The role of isotope mass on neutral fueling and density pedestal structure in the DIII-D tokamak

Experimental measurements on DIII-D of hydrogen neutral penetration lengths ( λn0 ) on the high field side (HFS) are longer by a factor of 2 than for deuterium consistent with the thermal velocity ratio for neutrals at the same temperature (vthH/vthD=2) . This ratio is constant for both low and high pedestal electron density. At low pedestal density (ne∼4×1019 m −3) , the neutral penetration length is greater than the density pedestal width for both isotopes, and the additional 40% increase of neutral penetration in hydrogen widens the pedestal by the same amount. As the density pedestal height increases (ne∼6×1019 m −3) , the neutral penetration lengths drop below the density pedestal widths for both isotopes, and the increased penetration of hydrogen has no increased effect on the pedestal width compared to deuterium. Extrapolating to future reactor-relevant high electron density pedestals, the isotope-mass change in neutral fueling on the HFS from the deepest neutral penetration of hydrogen, to the shortest neutral penetration of tritium will be negligible (0.2–0.4 cm) in comparison to estimates of the density pedestal width (6–8.5 cm).


Introduction
In this paper, we compare neutral density decay lengths for dimensionally matching deuterium and hydrogen discharges Original Content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence.Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. which show the expected isotope difference of a 40% deeper penetration for hydrogen with respect to edge neutral penetration inside the separatrix.The data supports the premise that the pedestal electron density structure is not purely determined by the ionization of edge neutrals.Understanding the isotope-mass effect on fueling is crucial because the development and operation of tokamaks as fusion pilot plants relies heavily on the operation of multiple plasma species, including hydrogen, deuterium, tritium, and helium [1,2].Generally, the 'isotope effect' refers to the increase in confinement with increasing isotope mass, a reversal of gyro-bohm predictions [3].However, the choice of hydrogenic isotope also has a strong influence on the power threshold for the L-H transition, pedestal structure, and gas through-put [4][5][6][7][8][9].As a consequence, the various aspects of isotope effect have a direct impact on many engineering aspects of future plants, such as the required auxiliary heating power, tritium inventory, and size of plant if we extrapolate from current devices [10].To distinguish the aspect of the isotope effect we are studying, for the rest of this paper, we refer to the 'isotope-mass effect' on neutral penetration and its resulting impact on the radial dependence of ionization between hydrogen and deuterium in the edge.The purpose of this study is to develop models for neutral fueling and the edge density pedestal structure in Hmode.
A recent theoretical overview paper focused on particle transport in JET isotope experiments [11], and a wider study in multiple devices for both L-and H-mode [12] reach the same conclusion: the dominant impact of the isotope effect on confinement is linked to the plasma edge.To illustrate, in previous L-mode JET isotope experiments, core turbulent transport is dominated by ion temperature gradient (ITG) unstable modes, and the gyro-Bohm normalized thermal energy confinement time and the core plasma heat diffusivity are identical in hydrogen and deuterium within error bars [13].Core profiles in Lmode and H-mode with the same dominant turbulent modes have will have their gradients clamped at similar values [12], leaving a mechanism in the edge to cause the isotope effect transport differences.Separately, in regimes where ITG turbulence is not dominant, and thus transport is not considered stiff in the plasma core and a large deviation from gyro-bohm scaling is observed, gyrokinetic modeling demonstrates that non-adiabatic electron and electron-ion heat exchange in the edge may be playing a role [14,15].This result is consistent with observations in JET of stiff gradient scale lengths (L T = T/∇T) for core temperature profiles and a weak negative isotope mass dependence in the core [6,12].However, examining the isotope effect in the edge is complicated since in future fusion pilot plants the edge will differ substantially from current day devices.This requires us to develop a fundamental understanding of the various physics contributions, of which, neutral-plasma interactions have been under-diagnosed [16].
While the isotope effect arises from the edge, transport is not the only mechanism involved, and this work focuses on the other physical mechanism in the edge which is altered by the isotope mass: neutral fueling.For neutral particles at the same temperature, as the particle mass increases, the neutral thermal velocity decreases as does the mean free path of the particle in a plasma before ionizing.Comparing hydrogen to deuterium, the neutral velocity is 41% higher 41 and comparing tritium to deuterium the neutral velocity is approximately 19% lower v T /v D = √ 2/3 ∼ 0.81.In section 3 we directly measure neutral particles in the edge of DIII-D and show a clear isotope mass effect of a 40% increase in penetration between hydrogen and deuterium.This effect is present for both low and high electron pedestal density discharges, and we also show how the known poloidal asymmetry [17] in neutral density complicates the penetration measurements between the high field side (HFS) and low field side (LFS).
The Madhavi model [18][19][20] is one method used to predict density pedestal structure on future machines such as ITER [21].The model stipulates that the density pedestal width (∆ ne ) is set by the neutral penetration length (λ n0 ) and a factor to account for flux expansion at the fueling location.Earlier work on DIII-D [22] using the Mahdavi model demonstrated the deuterium density pedestal width could be predicted well over a range of pedestal densities using the analytic estimate of neutral decay length from a slab plasma and ion-temperature neutrals [20].However, studies on Alcator C-Mod at high electron pedestal densities (n e > 10 20 m −3 ) show the measured λ n0 is lower than both the analytical values of the neutral decay length and the electron pedestal density width [23].Furthermore, when scaled to JET, this model was shown to be in good agreement with deuterium data, yet it was unable to accurately model hydrogen discharges [24].These studies weaken the model's connection between the neutral scale length and the pedestal width.However, the model also predicts the electron density pedestal width is inversely proportional to the electron density height ∆ ne ∝ 1/n ped e , and this result has some support in the C-Mod and DIII-D data with caveats such as widening from lower I p (poor confinement) or transition to different confinement states such as EDA Hmode.In section 4 we use isotope neutral penetration differences to test the model and show that neutral penetration has a stronger influence at low pedestal densities, but as discharges move to higher DIII-D and C-Mod levels of pedestal density n ped e > 0.7 − 1 × 10 20 m −3 , neutral penetration cannot solely account for setting the pedestal width, and other mechanisms must take over.
The Mahdavi model also assumes the neutrals have the temperature of ions at the separatrix.By back-calculating the temperature given our decay length measurements we infer much lower neutral temperatures of 0.5-7 eV which are are inconsistent with the assumption of ion-temperature neutrals.A new paper by Saarelma et al [25] attempts to reconcile the model and JET data by extending the model to include a population of charge exchange neutrals and allow for the more realistic boundary condition of finite core density gradients.The new model is able to accurately predict the decrease in density pedestal height for hydrogen given a test set of low density pedestals (n ped e < 5 × 10 19 m −3 ) where the neutral influence is stronger.However, both the old and new models remain sensitive to the separatrix electron density which remains a user-supplied input, therefore reducing the model's predictive capacity.An active area of research is focused on integrating scrape-off layer (SOL) and pedestal models to attempt to remove the separatrix density as an input.
This paper leverages the newly installed LLAMA (Llama is the Lyman Alpha Measurement Apparatus) diagnostic on DIII-D to analyze highly resolved radial and temporal measurements of neutral hydrogenic particles on the HFS and LFS simultaneously [26,27].The LLAMA measurements allow us to directly quantify the neutral penetration for hydrogen and deuterium and compare these values to those used by the models.To do this, in this study we examine the isotope mass effect on neutral fueling and density pedestal structure using two pairs of dimensionally matched hydrogen and deuterium discharges, one pair with a low electron density pedestal and the other with a high electron density pedestal.Section 2 will discuss the details of the dimensional matching experiment and an overview of the discharges, section 3 directly compares the isotope-mass effect on neutral density decay lengths inside the separatrix, and section 4 examines how the isotope-mass driven changes in neutral fueling affect the density pedestal structure.

Experiment design and analysis
In this paper we focus on comparing two pairs of dimensionally matched hydrogen and deuterium discharges shown in figure 1(a).The first pair referred to as 'low density' with line averaged electron densities of n e ∼ 4 × 10 19 m −3 , and the second pair is referred to as 'high density' with n e ∼ 7 × 10 19 m −3 .The toroidal magnetic field in all discharges is set to B T = −2T with ∇B × B drift direction towards the X-point.The plasma current in the low density discharges is I P = 0.8 MA, resulting in a safety factor at the 95% poloidal flux surface of q 95 ∼ 6.The plasma current in the higher density discharges is I p = 1.5 MA, reducing q 95 ∼ 3.1.To achieve a dimensional match in n e and T e for each pair, the heating power is adapted to match the pedestal temperatures using both NBI and ECH heating.The low density hydrogen discharge (dark red) has 5.8 MW of NBI heating and the high density hydrogen (pink) has 6.4 MW.As required power to remain in H-mode is lower in deuterium compared to hydrogen, the deuterium discharge at low density (dark blue) discharge only had 2.25 MW NBI power and the high density deuterium (light blue) discharge had 4.2 MW.The ECH heating location for the low density discharges is located at ψ n = 0.3 with 1.5 MW injected in both hydrogen and deuterium.The high density deuterium has 1 MW ECH injected at ψ n = 0.7 and there is no ECH input for the high density hydrogen discharge.Similarly, the gas injection was varied as shown in figure 1(d), to match the electron density and was typically higher for deuterium due to a recent boronization.All discharges operate in an adapted ITER Similar Shape to optimize LLAMA diagnostic coverage and keep the outer strikepoint close to the pump location for density control as shown in figure 1(e).For all plots in this paper the colors represent the relationships between the discharges, low density discharges are darker colors, and high density discharges are lighter colors, while the red hues (dark red and pink) indicate hydrogen and the blue hues (dark blue and light blue) indicate deuterium.
To provide matching pedestal conditions, we chose specific time windows for each discharge as indicated by the shaded boxes in figure 1.The electron density (figures 2(a) and (d)) and temperature 2(b) and (e)) measurements from Thomson scattering (TS) [28] are fit with a hyperbolic tangent function [29,30] and the carbon ion temperature from charge exchange recombination (CER) [31] is fit with a spline as shown in figures 2(c) and (f ).To avoid the influence of edge localized modes (ELMs), only experimental measurements from TS and CER during the last 80%-99% of the ELM cycle are included using appropriate time windows (ranging from 300-600 ms in length) where conditions are steady-state, as shown in figure 1(a).The separatrix location for all discharges is set where the electron temperature reaches 80 eV, a typical value from power balance [32].The pedestal electron density and temperature as well as the ion temperature for both the low density and high density cases agree within experimental error (10%-15%) for hydrogen and deuterium.The electron temperature and density gradients for hydrogen and deuterium at high density are similar while at low density the hydrogen discharge has a notably wider electron density and temperature pedestal.An overview of both pedestal height (n ped e & T ped e ) and width (∆ ne & ∆ Te ) of the tanh fit for each discharge as well as dimensionless parameters defined below are shown in table 1.
Dimensional matches prevent the matching of dimensionless parameters that would guarantee similar underlying plasma transport dynamics [3,33].The dimensionless gyroradius (ρ * = c √ mi Ti eaB with m i the ion mass, T i the ion temperature, B the total magnetic field, and a the minor radius) cannot be matched without altering the toroidal magnetic field, and the ratio (ρ * D /ρ * H ) for perfectly matched plasmas is directly proportional to √ 2 ∼ 1.41) as a result of the difference in mass.For the high density discharges, the ratio (ρ * D /ρ * H = 1.31), and for the low density discharges, the ratio (ρ * D /ρ * H = 1.47).By dimensionally matching n e , T e , and T i we were able to match a subset of dimensionless parameters which are independent of isotope mass including where n tot and T tot are the sum of the electron and ion contributions to density and temperature and B θ is the poloidal magnetic field [3].β θ specifically is used to demonstrate similarity when comparing to the scaling of pressure pedestal width (∆ Pe ∝ √ β θ ) from the EPED model [34,35].The collisionality ν * ped = q 95 Rϵ −3/2 λ −1 e (where the inverse aspect ratio is ϵ = a/R, and λ e = v Te τ e is the mean free path of electrons) [36] is also matched, and q 95 are similar.In addition to these dimensionless parameters, we also calculated the dimensionless η e = L ne /L Te which is the ratio of density to temperature scale lengths (L x = X/∇X) calculated at the density symmetry point where the density gradients are largest.The much lower η e for the low density discharges suggests there may be transport differences between the low and high density pairs [37][38][39].However, the similarity within the pairs is more critical to this study where transport is beyond the scope of this paper on the effect of isotope mass fueling.
The pedestal pressure structure may be explained by the combination of peeling (current driven) modes and ballooning (pressure driven) modes represented by the Peeling-Ballooning (PB) stability diagram [41].Stability diagrams calculated with the ELITE code are shown in figure 3(a) with the low density discharges (red and blue rectangles) both peeling limited and the hydrogen discharge (red) experimental point having a lower normalized pressure gradient due to its wider pedestal.The high density discharges (light blue and pink) are both in the stable region near the upper right corner where they are potentially peeling or PB limited.The experimental point for the hydrogen discharges is notably deeper in the stable region compared to the deuterium discharge which may be attributed to the lower diamagnetic stabilization from decreased ITGs in hydrogen [42] partially due to the lower ion dilution (lower Z eff ).The primary function of the stability diagram in this case is to demonstrate that for all the discharges in this study that despite the slightly different shapes of the Previous work on ASDEX and JET has shown that hydrogen typically has a factor 1.5-3 higher frequency ELMs than deuterium [7,43,44].The ELM behavior, shown in figure 3(b), also varies between hydrogen and deuterium with f ELM in hydrogen typically being a factor of 1.2-2 faster than deuterium.In our study, the ELM frequency ratio between hydrogen and deuterium is difficult to quantify due to the extremely large error bars where the low density hydrogen discharges has an ELM frequency of f ELM,H = 29 ± 8 Hz and the deuterium discharge has an ELM frequency of f ELM,H = 27 ± 28.The frequency is the average of the inverse waiting times for each ELM and the uncertainty is the inverse of the standard deviation.This applies to all the discharges, the low density discharges are barely above the LH threshold and therefore have a very low natural ELM frequency, the high uncertainty (and different ELM sizes) is likely due to sawtooth heat pulses causing small ELM crashes.At higher densities, the increased heating power increases the ELM frequencies of f H ELM = 83 ± 40 Hz and f D ELM = 25 ± 8 Hz.The changes in ELM frequency are similar to those found in other studies which have concluded they are not sufficient to explain the lower confinement and particle transport in hydrogen from the isotope effect [7].Furthermore, by conditionally averaging around them, the ELM differences do not affect the results in this paper.

Comparison of neutral densities between hydrogen and deuterium
The LLAMA diagnostic measures ionization profiles inside the last closed flux surface both on the HFS and the LFS, using Lyman-α radiation as shown in figure 1(e).A significant advantage of this diagnostic over the Balmer-α filterscopes [45] is the lack of parasitic line radiation from molecular ionization and near-zero wall reflections contributing to the signals.
The LLAMA measurements are taken during the same time windows as the pedestal profiles (see figure 1(a)) and similarly limited to the last 80%-99% of the ELM cycle.The brightness is tomographically inverted along the tangency radius to infer the local emissivity [26,27,46].The ionization source term (S) is calculated using [46]: where the emissivity E ly−α is in units of sr is the ADAS Photon Emissivity Coefficient for excitation, and SDC 2→1 is the ADAS Effective Ionization Coefficient [47].
Both coefficients in the equation ( 1) are a function of the electron temperature and density.The electron density can vary poloidally in the SOL as has been shown by previous edge modeling and experiments [17,[48][49][50].Therefore, the electron density data taken by the TS system in the SOL provides less of a constraint on density at the different poloidal location of the LLAMA measurements.This increased uncertainty from TS data results in larger errorbars on the calculated ionization profiles shown in figure 4 than we would expect if the measurements were co-located.However, this inherent complication is not as critical for this paper where we are primarily interested in the ionization profile inside the last closed fluxsurface (LCFS) which are the neutral particles that contribute to fueling.

Ionization profiles
The LLAMA ionization measurements on the HFS and LFS show a notable asymmetry of the inboard (HFS)/ outboard (LFS) magnitude of the ionization source.Our discharges have a HFS/LFS ionization asymmetry ratio between 7-10 shown in figure 4 by the magnitude variation of the y-axis maxima for ionizations on the HFS (subplot (a)) compared to the LFS (subplot (b)) which is consistent with SOLPS simulations of DIII-D [51].The asymmetry exists in lower single null discharges with the favorable ∇B × B drift direction for H-mode access (towards the X-point) but the asymmetry disappears when the ∇B × B drift is unfavorable (away from the X-point) suggesting the importance of SOL flows [52].The source term in figure 4 shows there are clear differences between the isotopes.Qualitatively, for both the HFS and the LFS the peak in the source term is further inward for hydrogen compared to deuterium.The ionization source and neutral density measurements are provided in machine coordinates with respect to the separatrix location because neutrals are not bound to the magnetic field.The deeper ionization of hydrogen is generally consistent with a higher thermal velocity at a similar neutral temperature for hydrogen given its lower mass resulting in a longer mean free path before ionization.We observe that on the HFS the ionization peaks outside the separatrix, in the SOL, independent of plasma density and isotope.On the LFS, both deuterium discharges peak in the SOL while the hydrogen source peak has moved inwards.The highdensity HFS hydrogen source has a secondary smaller peak about 8 cm inside the separatrix which has been observed in many other discharges and for which the cause has not yet been determined [46,52].This inner peak is the subject of active investigation and outside the scope of this paper as it is not an effect specifically linked to isotopes.
Comparing the source terms quantitatively is difficult without at least 1-D transport modeling.Therefore, to allow direct comparison of the neutral behavior, building on previous analysis from Alcator C-Mod [23] and SOLPS modeling [17], we model the neutral density in the near SOL and pedestal as an exponential decay.The parameters of this exponential decay are directly compared to understand the influence of the isotope-mass in the next section.

Neutral density profiles and penetration length
The neutral density is calculated from the ionization source (1) by dividing by the ionization rate and local electron density: The neutral particle penetration into the pedestal can be treated analogous to light attenuation through an opaque medium.We approximate the neutral density profiles through an exponential fit with a decay length that is similar to the concept of light opacity [16,17].Because neutrals do not adhere to magnetic + ∆n e /2) are given in table 2.
field lines, it is appropriate to fit them in the real space radial coordinate at the LLAMA location x = R − R sep on the LFS and x = R sep − R on the HFS (in figure 5 the x-axis 'Distance from Separatrix').Because we are only fitting inside the separatrix, more negative values of x represent being increasingly deeper inside the separatrix.The neutral density is fit as an exponential decay: where n sep 0 is the neutral density at the separatrix, and λ n0 is the neutral decay length.We chose spatial ranges for fitting each discharge based on the pedestal location as shown by the extent of the black lines in figure 5.The majority of the error (highlighted regions) in this analysis comes from the noise in the LLAMA data.By using a conditional averaging method and mapping to the same EFIT the mapping error is reduced to the error on the EFIT which is on the order of 7 mm.Additionally, the separatrix position is fixed for all discharges at 80 eV which is a standard value used in DIII-D analysis from power balance [32].
We conducted a sensitivity analysis on the domain (x-axis extent) of the exponential decay fit and determined there was no change in λ H n0 /λ D n0 ratio on the HFS where the majority of the fueling is occurs.This analysis is required because the density pedestal shifts outwards with increasing fueling as seen on many tokamaks [53][54][55], and we need to ensure our choice of domain is not influencing the final results of our analysis.The first domain is the electron density pedestal width defined as n sym e − ∆ ne /2 < x < n sym e + ∆ ne /2 (where n sym e is the symmetry point of the hyperbolic tangent fit to the density profile).The second domain we choose is the separatrix to the top of the pedestal (described here as 'separatrix inwards') because all neutrals ionizing inside the separatrix contribute to the fueling of the plasma.The top of the pedestal serves as a standard delimiter to end the fit domain because the neutral density has decreased by 1-2 orders of magnitude, is reaching the end of the LLAMA inversion domain, and typically flattens out at a constant value.The specific extent of each discharge's domain on the HFS and LFS is shown in table 2. For each pair of isotopes, the fractional difference between the two fitting domains is similar; for example ∆ sep−inwards  This sensitivity analysis demonstrates that the ratio of 2 on the HFS is unaffected within error by the choice of domain.The underlying fits for the low density discharges increase by a similar fractional amount (37%) further validating our comparison of H-D pairs for this comparison.Investigation of the effects of LFS neutral penetration structure, specifically from turbulent transport, is fertile ground for for more research, but is outside the scope of this paper.
To remain consistent when comparing these data to past experimental work [23] and modeling [17], we will use the pedestal-width domain for analyzing the influence of the isotope mass effect on neutral behavior and its influence on the electron density pedestal structure.

Pedestal density structure
Models for the neutral penetration effect on the electron density pedestal, such as the Mahdavi model, suggests that ∆ ne ∝ λ n0 and therefore ∆ ne ∝ 1/n ped e .Previously, the only data available for neutral penetration lengths came from C-Mod [23] at high electron pedestal density (n e > 10 20 m −3 ).The LLAMA measurements of pedestals in DIII-D allow an expansion of this data to lower pedestal density range (n e < 10 20 m −3 ).
We examine the neutral penetration isotope differences on the pedestal density structure by comparing the LLAMA measured λ n0 to the analytical values.Assuming a slab plasma of a given electron density and temperature, the analytic value of the neutral decay length is given by where v th ∝ √ T n0 is the neutral velocity, T n0 is the neutral temperature, and ⟨σv⟩ coll is the collisional ionization rate coefficient taken from the KN1D [56] analytic model [57] and is a function of electron density and temperature at typical DIII-D values shown in figure 6(a).The values of the analytic λ n0 vs. T n0 for hydrogen at the extrema of the pedestal parameters in these discharges are shown in figure 6(b).
The neutral temperature used in the numerator of equation ( 4) which is obtained from the Mahdavi model is dependent on the ion temperature in the SOL [18].Ion temperatures for each species within the CER measurement capabilities are similar at the separatrix T C 6+ , sep ∼ 250 eV.Previous work on DIII-D through the Main Ion CER diagnostic has shown the main ion separatrix temperature is <50% of the CER C + 6 experiment measurement placing T i ∼ 100 eV [58].The CER ion temperature is not directly used in any analysis for this study; the point is to note that even estimates adjusted lower are still an order of magnitude higher than the neutral temperatures back-calculated in this work which are on the order of 0.5-7 eV.
The effect of T n0 on λ n0 for the pedestal extrema is shown in figure 6(b).The green point in figure 6(a) represents the choice of Rate Coefficient (⟨σv⟩ coll ) for the mean of all four discharges average pedestal density and temperature n ped e ∼ 4.75 × 10 19 m −3 and mean T ped e ∼ 300 eV .The green dotted line in figure 6(b) demonstrates analytic λ n0 given the chosen rate coefficient.This is meant to demonstrate that using the average pedestal quantities for the rate coefficient yields analytic λ n0 close to the smallest possible values if the high density pedestal parameters were used and does not unfairly bias the analytic value away from the measurements (figure 6(b) blue solid line).
Figure 7 shows the role of the neutral particles in setting the electron pedestal density structure decreases as the electron density pedestal height increases.The analytic values for hydrogen and deuterium (red and blue lines with shading) use 20 eV neutrals to remain consistent with previous literature [23], and the rate coefficient is the green point chosen in figure 6(a).The opacity of the pedestal is a measure of the influence of neutrals: The green line is the neutral penetration length with the selected green dot rate coefficient showing that the value of neutral penetration we are comparing to is not cherry-picked to be longer based on the rate coefficient chosen.The value of η ∼ 1 represents the transition where at lower opacity the neutrals penetrate deeper compared to the pedestal width and will potentially have a larger influence on the structure of the electron density pedestal and at η > 1 the neutral impact on the density pedestal diminishes.
At low density (dark red and dark blue) for the HFS (squares) the opacity for hydrogen and deuterium is 0.85 and 0.95 respectively.Visually, in figure 7 this corresponds to the neutral penetration lengths (solid squares) being larger than the density pedestal width (open squares).The results of wider density pedestals at lower electron density are consistent with results from ASDEX [8] and JET [7,44,53,59,60].
Moving to the high density discharges, the increased opacity decreases the influence of neutrals on the density pedestal width.The opacity for the high density discharges (pink and light blue) is 1.7 for hydrogen and 2.7 for deuterium both of which have higher opacity larger than η ∼ 1.On the plot this is represented by the open symbols being higher than the closed symbols at high density (for the HFS squares).
These data show that at low density neutrals penetrate beyond the pedestal and penetrate more deeply in H than in D; this may help to explain the formation of wider pedestals in H than in D at low density.However, at high density the neutral penetration distance on the HFS is much narrower than the density pedestal width in both species, suggesting that there is no clear role of the neutral penetration distance in setting the density pedestal width.For the low density discharge pair, the 40% increase in neutral penetration from the isotope velocity ratio (λ H n0 /λ D n0 = √ 2) for hydrogen corresponds to a 1.9 ± 0.9 cm longer neutral penetration length.This value is 1/2 to 2/3 of the density pedestal width and in absolute terms is on the order of the increased density pedestal width in hydrogen being 1.3 cm wider than deuterium.At high density, the absolute isotope mass driven difference between hydrogen and deuterium is only 0.4 cm which is less than 20% of the pedestal density width demonstrating that as we move to higher opaqueness pedestals, the influence of the neutrals decreases.
Finally, extrapolating to even higher n ped e , the isotope mass effect from neutral fueling will diminish even further.ITER pedestal densities are estimated to be on the order of n ped e ∼ 0.7 → 1 × 10 20 while the pedestal width estimates are usually linked to β θ and are on the order of 0.04 ± 0.02 ψ n [21].Given the 2 m minor radius for ITER, the pedestal width on the HFS is estimated to be in the range of ∆ ∼ 7 ± 1.5 cm.The estimated λ n0 on the HFS at the estimated ITER pedestal densities will be 0.6-1 cm with a corresponding √ 2 isotope-effect increase in hydrogen penetration of 0.2-0.4cm.This gives a final opacity estimate of η ITER ∼ 5 which is well above the threshold for neutral penetration to influence the pedestal structure and implies the isotopemass effect on neutral penetration will be minimal in future reactors.Squares should be compared to squared and circles to circles..

Discussion and conclusion
In this article we examine the isotope effect on fueling using direct measurements of neutral penetration in the pedestal of DIII-D.In particular, we test whether the pedestal electron width can be explained by the neutral penetration depth.Two pairs of dimensionally matched pedestals allow direct comparison of neutral penetration length across isotope species.We show that the hydrogen neutral penetration length on the HFS is λ H n0 ∼ 1.4λ D n0 consistent with the √ 2 velocity ratio for hydrogen and deuterium neutrals at the same temperature.Furthermore, we show on the HFS where there are an order of magnitude more neutrals, this ratio is not sensitive to the fit domain as the density pedestal shifts outwards with increasing fueling.These data are consistent with previous findings on C-Mod which show the neutral penetration length at high n ped e is lower than both the analytical estimate of λ n0 from a slab model and the density pedestal width [23].The role of the neutrals in setting the pedestal width changes with increasing n ped e ; at low density (opaqueness) λ n0 > ∆ ne and the 40% higher penetration correlates with wider pedestals in hydrogen.In contrast, at high density (opaqueness) the λ n0 > ∆ ne and similar widths for the density pedestal are observed for both isotopes.
An unknown factor in the pedestal density is impurities.Our deuterium discharges have a higher Z eff (2.5) than their hydrogen counterparts (1.5).This is most likely due to the factor of 10x physical sputtering yield from the increased mass in deuterium [61,62].The ion dilution from C 6+ (n i = n e (6 − Z eff )/5) gives main ion densities of 0.9n e in hydrogen and 0.7n e in deuterium.The increase in ion dilution for deuterium means that as similar fractions of beam heating go to the ions for both isotopes, the lower number of ions that require heating in deuterium will increase the ITG.This increase in ITG increases the ion diamagnetic stabilization (unstable when γ/(ω * i /2) > 1) where γ is the growth rate of the most unstable mode and ω * i = − ntor ene ∂pi ∂ψ is the ion diamagnetic frequency which is set by the n tor toroidal mode number and ( ∂pi ∂ψ ) the ion pressure gradient with respect to normalized magnetic flux.The increase in ion diamagnetic stabilization extends the stability region of the corner of the peelingballooning pedestal, in essence causing the carbon impurities to allow higher pedestal pressure in deuterium compared to hydrogen [42].Impurities also affect the resistivity of the plasma, and at the PB corner, work on JET has demonstrated that resistive effects from the isotope mass change are required to correct the differences in stability between H, D, and T [63].
We can see the effect of the impurities in our stability diagrams (figure 3) where the pink boundary is shifted left (lower pressure) from the light blue boundary while the low density discharges which are peeling limited only remain unchanged.However, this only affects the attainable pressure and does not alter the fueling results studied in this paper.For metallic wall machines (such as future reactors) the lack of carbon impurities removes this confounding factor.In studies on ASDEX and JET where the Z eff between hydrogen and deuterium is similar (∼1.5), the maximum pressure has been linked to the stability and shows good agreement between H and D with sufficient fueling [8].
Finally, extrapolating these results to deuterium and tritium behavior in a future reactor implies there will be little difference between the edge fueling for each isotope.The neutral velocity of tritium is ∼20% lower than that of deuterium, meaning the magnitude of the isotope-mass fueling effect will be half of the difference between hydrogen and deuterium.This result coupled with the higher density pedestals in a reactor reducing the neutral penetration, implies that isotope mass driven differences in edge fueling will be negligible.This conclusion is separate from any isotope induced transport changes which have been demonstrated to be consequential.Science, Office of Fusion Energy Sciences, using the DIII-D National Fusion Facility, a DOE Office of Science user facility, under Awards DE-FC02-04ER54698, DE-SC0019302, DE-SC0014264, DE-SC0020287 and DE-AC02-09CH11466.

Disclaimer
This report was prepared as an account of work sponsored by an agency of the United States Government.Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights.Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof.The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.

Figure 1 .
Figure 1.Time traces for four DIII-D H-mode discharges with the red/magenta representing hydrogen and blue/cyan deuterium shown on the left.For each discharge, the chosen time-window to extract steady-state profiles using conditional averaging as function of the ELM cycle is shown with a shaded box.Panel (a) shows the line integrated electron density, (b) the pedestal density, (c) the total Neutral Beam Injected Power, and (d) the integrated gas input.(e) The LLAMA views for the HFS (orange) and LFS (green) and the LCFS for the hydrogen (red) and deuterium (blue) discharges.

Figure 2 .
Figure 2. (top row) (a) Electron density, (b) electron temperature, and (c) ion temperature for the low pedestal density matched discharges.(bottom row) (d) Electron density, (e) temperature, (f ) and ion temperature for the high density pedestal cases.Hydrogen shots are colored in red and magenta and deuterium shots are shown in blue and cyan.

Figure 3 .
Figure 3. (a) Stability diagrams for the 4 discharges overlaid on one another.The squares are the experimental point with 15% error, and the boundary represents the location where the most unstable mode growth rate (normalized to its effective stabilization rate) r = γn γω i,eff ⩾ 1 [40].Figures (b) and (c) are the divertor D-α Filterscope traces for low density (b) and high density (c) discharges showing the ELM behavior.The dark red line from the bottom is the ballooning boundary of the low density hydrogen discharge which does not connect with the peeling-limit.

Figure 4 .
Figure 4. Neutral ionization on the high field side (a) and low field side (b) from the far SOL inwards.The error bars are propagated from the combination of TS measurements and statistics on the LLAMA data in the profile time windows.The x-axis is the distance from the separatrix in major radius coordinates (Rsep − R) on the HFS and R − Rsep on the LFS to allow better visual comparison.

Figure 5 .
Figure 5. Neutral density vs. distance from the separatrix in major radius coordinates for each of the 4 discharges as calculated from the LLAMA data using equation (2).The top row are the low density discharges on the HFS (a) and LFS (b).The bottom row are the high density discharges for the HFS (c) and LFS (d).The black lines are exponential fits (equation (3)) show the radial extent of the density pedestal width.Numerical values for the pedestal width domain (n sym e − ∆n e /2 < x < n sym e H−low /∆ width H−low = 6.8/4.6 ∼ 1.47 and ∆ sep−inwards D−low /∆ width D−low = 5.1/3.3=∼ 1.54.

Figure 6 .
Figure 6.(a) Rate Coefficients for relevant pedestal electron temperature and density parameters.The numerical values for the legend elements are: T sep e = 80 eV, n sep e = 3.3 × 10 19 , n ped e = 6.6 × 10 19 , T ped,low e

Figure 7 .
Figure 7.The red and blue lines are the analytic values of λn 0 vs. n ped e for 20 eV neutrals consistent with the choice from [23].The uncertainty (shaded region) is taken from evaluating the rate coefficient with T sep e as the upper bound and T ped e as the lower bound.Overlaid are the measured values on the HFS (squares) and LFS (circles) of λn 0 (closed symbols) and ∆n e (open symbols) for each discharge studied.Red and magenta are hydrogen, and blue and light blue are deuterium.Note: the low density hydrogen λn 0 (red solid circle) overlaps with the hydrogen ∆n e (open square).Squares should be compared to squared and circles to circles..

Table 1 .
Overview of dimensionless parameters and pedestal characteristics.Hydrogen discharges are 183 508 (red) and 183 766 (pink) and deuterium discharges are 191 725 (dark blue) and 192 012 (light blue).All dimensionless values are taken at the top of the pedestal except ηe which is taken at the density tanh-fit symmetry point.

Table 2 .
Neutral density fit parameters sensitivity to fit on the (R − Rsep) axis over the pedestal width or separatrix inwards.(shotcolorscorrespond to the colors in all figures and the 'Side' colors correspond to the measurement location from figure1(e))The low density discharge domains have a greater difference with the separatrix-inwards domain which are ∼50% larger, while for the the high density discharges the separatrixinwards domain is only ∼3% larger.This analysis is summarized in table2where the data are separated into the 'Pedestal Width' columns and the 'Separatrix Inwards' columns with the HFS data on the top half and the LFS data on the bottom half.