criterion for obtaining a neutral flux entering the plasma. A neutral transport model is then used to compute the resulting neutral density and ionization profiles that are consistent with the plasma inside the separatrix. Assessing the accuracy of these models is difficult. Due to the reduced physics of these models, we would expect them to be of lower accuracy than the coupled edge plasma-neutral models. Nevertheless, in some tests, the reduced models have provided ionization rates comparable to more complex models [110]. Due to their ease of use, reduced models are used in many transport studies of the pedestal.

Experimental pedestal transport coefficients
Our interest here is in evaluating transport in the pedestal during the inter-ELM phase, usually late in the period between ELMs. We will not study the effect of ELMs on heat or particle transport. The ELM transport mechanism is important, of course, but is smaller than inter-ELM transport for ELMing H-modes. For example, the fraction of heating power transported by ELMs is ∼20%-30% in JET, DIII-D, and ASDEX Upgrade Type-I ELMing discharges [118].
A number of studies, using primarily power balance analyses as described above, have evaluated one or more pedestal transport coefficients. The results of several such studies are summarized in table 1, which shows transport coefficients for electron thermal transport χ e , ion thermal transport χ i , perpendicular particle transport D ⊥ , various ratios of these coefficients as well as ratios of χ e and χ i to their neoclassical values, χ neo e and χ neo i , respectively. These studies include data from four tokamaks and a number of different approaches, including an analytic model, 1.5D transport models GTEDGE [119,120], ASTRA [121], ONETWO [122], the plasma-neutral edge models SOLPS [123], UEDGE [124], OEDGE [125] and the integrated modeling package JINTRAC [93]. The 1.5D codes contain reduced models for the ionization source as compared to the edge models. In contrast, the edge models typically obtain electron and ion power flows into the pedestal from a core transport code or else make assumptions of the power split, such as assuming a 50/50 split of the transported power between ions and electrons.

Experimental transport coefficients.
Experimental χ i and χ e profiles show minima in the steep gradient region of the pedestal. Figure 18 shows this behavior in χ i and χ e obtained for an ASDEX Upgrade discharge [116]. The minima in χ e and χ i occur near ρ pol ≈ 0.98 in this example.
The coefficients in table 1 are approximate minima in the pedestal (or at the separatrix for [111]). The values listed for D ⊥ have different meanings depending on the study. Various studies quote particle diffusion coefficients for electrons or ions and some are not specific as to species. The transport coefficients are quoted for profiles obtained during the inter-ELM phase, typically shortly before ELM onset.
The primary goal of table 1 is to provide an order of magnitude comparison of experimentally determined pedestal transport coefficients and some ratios using those coefficients. The uncertainties for the transport coefficients are potentially large, particularly for D ⊥ and are generally quoted to one significant figure. Error bars or other sensitivity analysis have been generated for the research of [91,113,115,116] and can be examined in those references.
The values of χ e and χ i are primarily between 0.1 and 1 m 2 s −1 and there are no major differences between the machines. These yield values of the ratio of ion to electron thermal diffusivities of order unity, with the exception of some large values for a few ASDEX Upgrade discharges. In these Table 1. Pedestal transport coefficients (m 2 s −1 ) and ratios of coefficients for several studies, shown by machines in column 1. Column 2 is name of code or code suite used to obtain transport coefficients. Models for χ neo i vary between studies.

Machine
Code  discharges, the evaluation of χ e was dependent on radiated power which had large uncertainties [115].
The values of D ⊥ are generally significantly less than the thermal diffusivities. This results in the ratio D ⊥ /χ e being less than unity with D ⊥ being ∼0.03-0.3 of χ e for the available data.
Some of these studies also computed values of the neoclassical ion thermal diffusivity χ neo i predicted by various models. The values of experimental χ i normalized to χ neo i are found to be close to unity for most of the comparisons from ASDEX Upgrade and slightly less than unity for a DIII-D data set. When χ neo i is available, an approximate value for the electron thermal diffusivity χ neo e is computed from (m e /m i ) 1/2 χ neo i [21]. With this assumption, the ratio χ e /χ neo e is computed and χ e is found to be 1-2 orders of magnitude larger than χ neo e for all cases. Figure 19, obtained in ASDEX Upgrade [115] provides a good pictorial summary of these general results. In a scan of ν * i from ∼0.4-1.5, the following transport ratios are obtained: and χ e /χ neo e ≫ 1. These types of ratios are 'transport fingerprints', which could provide clues to the nature of underlying turbulence that might be driving transport in the pedestal [28].

Code benchmarking.
Two of these studies performed benchmarking of codes. The ASDEX Upgrade study of [115] compared calculations of χ neo i between the codes NEOART [126], NEO [127] and NCLASS [128]. As shown in figure 19, the χ neo i values from NEO and NCLASS are very close with the NEOART values being about ∼15%-20% lower.
In the DIII-D study of [110], the codes GTEDGE, ONETWO, SOLPS and UEDGE computed transport coefficients from the same set of input data. The inferred minimum values agree to within about 30% for χ e and to within about a

Ion transport above neoclassical.
As the preceding discussion shows, a picture has developed that ion thermal transport in the pedestal is generally at levels predicted by neoclassical theory. However, recent analysis, based on measurements of main ion T i and n i , provides evidence that experimental ion heat fluxes can be above neoclassical in some conditions in DIII-D. The data are from a scan in which the pedestal ν * i was varied from 0.1 to 1.3. As shown in figure 21, the experimental ion power flux was near neoclassical levels at the highest ν * i but departed further (became higher) from neoclassical predictions as ν * i was decreased in a collisionality scan [129].
This finding is in contrast to previously reported values of χ i on DIII-D that have routinely been at or below neoclassical levels [110]. The new results follow from the main ion T i being systematically lower than the carbon impurity ion T i , which has been used in previous power balance analysis [129]. The   differences are small in the core but can be significant in the pedestal.
A correction for Zeeman and fine structure splitting of the carbon charge exchange line largely eliminates this difference [129]. The correction is small, but when integrated over the plasma cross section, the uncorrected carbon temperatures can produce substantially smaller pedestal ion heat fluxes than obtained from the main ion measurements, resulting in low values of χ i . It should be noted that the χ i values reported here from ASDEX Upgrade have been made with a correction for the Zeeman and fine structure effects on impurity ion measurements [130].

Diffusive vs non-diffusive transport.
The previous sections, which are based on analysis with interpretive, onedimensional transport codes, have discussed pedestal transport in a diffusive framework. Does that mean that all pedestal transport is diffusive? Definitely not! Thermal and particle diffusivities, as presented here, are convenient metrics for comparing transport between different regimes and machines.
This question is particularly relevant for the density pedestal. If the particle transport is purely diffusive, there are predictions for ITER [131] and expectations for other future machines that high density scrape-off layers will shut off neutral fueling in the pedestal and result in flat density pedestals. Such pedestals might have negative effects on the height of the H-mode pedestal. Such negative effects would be reduced if the particle transport in the pedestal has an inward convective component ('particle pinch'). As reviewed recently by Mordijck [88], the evidence for the presence of a particle pinch is mixed and conclusions in the literature are sensitively dependent on assumptions regarding the particle source. It is our opinion that questions about the existence of this pinch will not be settled until there are adequate measurements of the particle ionization profiles.
Evidence exists for outward non-diffusive transport in the plasma edge. There are measured bursting events which carry particles (and energy) in the form of 3D filaments across the separatrix into the SOL. Such events are important for transport in L-mode and may be important during inter-ELM periods in H-mode. Filaments will be discussed in slightly more detail in section 5.2.9.

Summary
Quantitative knowledge of heat and particle sources and of coefficients for thermal and particle transport are important constraints on theoretical models of pedestal transport. Direct measurements of the sources do not exist; thus, computational models are required to obtain these sources. There may be systematic uncertainties in the resulting sources, particularly for particles. Obtaining measurements of the pedestal particle source is a crucial need for advancing understanding of particle transport.
Transport models are used to obtain heat and particle transport coefficients. The primary purpose of this section has been to summarize transport coefficients from several devices and studies and to evaluate ratios of transport coefficients. These ratios are 'transport fingerprints' that can be used to help identify mechanisms for pedestal transport [28]. Most of the data examined here are roughly consistent with the following order of magnitude transport ratios: χ i /χ e ∼ 1, χ i /χ neo i ∼ 1 and χ e /χ neo e ≫ 1. For conditions where χ i is approximately neoclassical, (χ i − χ neo i ) ≪ χ e . These conclusions should not be taken as results that apply to all data. For example, recent studies on DIII-D with main ion measurements show that the ion transport is above neoclassical in some conditions. In addition, we will examine gyrokinetic modeling in section 5.8 which concludes that turbulence drives significant ion transport in some JET-ILW pedestals.
Finally, we note that the discussion has had a strong focus on metrics for diffusive transport, since these are easily obtained and provide a simple metric for a variety of comparisons. Nevertheless, non-diffusive transport processes, such as caused by intermittent filaments, may be important in the pedestal.

MHD stability
MHD instabilities, called ELMs, occur in the pedestal and provide hard limits on the achievable pedestal pressure profiles. Here, we will discuss some phenomenology of ELMs, a theory for the ELM instability, experimental tests of the theory and some open issues. Progress in the understanding of ELMs has been documented in reviews such as Zohm [132], Connor [133], Suttrop [134], Lao [135], Wilson [136], Kirk et al [137] and Leonard [138].

Experimental characteristics of pedestal MHD limits
4.1.1. Transient nature of ELMs. The most common operating mode for H-mode plasmas is the ELMy H-mode, where periodic bursts of energy and particles called ELMs relax the pressure gradient near the plasma edge. After the crash, the pressure gradient usually recovers quickly to near its value before the ELM crash and then stays there until the next crash. The ELM crash is often preceded by precursors [139]. The precursor activity and the violent crash indicate that the pedestal recovery is ultimately limited by MHD and not by turbulent transport processes. ELMs are of concern for ITER and future machines because the ejected energy and particle fluxes can damage plasma facing components [140].

Theory of peeling-ballooning modes
The most likely candidates for the MHD that limits the pedestal and causes the ELM crash are kink-peeling modes [141], ballooning modes [142] and the coupled peeling-ballooning modes [133]. The peeling mode is driven by a strong gradient in current density near the plasma edge. The most unstable peeling modes have low toroidal mode number n and are localized so that they peak at the plasma boundary.
The ballooning modes have higher n and are driven by the pressure gradient with ∇P · κ as the driving term, where κ is the curvature of the magnetic field. Since the curvature changes sign along the field line, the ballooning mode is localized on the low field side of the tokamak plasma where the curvature is most unfavorable for stability. The ballooning mode is stabilized by local magnetic shear. At intermediate n, the peeling and ballooning modes can couple to so-called peeling-ballooning modes that are driven by both current density and pressure gradient.
Since the pressure gradient drives bootstrap current, which dominates the pedestal current, the steep pressure gradient implies there is a large current peak in the pedestal. As a consequence, peeling-ballooning modes are expected to be the most unstable modes. The exceptions are very low collisionality pedestals, where the pedestal current is high and pure peeling low-n modes become dominant, or very high collisionality pedestals, where the bootstrap current is very low and pure high-n ballooning modes are the most unstable modes. The pedestal pressure and current profiles must be reconstructed accurately in order to generate accurate experimental equilibria for the analysis of MHD stability. As described in section 2.2, the pedestal density and temperature profiles are measured at sufficient resolution to allow reconstruction of the pedestal pressure profile. The fast ion population is usually small near the plasma edge and can be ignored in the calculation of total pressure. However, the impurity content of the pedestal can be substantial and has to be taken into account due to the dilution of the plasma composed mainly of one of the hydrogenic isotopes. The separatrix location has small uncertainties; these are potential sources of systematic errors in mapping temperature and density profiles and obtaining the most accurate pressure profile.

Calculation and measurement of current.
For most studies, the current density is not measured directly. Instead, models for the bootstrap current and inductively driven current components are used to compute the current density from experimental temperature, density, effective ion charge and magnetic geometry data. The most commonly used formula for bootstrap current is from Sauter et al [143].
The newer and more complete numerical models XGC0 [144], NEO [127] and XGCa [145] find that the Sauter model over-predicts the bootstrap current at high collisionality [145][146][147]. Modified versions of the Sauter formula have been obtained from computations with both XGCa [145] and NEO [148] to provide improved analytic models for the bootstrap current. These modified formulae are convenient for providing rapid calculations of the bootstrap current in modeling and analysis codes. The differences in bootstrap current could have some effect on modeled peeling-ballooning stability.
Beam-based diagnostics have provided local measurements of the pedestal current, computed from internal measurements of magnetic field components. These techniques include a system on DIII-D measuring the Zeeman effect of atoms in a lithium beam [150] and a system on MAST measuring the motional stark effect of a deuterium neutral beam [149]. These studies have confirmed that there is a current peak in the pedestal. Moreover, both systems have shown that neoclassical bootstrap models are consistent with the measurements within error bars. Figure 22, shows that the HELENA [151] equilibrium code and the CRONOS [152] code suite (using NCLASS [128] for bootstrap current) compute neoclassical current densities which are close to experimental values in MAST. The DIII-D work also used the NCLASS code.
Techniques based on high quality magnetic equilibria (without internal measurements of magnetic field) have also provided tests of neoclassical models. Studies in both DIII-D Figure 22. Current density J ϕ vs major radius in pedestal of MAST just before an ELM. Blue curve shows J ϕ derived from internal measurements of magnetic pitch angle from an MSE diagnostic. Red dotted line shows bootstrap current density from HELENA code; red dashed line, from CRONOS code suite. Reproduced from [149]. © IOP Publishing Ltd. All rights reserved. [153] and ASDEX Upgrade [154] have confirmed that there is a peak in the edge current density; moreover, neoclassical theory provides good agreement with the experimental current density in the equilibria.
There can be little doubt that neoclassical theory predictions of current density provide a good description of pedestals that have recovered from an ELM crash. Whether they are adequate for all purposes cannot be known. However, there are many reasons why more and improved internal measurements for pedestal current density would be valuable to pedestal studies. These measurements remain very challenging and rare.

Experimental tests of peeling-ballooning stability
The stability limits of the pedestal plasma to peelingballooning modes are determined by first reconstructing the experimental equilibrium, including an accurate pedestal pressure profile and current density profile. Subsequently, the pedestal pressure gradient and current density are varied about the experimental point and used to produce new Grad-Shafranov equilibria. This variation produces a map with pressure gradient as the X-axis and the current density as the Y-axis.
An ideal stability code, such as ELITE [155,156], MISHKA [157], KINX [158] or MINERVA [159], solves for the stability of each of the equilibria. A 'stability diagram' is produced by plotting the growth rate of the fastest growing linear mode onto the map of current density vs pressure gradient. Stability boundaries are drawn on the map where the growth rate crosses the threshold value for onset of MHD instability. This workflow produces a stability diagram such as the one shown in figure 23, where unstable equilibria are colored red, stable are left open and the experimental equilibria noted with stars. Careful equilibrium reconstructions, using the measured pressure profile and self-consistently calculated bootstrap current, show that the operating points of the equilibria before a Type I ELM are within the error margins of the threshold for peeling-ballooning instability in several tokamaks. These include DIII-D [156], ASDEX Upgrade [77], MAST [23], JT-60U [161], JET [160], NSTX [162], EAST [163], KSTAR [164] and TCV [84]. These observations provide much evidence for Type I ELMs being due to peeling-ballooning modes. Figure 23 shows a typical example from JET-C. An experimental point before a Type I ELM (blue star) is at the threshold for peeling-ballooning instability. In contrast, experimental points in L-mode (black star) and during Type III ELMs (red star) are well into the stable region.
As noted in section 2.3, the equilibrium pressure gradient recovery from the ELM crash often saturates near the peelingballooning limit and the pedestal spends a considerable portion of the ELM period close to the stability limits. While it is not clear how the peeling-ballooning mode is triggered at the end of the recovery process, it is obvious that peeling-ballooning modes play a key role in the dynamics of Type I ELM crashes. (We note that the width of some profiles can increase even after saturation of gradients-as discussed in section 2.3. This phenomenon might affect ELM triggering in some cases, but this idea is untested).
The pedestal stability of the small ELM regimes is mixed. On one hand, in Type III and IV ELMy plasmas, the pedestal gradient and pedestal current density are found to be in the stable region for ideal MHD peeling-ballooning modes [23,39,160]. However, Type II ELMy plasmas can be found equally close to the high-n ideal MHD ballooning stability boundary as Type I ELMs [70,165,166].
Changes in peeling-ballooning stability are able to explain some changes in pedestal structure observed in experiments. For instance, if the pedestal is limited by dominantly ballooning type modes, then increasing global β p increases the Shafranov-shift and improves pedestal stability [63,77,167,168]. Another example is that plasma shaping, e.g. increased triangularity, can expand the peeling-ballooning stability boundary, especially if the pedestal is limited by coupled peeling-ballooning modes instead of pure peeling or ballooning modes [156].
Also the relative position of the experimental equilibrium with respect to the stability boundaries can affect the maximum pressure gradient achieved. The position is mainly determined by collisionality because the bootstrap current decreases with fixed pressure gradient when collisionality increases. In a scan where density is increased and temperature is decreased, the equilibrium point on the stability boundary moves from the pure peeling-mode limited through the peeling-ballooning mode limited to the pure ballooning mode limited stability boundary. In strongly shaped plasmas, the maximum marginally stable pressure gradient is achieved at the intermediate point when the plasma is limited by peelingballooning modes [169].
The outward radial shift of the density profile relative to the temperature profile has been found to degrade the performance of the plasma. This behavior is connected to the destabilizing effect on the ballooning modes, caused by the shift of the maximum gradient closer to the plasma edge [80,97].
Despite such successes, there are also exceptions where the simple peeling-ballooning model seems to be failing to explain Type I ELMy pedestals. Most notable of these is JET-ILW. To protect the divertor from melting, most JET-ILW experiments have been conducted with significant gas puffing. This change combined with a reduction of low-Z impurities resulted in a change of character of Type I ELM crashes, which have a longer time scale for collapse than in JET-C [170].
Another problem is that JET-ILW [76,81,171,172] and ASDEX Upgrade [77] plasmas with large gas puffs operate below the threshold for onset of peeling-ballooning modes despite having nominal Type I ELMs. Distance of the operating point below the peeling-ballooning threshold tends to increase with gas fueling level, as shown in figure 24. In addition, this trend is correlated with the shift parameter between ∇n e and ∇T e in JET-ILW, as shown by figure 24. At low gas fueling rate (and low power), the shift parameter is small and the experimental normalized pressure gradient α exp is at the level α crit expected for onset of peeling-ballooning instability. As the gas fueling rate and shift parameter increase, α exp falls further below α crit . The reason for this behavior is not clear. It is plausible that non-ideal effects, such as resistive MHD, play a role in the MHD stability of these plasmas [76,83].

Non-linear simulations of peeling-ballooning modes.
In addition to comparisons of linear stability limits to experimental profiles, peeling-ballooning modes have also been simulated with non-linear MHD codes such as JOREK [173]  and BOUT++ [174]. The ELM crashes produced in these simulations with experimental equilibria show many of the characteristics of observed ELM precursors (MHD mode activity prior to the ELM crash) and of ELM crashes themselves. In particular the filamentary structures and heat loads on divertor structures observed during ELM crashes [53,175] have been found to agree well with non-linear simulations of DIII-D [176], ASDEX Upgrade [177], MAST [178] and KSTAR [179]. While the exact process of crossing the stability limit for peeling-ballooning modes is uncertain, it is clear that peelingballooning modes are playing a key role in the dynamics of an ELM crash.

Summary.
Most H-mode plasmas have frequent occurrences of MHD instabilities in the pedestal, called ELMs. These instabilities transiently transport energy and particles out of the plasma and they provide hard limits beyond which the pedestal cannot evolve.
Theory and simulation have developed a theory that Type I ELMs are triggered by coupled peeling-ballooning modes. This model is well validated by numerous tests. These show that operating points for ELMs of all types, as well as regimes without ELMs, operate at or below the predicted peelingballooning limit. Extended MHD effects, such as resistivity, may be needed to explain triggering of ELMs occurring below the predicted peeling-ballooning limit.

Fluctuation-driven transport
The large gradients of temperature, density and pressure observed in the pedestal have long been considered as likely triggers of pedestal turbulence for a range of microinstabilities. Such turbulence is viewed as a possible source of important pedestal transport. This section will review current understanding of the existence of turbulence and its role in controlling pedestal structure.

Measurements of pedestal fluctuations
Turbulence in the pedestal should manifest itself through fluctuations of perturbed quantities. Indeed, since the early days of H-mode research, measurements have shown fluctuations in or near the pedestal for a number of parameters. Most measurements have been of fluctuations in the radial or poloidal magnetic field (called B here) or of n e , fluctuations in n e .
Although many measurements of pedestal fluctuations exist, it has proven difficult to recognize clear patterns in them. More specifically, it has not been clear if measurements from different machines are related or even if different measurements within a given machine are related. This situation has improved since about 2014 and these advances will be discussed in the next section.

Correlation of fluctuations and gradients
Recent research has focussed on correlations between fluctuations and pedestal gradients. The goal has been to determine if gradients are driving fluctuations and/or if fluctuations are providing limits to gradients. As a result of this research, common features and phenomenology have been identified in a few cases [213]. We will now summarize some of this work.

Density fluctuations during gradient recovery in DIII-D.
Measurements of long-wavelength density fluctuations in the pedestal of DIII-D discharges at ρ * ≲ 0.6% showed that the amplitude of a mode propagating in the ion diamagnetic drift direction (in the plasma frame) increased for ∼5-10 ms during recovery from an ELM crash and then saturated [191]. The increase and saturation of the mode amplitude was correlated with the time behavior of both the pedestal ∇p e and ∇n e . The evolution of the mode amplitude showed weaker correlation with ∇T e .
A higher frequency band of density fluctuations propagating in the electron diamagnetic drift direction (in the plasma frame) was also observed in the pedestal of these discharges. This band of fluctuations showed less evolution during the inter-ELM cycle than the lower frequency band and showed some correlation with the behavior of ∇T e .

Magnetic field fluctuations during pedestal recovery in C-Mod.
Measurements on C-Mod, in which a probe held at 2 cm away from the separatrix was used to make measurements of B [208,209], showed a correlation between B and T ped e . As shown in figure 25, the power in B (b) and T ped e (c) both increased for ∼2-4 ms after an ELM crash and then abruptly reached a steady state. In this work, T ped e was considered a proxy for pedestal ∇T e ; thus, this behavior suggests a correlation between ∇T e and B. The B spectrum ( figure 25(a)) showed a relatively coherent feature with the mode frequency bandwidth being about 10% of the mode frequency. Due to its small but finite bandwidth, the mode was called a quasicoherent fluctuation (QCF) [209].
The QCF fluctuation was also observed on measurements of density fluctuations with PCI and reflectometry. Measurements from PCI were chord integrated and thus could not uniquely show the radial location of the fluctuations. Reflectometry, providing a local measurement of n e , showed that the QCF fluctuations occurred in the steep gradient region of the pedestal. Temporal evolution of the fluctuations during the inter-ELM cycle provided another signature that the fluctuations originated in the pedestal. The fluctuations were abruptly terminated by an ELM crash and were re-established a few ms after the crash as the pedestal gradients recovered. These measurements were important for showing that fluctuations with a magnetic signature were potentially causing pedestal transport and limiting evolution of T ped e .

Fluctuations in magnetic field and density during gradient recovery in DIII-D.
Subsequent measurements of both magnetic fluctuations from Mirnov coils and pedestal density fluctuations were made in DIII-D during pedestal recovery from ELMs [37]. The magnetic spectrogram in figure 26 shows fluctuations with a QCF character between ∼20-130 kHz which were not visible immediately after an ELM crash and which then increased rapidly in intensity for a few ms before reaching a steady state. Similar features were observed on local measurements of n e and these localized the fluctuations to near the pedestal top.
As figure 26(b) shows, the amplitude of the summed fluctuations between 23 and 60 kHz was correlated with the evolution of ∇T e with both reaching saturation ∼8 ms after an ELM crash. In contrast, ∇n e saturated in ∼3-5 ms, more quickly than ∇T e , and was not well correlated with the evolution of B. This behavior was more distinct at a higher current in which ∇n e saturated in <5 ms and ∇T e saturated in ∼15-20 ms.
Diallo noted the resemblance of the QCFs to similar features that had been reported previously [37]. These studies included measurements of 'washboard' modes in JET [180,214], other observations in DIII-D [190,215] as well as the measurements in C-Mod [208,209]. Correlations were observed between the evolution of QCFs and the pedestal top T e in JET [180] and C-Mod [208,209] and ∇T e in DIII-D [37]. These insights provided important advances in understanding similarities of fluctuations between devices and possible linkage of QCFs to the physics of pedestal T e .

Fluctuations in magnetic field during gradient recovery in ASDEX Upgrade.
Extensive studies of the linkage between pedestal gradient evolution and inter-ELM pedestal fluctuations have been performed in ASDEX Upgrade. A consistent picture has emerged over a range of plasma conditions, including a scan of pedestal collisionality [184], variation of main ion species [185] and a range of plasma triangularity [187]. As has long been observed in ASDEX Upgrade [35], these discharges showed a sequence of events in which ∇n e first saturates followed by saturation of ∇T e during ELM recovery. Figure 27 shows a typical observation of the evolution of B, ∇n e and ∇T e during an inter-ELM cycle in ASDEX Upgrade. The ELM crash is characterized by very intense B and a large pulse of current to the inner divertor, shown in panels 1 and 4 of figure 27. After the ELM crash, the B amplitude is very low for a short time. Subsequently, ∇n e increases until ∼3 ms into the inter-ELM cycle at which time ∇n e approximately saturates, coincident with the onset of QCFs in the frequency range ∼50-150 kHz. After this event, ∇T e continues to increase until ∼10 ms into the ELM cycle when ∇T e saturates, coincident with the onset of higher frequency QCFs near ∼240 kHz.
This phenomenology of gradient saturation correlated with the onset of fluctuations is observed over the wide range of ASDEX Upgrade conditions noted above. These results suggest that the lower frequency fluctuations may play a role in saturation of ∇n e whereas the higher frequency fluctuations are involved in the saturation of ∇T e .

Comparison of fluctuations in ASDEX Upgrade and
DIII-D. The evolution of inter-ELM fluctuations and gradients has been compared between ASDEX Upgrade and DIII-D for similar operating conditions [216,217]. As shown in figure 28, the two machines show very similar evolution of gradients and magnetic fluctuations during an ELM cycle for these discharges (details in [216]). In both machines, saturation of ∇n e is observed to be correlated with the onset of QCF modes up to ∼100 kHz. Subsequently, ∇T e saturates with the onset of higher frequency fluctuations. In both machines the increase of ∇n e ends at ∼5 ms into the ELM cycle whereas the ∇T e rise ends at ∼10 ms for ASDEX Upgrade and 20 ms for DIII-D. This comparison is a clear demonstration that there is some universality of inter-ELM fluctuations between machines.

Fluctuations between ELMs in HL-2A.
The HL-2A tokamak has observed a quasi-coherent mode in the pedestal in the frequency range 50-100 kHz [211]. This mode, occurring in both density and magnetic fluctuations, is observed between ELMs as well as during the initial ELM-free period after an L-H transition. This mode has been named the QCM. ('QCM' has also been used as an acronym for a mode observed in C-Mod EDA discharges; nevertheless, the modes in C-Mod and HL-2A might be different).
Gradients of T e and n e increase rapidly for a few ms after an ELM crash. The mode is excited by pedestal ∇n e ; in turn, the mode appears to limit the pedestal density evolution.
A variety of measurements indicate that these modes exist in the pedestal region. Local measurements of density fluctuations confirm this localization [218].
These modes are given different names in some of the papers noted above. For instance, a mode with the characteristics of ECM has been called CM (coherent mode) [201,202,207,219]. The ECM and CM have been identified as the same phenomenon in [206,219]. Likewise, [204] notes that the MCM was called LFM (low frequency mode) in early studies [199]. In addition, observations of the HFM mode show some differences of characteristics in different studies. Notably, the poloidal wave number of the HFM shows more than an order of magnitude difference for studies in [198] compared to [206].
We will use the acronyms ECM, MCM and HFM for these three modes, widely observed in EAST. Tables in [204, 206,  The ECM, MCM and HFM have sometimes been observed in the same discharge [206,218]. In some studies, only one or two of the modes is reported. All of these modes are observed in both ELM-free conditions and between ELMs in ELMy discharges. Of particular note, the ECM is observed in ELMfree regimes, obtained with the assistance of lithium wall conditioning [198,203]. Lithium increases the pedestal collisionality, which destabilizes the mode. The mode provides transport in the pedestal which enables these discharges to avoid the ELM limit.
Early studies of the ECM used diamond-tipped reciprocating Langmuir probes to make local measurements of T e , n e and plasma potential [198]. Measurements with these probes showed that the ECM fluctuation drove outward particle and heat fluxes Γ and Q, respectively. The temporal evolution of these fluxes showed a similar behavior to pedestal ∇T e but no clear correlation to the pedestal density. These observations were made in ELM-free conditions. However, we expect that the ECM mode in ELMy conditions would have similar dependencies.
In another study, measured pedestal profiles of T e and n e provide evidence that drive for the ECM has dependencies on pedestal pressure gradient ∇P and electron collisionality ν * e [203,218]. These dependencies, shown in figure 29, occur for a range of pedestal conditions, including discharges with no ELMs, Type III ELMs and Type I ELMs. Electron temperature and density profiles and relative ECM fluctuation intensities from 28 H-mode discharges are used to generate the color contour plot, showing the existence region of the ECM. Data points from three individual shots are also shown. Data points with the ECM are inside the color contour region. Points without the ECM are outside the ECM operating region. The figure indicates that the ECM operating region is bounded by pedestal ∇P ≈ 100-200 kPa and ν * e ≈ 2-5. Temporal evolution between ELMs of the two electromagnetic modes (MCM and HFM) has been studied in EAST [204,206]. The MCM shows correlations with both the pedestal pressure gradient [204] and pedestal top electron temperature [206]. With each ELM crash, the mode disappears and is reestablished early (within a few ms) in the pedestal buildup after the crash. This evolution shows similarities to that of the gradient of the pedestal SXR intensity ∇S, which is greatly reduced at an ELM crash and rebuilds to pre-ELM levels within ∼10 ms during ELM recovery. The MCM reappears shortly after ∇S starts increasing in ELM recovery [204]. Since the SXR intensity depends on T e and n e , ∇S can be taken as a proxy for pedestal ∇P. Thus, the inter-linked time behaviors of the MCM and ∇S may be indicative that the MCM is driven by ∇P or a related quantity.
In a separate experiment, temporal evolutions of pedestal top T e and n e have been compared with ECM, MCM and HFM fluctuations during the inter-ELM cycle of large ELMs on EAST [206]. Saturation of the MCM and HFM modes was correlated better with pedestal top T e than n e .

Fluctuations and transport.
A central question for pedestal studies is: do fluctuations cause radial transport of heat and/or particles? Some of the results presented here show correlations between temporal evolution of fluctuations and pedestal gradients or pedestal top values; i.e, fluctuations might be causing transport. Such results are suggestive but do not definitively show that fluctuations are playing a causal role in transport. Thus, we look for more direct signatures of fluctuations causing transport. Our focus remains the inter-ELM phase of H-mode discharges.
The ECM evolution between ELMs in EAST has sometimes shown bursting behavior followed by bursts of particle flux gamma Γ div to the divertor. As an example, figure 30 shows that the bursts of Γ div arrive in the divertor after the bursts of ECM fluctuations occur. The delay time is about 230 µs, which is about the timescale for parallel flow of particles from the outer midplane to the divertor. These results present compelling evidence that the ECM causes particle transport [202].
Similar conclusions follow from studies of similar type-I ELMy H-mode discharges in EAST, one discharge with and one without an ECM in the pedestal [207]. The discharge with the ECM has a higher value of Γ div . The ECM causes an increase of about 30% in energy and particle fluxes to the divertor. In addition, the widths of heat and particle flux patterns in the divertor are higher when the ECM is present.
In addition, as noted in section 5.2.7, probe measurements in ELM-free operation show that the ECM drive outwards fluxes of particles and heat at the midplane. In this experiment, divertor D α emission also showed correlations with the ECM in two ways. First, the intensity of the D α emission increased significantly when the ECM first appeared. Second, the temporal evolution of midplane particle flux, driven by the ECM, was similar to evolution of divertor D α . This study along with the two studies discussed above provide convincing evidence that the ECM in EAST does drive transport to the divertor.
High time resolution studies show that the electromagnetic MCM has a bursty nature and that the bursts have signatures on the ion saturation current measured with probes in the divertor [204]. Conditional analysis shows that the MCM changes the poloidal distribution of particle flux to the divertor. However, the MCM drives only a small net particle flux.
The quasi-coherent HFM, sometimes accompanied by a medium-frequency CM, also shows the ability to cause transport to the divertor [199]. This conclusion follows from studies of the temporal evolution of fluctuation amplitude and divertor D α emission.
Experiments in DIII-D, in which lithium powder has been added to ELMing discharges have exhibited bursts of density fluctuations [220]. These fluctuations, called the Bursty Chirpy mode (BCM), generate bursts of both D α and CIII emission in the divertor, as shown by the time delay of the emission relative to the BCM bursts. In addition to the divertor signatures, the BCM also causes flattening of the pedestal pressure profile, which modifies the stability to ELMs and enables the achievement of higher pedestal pressure. The BCM has also been observed in some discharges without injection of lithium.

Inter-ELM filaments.
There is a substantial literature showing evidence of non-diffusive transport at the plasma edge in multiple machines. A variety of diagnostics show that intermittent transport events, originating near or inside the LCFS, expel particles and heat into the SOL. These events occur between ELMs; they are not the large filaments caused by ELMs. Langmuir probes, a primary diagnostic for studying this process, shows these events as intermittent spikes in the time record of T e , n e and other parameters. These events are due to 3D filaments which propagate radially outwards from the pedestal into the SOL. This structure is well shown by 2D imaging diagnostics. For example, camera images of D α emission on MAST show the full cross section of the filaments and their outward propagation [221]. Imaging of a thermal helium beam on ASDEX Upgrade shows filaments originating inside the pedestal and propagating into the SOL [222].
We cannot do justice to this subject but note that there is a review of work up to 2009 by Boedo [223] with a brief update in 2014 [224]. This is an important topic because some of the studies show filaments might be transporting significant density across the separatrix.

Summary.
Observations on several machines show that growth and saturation of fluctuations are correlated with a pedestal gradient. By 'correlation', we mean that the fluctuation intensity and the pedestal gradient both increase and saturate in rough synchronization. Such correlations have most commonly been observed with ∇T e (or T ped e ) but correlations with ∇n e have also been seen.
In addition, the fluctuations often occur in one or more frequency bands which show a significant degree of coherence. Thus, the term 'Quasi Coherent Fluctuations' is loosely applied to these phenomena. Observations of QCF-like fluctuations have been made on many more devices than shown here. Laggner et al [212] present a comprehensive review of edge fluctuation characteristics from multiple machines.
Do these correlations imply cause and effect between fluctuations and pedestal gradients? This is a good question and it seems difficult to impossible to determine causality from measurements alone. Another question is: do fluctuations drive transport? There are some experimental observations of fluctuations sending particle fluxes to the divertor, but such studies have not been widely reported. Theory and simulation must be used in concert with experiment in order to provide a much more complete understanding of the interaction between gradients, fluctuations and transport. We will discuss such research in the next section.

Theory and modeling to identify fluctuations
Analytic theory and theoretical simulations, coupled to experimental data, have been providing insights into the identification of turbulent modes in the pedestal and the transport these modes might cause. Recent advances in capability of theoretical simulations have enabled many of these insights.
Gyrokinetic codes have been used in recent simulations to determine the role of instabilities in pedestal fluctuations and turbulent transport. Typically, the instabilities of interest are two electromagnetic modes: KBM and microtearing modes (MTM) and three electrostatic modes: electron temperature gradient (ETG) modes, ion temperature gradient (ITG) modes and trapped electron modes (TEM). In addition, extended fluid codes often find evidence of electromagnetic drift-Alfvén waves (DAWs). References [28,225] provide an overview of these modes and their characteristics. Evidence for the existence and transport caused by these modes is discussed below.
The workflow for these theoretical simulations uses experimental inputs of pedestal temperature and density profiles as well as magnetic equilibria. These equilibria are reconstructed to model as faithfully as possible the pressure and q profiles in the pedestal. The current density profile, required to obtain accurate q profiles, is not measured and is usually constructed from a bootstrap current model, using measured temperature and density profiles. In addition, there is an issue with the simulation boundary for ion scale turbulent modes that are simulated with a global treatment. Most codes are not able to extend the simulation into the SOL, which means that an artificial buffer region has to be created near the boundary. How this is done in practice may affect the results.
With this input, the simulations are used to search for predicted unstable modes plus a variety of mode characteristics. Determining if a predicted unstable mode is actually present in the plasma requires additional experimental data for comparison with simulation. A concept called 'fingerprints', proposed by Kotschenreuther et al [28], shows how confidence in the identification of instabilities causing transport is improved as more points of comparison between experiment and simulation are available. The fingerprints include ratios of transport coefficients between different channels, the fluctuation frequency in the plasma frame and ratios of normalized fluctuation amplitudes between different quantities. As will be shown, this method has enabled advances in understanding pedestal fluctuations and transport.

KBM
KBM are electromagnetic modes, which are predicted to be driven by the pedestal pressure gradient [67]. They are predicted to drive transport in all channels, including electron and ion thermal and particle transport [28].

Experimental search for KBM fluctuations.
Some experiments have measured fluctuations which have characteristics similar to those expected for KBM modes. For instance, long wavelength density fluctuations were observed in the DIII-D pedestal with propagation direction in the ion diamagnetic drift direction in the plasma frame, consistent with predictions of KBM. Moreover, during the inter-ELM cycle, the amplitude of n e had a similar time history, including saturation, as the pressure gradient [191].
The QCFs observed in C-Mod [208,209] and DIII-D [37] (discussed above) showed several characteristics expected for KBMs. Fluctuations were observed in pedestal density and magnetic fluctuations, had long wavelengths and were correlated with a rise in the pedestal ∇T e (with T ped e as proxy in C-Mod). After a rise in fluctuation intensity, saturation occurred in the T e profile and in fluctuation amplitudes. These characteristics are consistent with expectations for KBMs. In C-Mod, the propagation direction was determined to be in the ion diamagnetic drift direction, also expected for KBMs. Due to unanswered questions, though, the QCFs were not definitely identified as KBMs. For instance, simulations did not exist to explain the high coherency of the fluctuations, whereas KBMs were expected to have large spectral width [209]. MTMs were also a plausible explanation for the QCFs in DIII-D [37].

Linear simulations.
A number of gyrokinetic codes have computed the linear stability of KBMs for a range of experiments. These codes include GS2 [227], GTC [228], GENE [229], GYRO [230], GEM [231] and ORB5 [232]. In some studies, calculations of the stability of infinite-n ballooning modes have been used as a proxy for KBM stability.
KBMs have been predicted to be unstable in the pedestal in several local simulations, including MAST (GS2) [233], DIII-D (GYRO) [234], C-Mod (GS2) [209] and JET (ELITE) [235]. Figure 31 shows results for linear GS2 simulations of C-Mod which found the experimental operation point in a space of growth rate versus pressure gradient to be unstable to KBM modes. Conversely, KBMs have been predicted to be primarily stable in other local simulations, including NSTX (GS2) [114], JET (GS2) [236] and ASDEX Upgrade (GENE) [237].
Saarelma et al [238] proposes that a local assumption is not justified for the modeling of KBMs and that a global simulation is needed. Comparisons of local versus global simulations have differed in their conclusions. For example, global analysis of a JET discharge with ORB5 removed access for KBMs to second stability [238], which was observed with a local analysis [236]. linear local calculations find KBM to be unstable (figure 32 top panel) [226]. Some other global simulations, including DIII-D (GEM) [239] and DIII-D (GTC) [240], have found KBMs to be unstable in the pedestal.
The range of these results shows that the presence of KBMs in the pedestal has not been clearly established. One common feature among the simulation studies is that scans of pressure gradient often find the experimental operating point to be near the critical pressure gradient for the onset of instability. Thus, it is plausible that KBMs are present in the pedestal and acting to keep that pressure gradient near criticality. If so, the experimental data and/or theoretical models are not sufficiently accurate to prove that.
Definitively establishing the existence of KBMs may well require detailed comparisons of non-linear simulations with a range of fluctuation measurements. Such simulations may require advances in simulation capability. For example, since KBMs have a very long perpendicular wave length, even linear simulations are very demanding as local simulations lack the effect of equilibrium variation within the simulation domain. Global simulations, which would model the equilibrium variation, require a treatment of the boundary condition at the separatrix, which no current code can do correctly.

MTM
There is an expanding base of evidence that MTMs are present in many pedestals and may be causing significant electron thermal transport. MTMs are electromagnetic modes, driven by ∇T e , which drive transport primarily of electron heat [28,241]. Several observations of correlations between the amplitude of QCF fluctuations and ∇T e or T ped e suggest that QCF fluctuations may be linked to turbulence driven by ∇T e , as discussed in section 5.2. Two primary candidates for this turbulence are MTM and ETG modes [28,225]. This subsection examines modeling constrained by experimental data. The main results are that modeling strongly supports the identification of the QCFs in some studies as due to MTMs and that MTMs can drive significant electron thermal transport in the pedestal.

Evidence for MTMs from simulation.
Early simulations of MTMs near the plasma edge typically predicted MTMs to be present at the pedestal top or just inside the pedestal, but not in the steep gradient region. If present at the pedestal top, MTMs could limit the ability of the pedestal to penetrate further into the core. These studies include ASDEX Upgrade (GENE) [242], MAST (GS2) [233,243], DIII-D (GYRO) [234], JET (GS2) [236], NSTX (GS2) [114] and NSTX (GEM) [244].
Subsequently, Hatch reported the first nonlinear simulations in which MTMs produced transport at experimental levels in the pedestal [226]. These simulations of a JET-ILW pedestal with GENE produced MTMs in the steep gradient region, where they were predicted to generate much of the electron thermal transport. The combination of MTM, ETG and neoclassical transport accounted for the total power flow through the pedestal.
These simulations have been followed by research which shows increasing evidence that MTMs produce some observed magnetic fluctuations. We will now discuss this work.

Comparison of simulated and measured fluctuations.
Recent comparisons of experiment to theory and simulation provide increasing confidence that MTMs in the steep gradient region of the pedestal cause some observed QCFs. Simulations with GENE have predicted the measured frequencies of magnetic spectra as well as toroidal mode numbers for a number of discharges on DIII-D [28,[246][247][248][249] as well as on JET [245].
As an example, figure 33 shows that nonlinear GENE simulations of a JET discharge provide a good match to experimentally measured frequencies and mode numbers of washboard modes [245]. In addition, the experimental frequencies are larger than the maximum experimentally inferred Doppler shifts in the pedestal, indicating that the modes rotate in the electron direction in the plasma frame, as expected for MTM modes [28]. Another example is shown in figure 34. Global simulations with GENE predict MTMs in each of three observed bands of QCFs in a DIII-D discharge [246]. The simulated frequencies include the experimentally inferred Doppler shifts and the results also indicate mode propagation in the electron direction in the plasma frame.
Theory provides an explanation for the discrete bands of fluctuations (QCFs) as well as toroidal mode numbers (n) observed in magnetic spectrograms. The MTMs are predicted  at locations where the peak of the electron diamagnetic frequency ω e* coincides with a rational magnetic surface. With account taken for the Doppler shift due to the ExB velocity, this model has been shown to provide quantitative agreement with observed frequency bands and gaps in the frequencies in JET [245,247,250] and DIII-D [246,247]. Based on this understanding, a global analytic model has been developed for slab-like MTMs. Without need for a gyrokinetic simulation, this model predicts frequencies and observed mode numbers of magnetic fluctuations in JET [247,250] and DIII-D [247] discharges.
This theoretical explanation also provides a quantitative explanation for time variations of frequencies of magnetic fluctuations, observed during rapid vertical oscillations of the plasma equilibrium (jogs) in DIII-D [251]. Both up-chirping and down-chirping of the frequencies of magnetic fluctuations were observed in these experiments. The up-chirping was observed during pedestal recovery from an ELM crash. The increase of pedestal T e and n e profiles after the crash caused an increased of the electron diamagnetic frequency ω e* , thus causing an increase in mode frequencies. The down-chirping of a mode after a jog was quantitatively explained as due to inward motion of the q profile and temporal evolution of the ω e* profile.

Amplitude of magnetic fluctuations from MTMs.
Further evidence that MTMs are present in some H-mode pedestals is provided by Faraday polarimetry [252] measurements of both B and n e in DIII-D. These measurements are lineintegrated with chords passing through the pedestal. Strictly speaking, the measurement does not provide the location of observed QCF fluctuations. However, the inter-ELM temporal evolution of fluctuation intensity and comparison with pedestal-localized measurements of n e from a beam emission spectroscopy diagnostic show that the observed fluctuations originate in the pedestal [192,253]. The polarimetry measurement provides absolute amplitude of lineaveraged magnetic and density fluctuations in the plasma.
Polarimetry measurements show a non-monotonic dependence of B on the electron-ion collisionality [192]. Non-linear simulations with GENE reproduce this dependence and show a peak in B at the same collisionality as the experiment. The simulated B is about half of the experimental value [248]. (Curie et al [247] discusses caveats for both the experimental and simulated values of B).
The absolute amplitude shows the fluctuation level (∼10 Gauss) is relevant to stochastic field transport theory [254] and enables estimates of important metrics for the identification of observed fluctuations [28]. One such metric is the normalized intensity |δB r /B|, which was measured to be 0.08% over the frequency range 150-500 kHz [192]. This ratio is comparable to the ratio |δB r /B| = 0.15% obtained with GYRO [230] simulations of MTM turbulence in NSTX [254].
A second metric was evaluated with the addition of n e from BES [255]. The ratio of normalized magnetic to normalized density fluctuations |δB r /B|/|δn/n| was measured to be 0.08 ± 0.03 at its peak (frequency of 250 kHz) [192]. For the same data set, non-linear GENE simulations produced a ratio of 0.36 for MTM and 0.0038 for ETG [248]. The simulated value of |δB r /B|/|δn/n| for MTM is four times the experimental value whereas the value for ETG is 5% of the experimental value. This comparison cannot rule out MTM as being present in the experiment but suggests that other physics might be important [248]. However, the ETG simulations cannot explain the observed |δB r /B|/|δn/n|.

Simulations of transport from MTMs.
Studies with non-linear, electromagnetic simulations have concluded that MTM turbulence drives significant electron thermal transport in some pedestals. Simulations with GENE of a JET plasma produced ≈7.5 MW of transport from MTM turbulence in the steep gradient region of the pedestal with the input power being ≈12-13 MW [226]. Subsequent modeling of JET plasmas, with an emphasis on sensitivity studies, finds that MTM is likely to play a role in JET pedestals of two other discharges as well [100].
Nonlinear simulations of several DIII-D discharges with QCFs find that MTMs are likely to be present in the pedestal and to cause experimentally relevant levels of electron thermal transport [28,246,248,249]. These studies also find that transport levels are sensitive to variations of input parameters within uncertainties. Limitations of models might also be affecting accuracy of the results [28]. Nevertheless, all of these studies conclude that MTMs are likely playing an important role in pedestal electron thermal transport. 5.5.5. Summary. The combined results from theory, experiment and simulation provide compelling evidence that MTMs are present in some pedestals and are manifested through quasi-coherent magnetic fluctuations. The success of simulations in predicting the frequency spectra and other characteristics of observed QCF or washboard magnetic fluctuations provides the strongest support for the presence of MTMs. Non-linear simulations also predict that MTMs provide experimentally relevant levels of electron thermal transport in the pedestal of discharges with QCF or washboard fluctuations.
Although these types of fluctuations have been commonly observed in some machines, it cannot be concluded that these fluctuations are always present in these machines or are common in other devices. Neither can it be concluded that all QCFs are MTMs.

Drift-Alfvén turbulence
Drift-Alfvén turbulence (DAW), which is a coupling of drift wave turbulence to Alfvén waves at finite beta [256], has complex and rich physics [257,258]. Conditions in the H-mode edge can favor these modes. Three-dimensional fluid codes such as BOUT++ [174] and DALF [259] have been used in many studies of drift-Alfvén turbulence.
Simulations of QCFs in C-Mod and DIII-D ELMy H-mode discharges have been performed with the BOUT++ code suite, using a three dimensional six-field two-fluid electromagnetic model [260]. For both machines, the pedestal was near the threshold for ideal peeling-ballooning modes, but the collisional electromagnetic DAW was identified as dominant in DIII-D. Nonlinear simulations provide good matches to the measured frequency and wavenumber of a QCF in C-Mod and to the frequency of a QCF in DIII-D. A mode at a second frequency in DIII-D was not simulated.
We note that GENE simulations of the same DIII-D data set find an MTM mode with a frequency about 40% higher than experiment [28]. Thus, two different simulations are able to explain the data as being due to MTMs and drift-Alfvén modes. At first thought, these results present a conundrum.
However, a hybrid of a drift-Alfvén eigenmode and a microtearing mode has been proposed [28]. Local linear GENE simulations find evidence that such modes exist with low growth rates while global simulations find that they become primarily MTM-like [28].
BOUT++ simulations also find that the DAW has a role in the destabilization of the ECM of EAST [219,261]. Linear analysis in [261] finds that the resistive-ballooning mode and DAW instability are the main drivers of the ECM. Simulations in [219] find that the peeling-ballooning mode and DAW drive the ECM. Thus the DAW is important in both calculations. Moreover, both studies compute turbulence whose frequency and poloidal wave number are in the range of measurements on EAST. The mode is electrostatic in both studies, consistent with experimental findings that the ECM is primarily an electrostatic mode. In [261], the lower range of the simulated B/B θ ∼ 10 −4 -10 −3 is comparable to ECM measurements. Reference [219] finds that the electrostatic part of the DAW is much larger than the electromagnetic part.
As will be shown in section 5.8.3, studies with the gyrokinetic code GYRO have explained the ECM as a dissipative trapped electron mode (DTEM). Similar to the discussion two paragraphs above, two different modes, the DAW and the DTEM, provide explanations for the ECM. We do not have an explanation for this observation.
In summary, research discussed here shows that drift-Alfvén turbulence may be present in some pedestals.

ETG modes
ETG modes are electrostatic modes that are driven by the electron temperature gradient and that drive primarily electron thermal transport [28]. There is increasing support from simulations that ETG modes are an important source of electron thermal transport in some pedestals. Due to the small scale size predicted for ETG turbulence, it is currently very challenging to verify the presence of ETG turbulence from experimental measurements.

Threshold parameter for ETG instability.
Although ∇T e drives ETG modes, ∇n e stabilizes them [262]. Therefore, η e = L ne /L Te is a useful parameter for characterizing the onset of ETG instability, with L ne and L Te being electron density and temperature scale lengths, respectively. For a range of parameters in tokamak core and edge plasmas, GS2 linear gyrokinetic simulations find that 2/3 ≲ η e ≲ 1 triggers toroidal ETG modes [262]. Similarly, linear GENE gyrokinetic simulations find ETG instability for η e ≳ 1.2 in ASDEX Upgrade pedestals [263].
Experimental measurements in several tokamaks have consistently shown pedestal η e values are greater than unity, often by large margins. Measured pedestal values of η e include ∼1.3-2.5 for a range of studies in ASDEX Upgrade [112,[265][266][267], ∼1-4 for several discharge regimes in DIII-D [85,215,268], ∼1-3 for discharges with and without gas-puffing in C-Mod [215,269], ∼1-3 in NSTX including discharges Figure 35. Heat transport calculations due to ETG turbulence from GENE and CYGRO agree within ∼20% at two locations in a DIII-D pedestal. The calculated transport powers are ∼20%-30% of the total input power of 3 MW. For these calculations, ∇Te was increased by 20% and ∇ne was reduced by 20%. Reprinted from [264], with the permission of AIP Publishing.
with lithium coatings [196,215,[270][271][272] and ∼1-3 in JET [41,99]. In addition, the ETG metric R/L Te is measured to be above a theoretical value (R/L Te ) crit [242] for ETG onset during much of an ELM cycle in ASDEX Upgrade [273]. These results suggest that ETG modes may be present in many pedestals.

Benchmarking of ETG simulations.
The ordering of gyrokinetic codes is well met in the pedestal by the short wavelength ETG modes. Thus, these codes are expected to be excellent tools for studying ETG physics in the pedestal.
A recent code benchmarking activity supports this idea. Three different codes-CGYRO, GEM and GENE-each with different numerical algorithms, obtained very similar results when analyzing the same data set [264]. Linear simulations of a DIII-D data set showed good agreement on the simulated frequencies, growth rates, and eigenfunctions for the ETG instability. Moreover, nonlinear simulations with CGYRO and GENE produced electron heat fluxes which agreed within about 20%, as shown in figure 35.
In one of these studies, spatially resolved calculations with CGYRO showed that the electron temperature profiles of two DIII-D discharges were very near the simulated threshold for onset of ETG turbulence [275]. tracked closely throughout much of the pedestal. These results suggest that ETG turbulence may be active in limiting the T e profiles.

Nonlinear simulations of ETG instability.
Nonlinear simulations have predicted that ETG turbulence drives electron thermal transport at experimentally relevant levels (⩾5% of the power flow into the pedestal, as used here). These studies include ASDEX Upgrade (GENE) [237,263], JET (GENE) [100,226,276,277], DIII-D (GENE) [28] and DIII-D (CGYRO) [129,275]. Figure 35, discussed above, shows an example of simulated ETG power flows from GENE and CGYRO. Both codes predict transport due to ETG turbulence of ∼20%-30% of the total input power [264]. These simulations, as well as some of the other nonlinear simulations, showed significant sensitivity of the modeled power to the input profiles. For the data of figure 35, ∇T e was increased by 20% and ∇n e was reduced by 20% in order to obtain ETG transport comparable to the electron heating power. These adjustments are within nominal uncertainties. Both adjustments act to increase η e , the linear ETG drive. Similar adjustments have been used in other studies [237,275] and have increased the electron heat flow by up to an order of magnitude [237].
Since processes other than ETG turbulence can also cause electron thermal transport, more complete models may reduce the profile adjustments required to match experimental power balance. There is some evidence to support this. Simulations of a JET-ILW discharge used a model consisting of electron thermal transport due to MTM as well as ETG turbulence and ion transport assumed to be neoclassical [226]. With this model, GENE simulations matched the total experimental power balance at one point in the pedestal with no profile adjustments and at a second point with a 10% increase in ∇T e .
Simulations with GENE produced large transport from ETG turbulence in a study of four JET discharges with power and gas scans [276]. As shown in figure 37, a model of ETG turbulence plus neoclassical transport is in good agreement with the experimental balance for the two discharges with low gas. ETG explains most of the transport. These transport mechanisms likely are also dominant for the high gas discharges; experimental power balance is not available for these discharges due to high ELM frequency.
Simulations with CGYRO for turbulence and NEO for neoclassical physics [129] produce experimentally relevant transport for low and high collisionality discharges in DIII-D. No adjustments to input profiles were made. For a low collisionality discharge, figure 38 shows that the total simulated power is within uncertainties of the experimental power. For a higher collisionality case, the total simulated power is ∼40% lower than the experimental power. In these simulations, transport due to electrostatic ion modes dominates the electron thermal losses; transport due to ETG turbulence is small. The fraction of the ETG contribution to the total heat flux is much smaller than for the JET studies, just discussed. 5.7.5. Experimental evidence for ETG turbulence. ETG turbulence is generated at very small scales. Measuring fluctuations at these scales is a challenge, and we are not aware of such measurements at this time. The lack of such data is a serious impediment for validating ETG simulations.
With a suitable combination of simulation and measurements, there is a potential back door into the search for ETG. Fluctuation measurements are available at intermediate scales. Combined with suitable simulation, the prospects for identifying the source of the intermediate fluctuations, which might be ETG, are improved. An example follows.
A unique measurement in MAST of internal magnetic and density fluctuations at the same location has provided a ratio of magnetic to density fluctuation ratios to help identify intermediate scale fluctuations [210]. Measurements at the pedestal top near the end of the inter-ELM period show that (δB/B)/(δn/n) = 0.05. Linear GS2 simulations show both MTM and ETG being unstable at the measurement location and that (δB r /B)/(δn/n) = 0.02 for ETG and 0.4 for MTM. The simulated ratio for ETG was much closer to the measured ratio than for MTM. Thus, this work leads to the conclusion that ETG was present in the top of the MAST pedestal. This is perhaps the clearest measurement showing evidence for ETG turbulence in the pedestal region. 5.7.6. Summary. The combination of theory, simulation and experiment provides compelling evidence that ETG modes are commonly present in the pedestal. Experiments operate at values of η e where ETG modes are predicted to be linearly unstable, both by analytic theory and linear simulations. Fluctuation measurements do not exist at scales where ETG turbulence is generated and this lack prevents us from concluding that the presence of ETG has been definitively established.
What is more uncertain is the importance of ETG turbulence in driving electron thermal transport. Several non-linear gyrokinetic simulations show that ETG modes may be driving important levels of power. However, lacking quantitative fluctuation measurements which are needed to validate simulations of transport, there are large uncertainties about how much transport can be ascribed to ETG turbulence.

Ion temperature gradient modes (ITG) and trapped electron modes (TEM)
The ITG and TEM modes are long wavelength, electrostatic modes. The ITG mode is analogous to the ETG mode with η i = L n i /L T i ≈ 1 being a criterion for linear instability (with L n i and L T i being the ion density and temperature scale lengths). Thus, ITG modes are driven unstable by ∇T i and stabilized by ∇n i . The TEM instability threshold depends on several parameters, including ∇n and ∇T e [278,279].
ITG/TEM modes can cause significant transport in thermal as well as particle channels and are potentially dangerous modes. However, these modes can be suppressed by sufficient shear of the ExB velocity. Current understanding is that ExB shear is usually sufficient to suppress transport from these modes in present day devices and that this shear suppression enables the pedestal to exist [18,20,280]. Nevertheless, some studies show the possible existence of TEM or ITG turbulence under certain circumstances.

Evidence for existence of ion scale electrostatic transport early in inter-ELM cycle. Experiments in ASDEX
Upgrade and DIII-D may show evidence of transport from ITG/TEM modes in the pedestal region for a brief period, during and following an ELM crash. These phenomena last for a few milliseconds as the pedestal recovers from the ELM.
In ASDEX Upgrade, time-dependent power balance analysis of the pedestal has been performed with very high time resolution over an ELM cycle [116]. This analysis used ion profiles measured with 65 µs time resolution. At the onset of an ELM, the ion transport increased much above neoclassical in the pedestal. The transport returned to neoclassical values within ∼3-4 ms. It is plausible that ion scale electrostatic turbulence, due to reduced E × B shear, was present during this period and contributed to enhanced ion thermal transport.
In DIII-D, measured density fluctuation amplitudes at wavelengths expected for ITG were very high near the pedestal foot, immediately after an ELM crash. These fluctuations subsided as E × B shear increased during the ELM recovery [193]. TGLF [281] calculations show that ITG modes are consistent with the observations. GENE simulations have been performed early in recovery from an ELM crash in ASDEX Upgrade [237]. Analysis was done as ∇n e rapidly increased before the full recovery of the E r profile. Nonlinear simulations show that TEM was the dominant mode across the pedestal and may have generated most of the particle transport. There is uncertainty in the magnitude of this transport because the simulated transport was sensitive to small changes in ∇n e . TEM turbulence was present for simulations later in the ELM cycle but was likely suppressed by rising E × B shear.

Evidence for ion scale electrostatic transport for
pre-ELM conditions. Recent research provides evidence that ion scale electrostatic turbulence causes enhanced transport late in the inter-ELM period of some pedestals.
GENE simulations of JET-ILW discharges find evidence of ITG causing substantial transport and potentially accounting for the reduced confinement observed in these plasmas [277]. The onset of ITG is correlated with increase of η i due to an outward shift of the pedestal density gradient relative to the temperature gradient. Reduced E × B shear rates at low ρ * also help to enable the ITG turbulence.
As discussed in section 3.2.3, the ion power flux in DIII-D increased above neoclassical as ν * was decreased. CGYRO simulations for a discharge with pedestal top ν * ∼ 0.1 are shown in figure 38. The simulations identified ion electrostatic modes (unnamed) as the source of the dominant heat loss for ions and electrons in the steep gradient region. Neoclassical transport for ions was significant but smaller than turbulent transport. Ion scale density fluctuations in the pedestal were larger at low than at high values of ν * , consistent with expectations for ion scale electrostatic turbulence from the simulations.
In a separate DIII-D study, density fluctuations at intermediate scales develop as pedestal gradients increase early in the recovery phase after an ELM [193]. The intensity of these fluctuations varies with T i /T e as predicted for TEM by theory and simulations [279]. TGLF modeling also supports the identification of these fluctuations as being due to TEM [193]. 5.8.3. Evidence for ion scale electrostatic mode as source of ECM. As discussed in section 5.2.7, a mode with a strong electrostatic character, called the ECM, is commonly observed in EAST in both ELM-free and ELMy conditions. Linear GYRO simulations of an ELM-free discharge exhibit a mode whose characteristics closely match several measurements, including mode frequency and structure, dispersion relationship and magnetic versus electric potentials [198]. A scan with GYRO shows that the linear growth rate γ has a strong dependence on ν * e with γ peaking near ν * e ≈ 2.2. This dependence is consistent with observations that lithium injection increases ν * e and can destabilize the ECM [198,203]. This dependence on ν * e helps lead to an identification of the mode as a dissipative trapped electron mode [198].

Summary
There have been few reports of ion electrostatic turbulence causing significant transport in the pedestal of current machines. This situation is consistent with the paradigm that these modes are normally suppressed by E × B shear. This interpretation is supported by theory and simulation [280].
However, there is also evidence that these modes exist in some discharges of present day machines, including JET discharges with its ITER-like wall, DIII-D in a low collisionality regime and EAST discharges with an electrostatic edge mode. The JET-ILW discharges provide the closest approach to expected ITER pedestals of current machines. Theory and simulation predict that ion scale electrostatic modes will occur and be dangerous in ITER pedestals [280]. Thus, it is important that these modes be understood in current machines in order to enable improved predictions for their effects in ITER pedestals.

Pedestal models
Since the pedestal plays such an important role in the H-mode confinement, it is vital to be able to predict its characteristics to plan and optimize experiments in existing devices and to design future tokamak fusion reactors. Transport and radiation determine the profiles from the core region to the pedestal and the resulting profiles can be solved with reasonable accuracy [282][283][284], especially in cases where the transport is stiff. However, the pedestal is significantly more complicated.
In the case of ELMy H-mode, unlike the core, the pedestal is not in steady-state. Instead, it cycles through inter-ELM phases during which the pedestal builds up, followed by ELM crashes which relax the profiles. This cyclic nature makes the profile prediction significantly more difficult than in the core, where it is sufficient to find the steady state profiles that satisfy the power balance between the sources and transport. Furthermore, as described in section 3.1 the sources in the pedestal are generally more difficult to measure and model. At the moment, no model exists that can predict and simulate the full physics of the ELMing pedestal from first principles.

Description and validation of models
The problem of pedestal prediction can be simplified. Rather than simulating the entire pedestal evolution through the ELM cycle, we can strive to predict the pedestal structure at the end of the ELM cycle, i.e. just before the ELM crash occurs. The reason this approach simplifies the situation is that, as shown in section 4, the Type I ELMy pedestals are close to the ideal MHD peeling-ballooning mode stability limit at the end of the ELM cycle. Thus, this limit can be used as one of the constraints for a predictive model. 6.1.1. EPED model. However, the peeling-ballooning limit is mainly a constraint for the pressure gradient and is not sufficient to determine the pedestal height. A unique solution for the pedestal pressure width and height is obtained when the peeling-ballooning limit is combined with the width scaling ∆ = c(β ped θ ) 0.5 , based on a model for KBM. The coefficient c is ∼0.1 and is obtained from experiment or a theoretical model, as discussed below. (Density, temperature and pressure profiles are modeled with the same width). This is the EPED model, developed by Snyder et al [67,285]. Since the peeling-ballooning stability for a given pressure gradient depends on the plasma shape, collisionality and core pressure (through Shafranov-shift), the inputs EPED requires are the shape of the plasma, plasma current, toroidal field, pedestal density and global β. The width scaling in EPED is supported by experimental scaling, discussed in section 2.5.6.
The model works by generating a set of equilibria with different pedestal widths, all fulfilling the width and global constraints set by the input. The peeling-ballooning stability of all the equilibria is solved, yielding the growth rate as a function of the pedestal width. The solution of the prediction is the width and height combination that corresponds to the growth rate matching the threshold criterion, γ > ω * max /4 where ω * max is the maximum of the diamagnetic frequency in the pedestal.
The resulting EPED model [67,285] is very powerful as it requires only a few inputs and avoids the problem of solving the complicated transport processes during the ELM recovery. Most of the computational time is spent on the linear MHD stability calculations that are relatively fast compared to nonlinear gyrokinetic turbulence simulation. Thus, it is possible to validate the model with large pedestal databases. This was done for pedestals on six tokamaks, with the lowest to highest measured pedestal pressures spanning a factor of 70. As shown in figure 39, the model agrees with the data within ±20% nominal error bars. Data from C-Mod are close to the predicted pedestal pressure for ITER, shown with a black diamond.
The original version of the EPED model, sometimes called EPED1, used a value of c = 0.076 in the formula for pedestal width. A revised version of the model, called EPED1.6, replaced the analytic width with the use of ballooning stability calculations and a criterion that the pedestal was unstable to ballooning modes over half of its width [285]. The two versions of EPED give similar results. Calculations with model equilibria in ref [285] showed that the pedestal pressure from EPED1.6 was nearly identical to the pressure from the analytic formula, using a value of c = 0.089.

IMEP model.
An alternative to the EPED model for predicting pedestal height is the IMEP model by Luda [284,287]. This model assumes that the pedestal transport is stiff, leading to the inverse T e scale length ⟨∇T⟩/T e,ped being fixed to 0.5. This value is obtained from empirical observations on ASDEX Upgrade, JET and DIII-D [288]. Here the average temperature gradient is defined as ⟨∇T⟩ = (T e,ped − T e,sep )/∆ ped , where ∆ ped is the pedestal width.
This constraint replaces the width scaling in EPED. As in EPED, it is used to generate a set of equilibria with different widths that fulfill the stiffness constraint and then the prediction is the one that is at the peeling-ballooning stability boundary. The model has predicted ASDEX Upgrade pedestals with less than 10% error. It has not yet been tested on other tokamaks [284].

Limitations to models.
We will briefly discuss limitations of these models. An important situation is pedestals that do not reach the peeling-ballooning limit. In such cases, the two models discussed here should not be expected to predict the pedestal height. Important examples of this limitation are JET-ILW discharges with high gas fueling. These discharges do not reach the peeling-ballooning limit (discussed in section 4.4) and the pedestal pressure is lower than predicted by EPED [72,76,80,82,83].
A possible limitation for EPED is a pedestal in which there is a significant outward shift of the n e profile relative to the T e profile. The EPED model assumes that the T e and n e profiles are colocated. In addition, EPED uses a fixed value for the ratio n sep e /n ped e . Also, the model uses the assumption that the average of n wid e and T wid e is a good approximation for the pressure width. For a significant density shift, these assumptions might break down sufficiently to reduce the accuracy of EPED. Moreover, as discussed previously, the density shift might cause increased transport, possibly due to increased values of η e or η i . If such an increase were large enough, we would no longer expect the KBM width constraint to work well.
There is certainly evidence that the EPED width scaling becomes less reliable for high gas puffing which typically leads to the density shift. Figure 40 is an example from JET-ILW which shows that at low gas fueling, the pedestal width is in agreement with the KBM constraint of EPED (shown by dotted line) [41]. However, as gas fueling increases, the width systematically becomes larger than the prediction. This increased width is a signature of an additional source of pedestal transport not in the EPED model.
The effect of the density shift on pedestal width scaling remains an active area of investigation.

Self-consistent core and pedestal
While the model validation confirms that EPED can accurately predict pedestals in a large variation of parameters, it must be noted that two of the input parameters (n ped e and global β) are not known before the experiment and should be predicted along with the pressure (or temperature) pedestal height. The core profiles (and thus global β) can be solved self-consistently with the pedestal prediction by combining the pedestal prediction with a core transport model. This is done for validation purposes for DIII-D [290], JET [172] and ASDEX Upgrade [287]. Each method uses a different core transport model. However, the core transport tends to be stiff (∇T/T ≈ constant through most of the core) and the pedestal is not very sensitive to small changes in global β. As a result, even though the simulated core profile details may differ from the experiment, the pedestal prediction tends to be almost as accurate as if β were an input.

Pedestal density models
The pedestal and separatrix densities are a much more complicated problem as they depend on the unique features of each tokamak such as wall material, wall and divertor geometry, pumping and the details of gas fueling and pellets. As the main source of the particles is in the pedestal itself and is affected by ELMs, it becomes very difficult to solve from first principles or produce a model that is universal to all devices. The problem is mitigated by the fact that the density can be controlled to some extent with a feedback controller using gas puffing rate and pellets as actuators.
However, there are some attempts to model the density profile by semi-empirical models that have a simplified physics model for the density with a few free parameters that are fitted to a particular experiment. The Europed model [291] incorporates a neutral penetration model that is based on the idea that the density pedestal height is inversely proportional to its width [292]. With a small correction for fueling and triangularity, Europed has predicted JET pedestal densities in a wide range of discharges within 17% of the experiment [172]. The IMEP model solves the separatrix electron and neutral density from an SOL transport model that includes the gas puff rate and pumping with coefficients fitted to ASDEX Upgrade experiments [284,287]. The model then uses a similar neutral penetration model as above to calculate the ionization within the pedestal. With this source, it uses a transport model based on a combination of neoclassical and turbulent transport (proportional to the heat transport) to solve the pedestal density.
The model has been very successful for predicting ASDEX Upgrade pedestal density as well as other parameters, as demonstrated in figure 41. Modeled pedestal values for n e , T e , T i and core n e agree within less than a mean relative error of 10% with experimental values from an ASDEX Upgrade database [284]. The dataset includes 50 examples which largely cover the ASDEX Upgrade parameter range.
Both models discussed here apply only to the device where fits were done for empirical parameters. Thus, both models are unreliable for predicting other devices such as ITER. Nevertheless, they provide hope for the development of more complete pedestal models.

Pedestal turbulence models
Turbulence simulations are now being used to develop reduced pedestal models. Simulations of DIII-D discharges with CGYRO have been used to develop analytic models for pedestal T e and n e profiles, limited by ETG modes [275]. A database of GENE nonlinear simulations from DIII-D, JET, C-Mod and ASDEX Upgrade has been used to develop reduced models for electron thermal transport, driven by ETG turbulence [293]. In another project, GENE simulations have been used to develop a reduced model to predict the frequency spectra of MTM modes [247].
Such models can be components of more complete reduced models of pedestal turbulence and transport.

Super H-mode
The most interesting discovery made using the EPED model is the so-called super H-mode. Usually, the EPED solution for given parameters is unique. In a scan from low to high pedestal density, the limiting MHD mode changes gradually from a low-n peeling mode to an intermediate-n peeling-ballooning mode to a high-n ballooning mode. The maximal pedestal pressure does not vary significantly along the scan. However, in very highly shaped plasmas, a path opens for the peeling branch of the limiting instability to extend to high density and to allow very high and wide pedestals. This corresponds to the stability boundary in figure 23 extending to very high values of α at high values of pedestal bootstrap current.
In these extreme cases the EPED solution becomes multivalued as there is another valid solution at low pedestal height and width where the high-n ballooning mode is the limiting mode. Depending on the trajectory of the discharge, both solutions can be reached. The low pedestal ballooning-mode solution is the typical high collisionality solution, which can be reached without any plasma shaping. However, the low-n peeling mode solution with a very high pedestal pressure was found on DIII-D after its existence was predicted using the EPED model [294]. It has since been predicted and found on Alcator C-mod [286]. It is also predicted to be accessible in ITER which may have easy access to peeling limited pedestals due to having low collisionality.

Summary
Reduced predictive models have been developed to predict pedestal parameters. The EPED model shows good success in predicting pedestal pressure for a range of current tokamaks when the pedestal is at the peeling-ballooning limit. Experience with the model demonstrates that more complete predictive pedestal models require information both from core and edge physics. Self-consistent coupling of EPED to reduced predictive core transport models has solved this problem at the core-pedestal interface.
Two models have been developed for predicting the pedestal density, the Europed model used on JET and the IMEP model used on ASDEX Upgrade. Europed and IMEP are both coupled to core models. Both models successfully predict pedestal pressure and density, with some machine-specific parameters, but without input of values for core stored energy or pedestal density.
Results from gyrokinetic simulations have been used to model the effect of ETG turbulence on the pedestal as well as to predict frequency of magnetic fluctuations from MTM modes.
These models demonstrate very significant progress in understanding and predicting pedestal performance.

Summary
The goal of this paper is to review current understanding of important physics that forms the H-mode pedestal structure. As in any magnetic confinement system, pedestal structure (characteristics of pedestal density, temperature and pressure profiles) is determined by a self-consistent solution of sources, transport and MHD limits. Using a wide research base, we discuss evidence for how a number of physics processes may be contributing to the formation of the pedestal.
• Heat sources for the total power flowing into the pedestal are well understood. There are potential uncertainties about the power split between electrons and ions. • The particle source is poorly known.
• MHD stability imposes limits on the achievable pressure gradient and height. We can compute the limits for the very common peeling-ballooning modes. Some pedestals are limited below the peeling-ballooning limit. These phenomena are poorly understood. • There are multiple physics processes, primarily neoclassical and turbulent, that can contribute to transport in the pedestal. The ratio of transport from different processes is not fixed. The role of various processes can vary during an inter-ELM period, in different parts of the pedestal, as well as with discharge scenario. • Neoclassical processes are important for ion thermal transport and likely contribute to some particle transport.
Next, we will look at some findings regarding turbulent transport in the pedestal.
• Pedestals are typically operating near linear threshold for onset of several modes, including MTM, ETG, KBM and possibly ITG/TEM. Thus, modeling of experiments is sensitive to the exact profiles being used and computation of transport can have large uncertainties. • MTM and ETG are present in many pedestals at some level and are good candidates for electron thermal transport. • Ion electrostatic modes (e.g. ITG, TEM) are usually sufficiently suppressed by ExB shear in most current operating scenarios to not drive important transport. Such modes may drive significant transport (ion thermal and perhaps other channels) in some ITER-relevant regimes. • A model based on KBM provides a good prediction of the pedestal width (average of electron temperature and density widths) in a wide range of conditions and machines. There remains a conundrum about the role of KBM, since the evidence for its presence is mixed. • Particle transport is poorly understood. Particle source measurements and possibly simulation improvements are needed to address this problem. • Reduced models are making good predictions of pedestal pressure and density, subject to limitations previously discussed. Pedestal models have been coupled to core models and in one case, to an edge model.

Needs for further research
The goal of pedestal prediction with more comprehensive models highlights important needs for further research. At the highest level, we propose the following four needs.
• The most compelling need is to definitively determine how much transport is driven by the main candidates for pedestal transport. Ideally, measurements of transport would provide much of the solution. Since this approach is highly challenging, the most feasible approach is combined experiment/simulation studies which quantitively compare as many different types of measurements to modeling as possible. • Measurements of the particle source and models for particle transport are required to develop understanding of particle transport. • Reduced models that compute pedestal density as well as pedestal pressure for a range of devices are needed to advance predictive capability. • Models are needed that operate beyond the Type I ELM operating regime, as that is not where ITER and future reactors will be able to operate.
The following combined experimental/simulation approaches may be very powerful to advance understanding of mechanisms for pedestal transport.
• To identify fluctuations and understand the role of turbulent transport, we need quantitative comparisons of simulations to as many fluctuation properties as possible, e.g. fluctuation intensities, frequency spectra, with wave number, etc • Ratios of normalized intensities for fluctuations in different quantities may be very useful for identifying turbulent processes. • Uncertainties of experimental as well as simulated power flows in ion and electron channels are important for validation of models. • Transport mechanisms outside the usual suspects should be considered. For example: ion orbit loss and finite width orbit effects may drive ion heat and particle transport at low collisionality [144,295,296]; low amplitude MHD activity might be a source of transport in multiple channels [181,249]; most measured fluctuations are unidentified and some may be signatures of transport processes. It should not be forgotten that ELMs transport some heat and particles.
We suggest experimental measurements that would aid in the identification of transport processes.
• Fluctuation measurements at wavelengths where ETG is generated would be very valuable to validate the role of ETG. • Measurements with error bars of the propagation direction of fluctuations in the plasma frame are important to identify fluctuations. • Accurate measurements of current density are highly desirable for many reasons, e,g., improving the benchmarking of neoclassical codes, looking for deviations from neoclassical processes, improving measurement of the q profile and magnetic shear.
We suggest simulation efforts that would aid in the identification of transport processes.
• Simulation predictions of the frequencies and wavelengths where KBM should be observable would be very helpful for experiment in looking for signatures of these modes. • Simulations which include multiple processes in the pedestal provide the most accurate evaluation of transport. • Simulations that cross the separatrix may ultimately be needed for full first principles models.
Due to continued combined experimental, theoretical and simulation research, the pedestal is reluctantly yielding its secrets. We (the research community) now understand some of the basic physics forming pedestal structure and we have very good candidates for processes that control pedestal transport. This understanding has developed predictive capability of some elements and the prospects for improving this capability are very good. We eagerly look forward to the day when models predict the pedestal 'weather' as their meteorological cousins currently predict the atmospheric weather.

Data availability statement
The data that support the findings of figure 1 are available from the corresponding author upon reasonable request. No other new data were created or analysed in this study.

Acknowledgments
The preparation of this review, including the experimental, numerical and theoretical material provided by the DIII-D program, has been supported by the U.S. Department of Energy, Office of Science, Office of Fusion Energy Sciences, using the DIII-D National Fusion Facility, a DOE Office of Science user facility, under Award DE-FC02-04ER54698. This work has been partly funded by the EPSRC Energy Programme (Grant Number EP/W006839/1). We gratefully acknowledge discussions with Drs B A Grierson, J Chen, S R Haskey, A Kirk, F M Laggner, A W Leonard, C F Maggi, T H Osborne, A Y Pankin, C C Petty, E Viezzer, X Q Xu, H Q Wang and Y Ye.

Disclaimer
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