On the origin of the DIII-D L-H power threshold isotope effect

The increased low to high confinement mode (L to H-mode) power threshold PLH in DIII-D low collisionality hydrogen plasmas (compared to deuterium) is shown to result from lower impurity (carbon) content, consistent with reduced (mass-dependent) physical and chemical sputtering of graphite. Trapped gyro-Landau fluid (TGLF) quasilinear calculations and local non-linear gyrokinetic CGYRO simulations confirm stabilization of ion temperature gradient (ITG) driven turbulence by increased carbon ion dilution as the most important isotope effect. In the plasma edge, electron non-adiabaticity is also predicted to contribute to the isotope dependence of thermal transport and PLH , however its effect is subdominant compared to changes from impurity isotopic behavior. This L-H power threshold reduction with increasing carbon content at low collisionality is in stark contrast to high collisionality results, where additional impurity content appears to increase the power necessary for H-mode access.

(Some figures may appear in colour only in the online journal) Heat and particle transport in magnetically confined plasmas has been found to depend on hydrogenic isotope mass, with a vast majority of experiments (fusion devices with both carbon and metallic wall materials) demonstrating larger transport in hydrogen, compared to deuterium and tritium plasmas [1][2][3][4][5][6][7].This is contradictory to 'naive' gyro-Bohm transport theory, which predicts more heat transport (higher radial heat flux, Q) with increasing main ion mass: 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.
Above, c 0 is a mass-independent constant, m i and m D are the main ion and deuterium ion mass, Q GBD is the normalized deuterium ion gyro-Bohm heat flux, n e and T e are the electron density and temperature, c s = √ T e /m D is the deuterium ion sound speed, and ρ * = √ T e m D /(a e B) is the normalized deuterium ion-sound gyro-radius (a, B, and e are the plasma minor radius, magnetic field, and elementary charge, respectively).The gyro-Bohm scaling above predicts ion thermal flux Q i ∝ √ m i , opposite to experimental observations.Gradient driven turbulent transport physics, which can break this gyro-Bohm scaling, is a leading framework for explaining this isotope effect.This effect is particularly important for efficiently achieving high-confinement (H-mode) plasmas, where fusion reactor relevant conditions are most easily met.This H-mode state, which can only be accessed by exceeding a minimum threshold input power P LH , exhibits roughly double the energy confinement time compared to low confinement (L-mode) plasmas [8].Modern tokamak experiments routinely observe a L-H threshold isotope effect, with reduced P LH in plasmas with higher main ion mass [4][5][6][9][10][11][12][13].This mass dependent threshold power is important for projecting auxiliary heating power requirements on existing tokamaks, mostly in deuterium, to future reactors, which will operate with a 50:50 deuterium-tritium mixture.For example, the International Thermonuclear Experimental Reactor (ITER) [14] is designed to achieve a fusion gain of 10 using the H-mode operating scenario in a mixed deuterium-tritium plasma.ITER is especially vulnerable to the isotope effect during initial nonnuclear Pre-Fusion Power Operation phases 1 and 2 (PFPO-1/2) due to the use of hydrogen main ions, and may have insufficient heating (20)(21)(22)(23)(24)(25)(26)(27)(28)(29)(30) for reliable H-mode access.
Developing schemes for reducing this power requirement is therefore crucial to ITER's success, and motivates improved understanding of this effect.In this paper, we will elucidate the possible origin of the L-H power threshold isotope effect in the DIII-D tokamak [15].The DIII-D device is a conventional medium sized, graphite armored, diverted tokamak with flexible shaping capabilities and a large array of available plasma diagnostics, in operation in San Diego, USA since 1986.By comparison, ITER is approximately nine times larger by plasma surface area compared to DIII-D, and is expected to employ a tungsten divertor and main chamber, with a lower anticipated (metallic) impurity content of Z eff = 1.1.In the following sections, we will demonstrate that the L-H transition power threshold in DIII-D depends strongly on main ion dilution (the effective charge state Z eff ) at low collisionality, which is shown to be significantly larger in deuterium than in hydrogen plasmas.Based on recent research in the Joint European Torus (JET) with ITER-like metallic walls, the isotope dependence of main ion dilution does not appear to be unique to carbon machines, and may contribute to the isotopic dependence of P LH in other devices [16][17][18].
From DIII-D's suite of diagnostics, key parameters relevant to the L-H transition were documented for approximately 500 recent (>2010) hydrogen and deuterium discharges.Parameters at transition, such as plasma current (I p ), impurity content (Z eff ), and ion temperature (T i ), were recorded in addition to other quantities relevant to the L-H power threshold (power sources and sinks).The threshold power is calculated as: The injected neutral beam, electron cyclotron, and ohmic powers are P NB , P ECH , and P OH respectively.The power consumed by changing the diamagnetic stored energy and lost by core plasma radiation are ∂W dia ∂t and P rad,core respectively.All quantities were time-averaged over the 30 ms window preceding the L-H transition.Identification of the transition time was performed by inspecting discharges for a simultaneous drop in Balmer α recycling light emission and rise in line-averaged density (n).An example of such a transition can be found in figure 1.
Historically, P LH is often observed to have a minimum vs. line-averaged density n [19].From the DIII-D database, in ITER similar shape with n = 1-2.5 × 10 19 m −3 , below the density where P LH exhibits a minimum at DIII-D (n min = 3-4 × 10 19 m −3 ), the L-H power threshold was found to decrease strongly with increasing Z eff .Z eff is measured by Charge Exchange Recombination Spectroscopy (CER) [20] and Thomson Scattering [21] using the fully ionized carbon and electron densities n C 6+ and n e at a normalized minor radius ρ = √ ψ t = 0.7, as shown in figure 2(a).Noteworthy is that DIII-D hydrogen plasmas almost never reach the impurity levels of their deuterium counterparts.This difference is attributed to the larger (mass dependent) physical and chemical sputtering yield of the graphite (carbon) divertor and main chamber tiles by deuterium, compared to hydrogen [22].
To determine how changes in Z eff may be altering the threshold power, profile fitting analysis of an ensemble of nearly 80 L-H transitions, with a range of line-averaged density n = 1-5.5 × 10 19 m −3 , edge safety factor q 95 = 3-7, and neutral beam injected torque T inj = 0-5 N-m was undertaken.During fitting, correction of impurity ion temperature (T i ) measurements for Zeeman and Fine Structure effects [23], and checking Z eff measurements against visible bremsstrahlung continuum emission [24,25] was performed to ensure high data quality.TRANSP power balance analysis was performed using these profiles, taking care to match transport metrics (neutron rate, plasma stored energy, loop voltage, inductance, n) to minimize errors in power accounting [26].
Detailed power balance analysis of 10 of these hydrogen and deuterium L-H transitions, shown in figure 2(b), indicates that both electron and ion heat fluxes (Q e , Q i ) in L-mode just before transition contribute to P LH .Figure 2(b) illustrates this by showing the pre-transition separatrix (ρ = 1) ion and electron loss power, overlayed with P LH .On average, Q e + Q i ⩽ P LH due to TRANSP accounting for additional loss channels, such as charge exchange for ions and neutral ionization work for electrons.Both ion and electron loss powers are observed to decrease with increasing Z eff .Discharges in this limit were found to have low collisionality (ν * i , ν * e ≲ 1 at ρ = 0.95).At higher collisionality (above the P LH density minimum), the hydrogen and deuterium power thresholds increase with increasing Z eff (figure 2(c)), consistent with past findings at high L-mode density [27].Experimentally, T e ≈ T i for almost all transitions in figure 2(c).Assuming T e = T i , power balance analysis indicates Q i ≲ Q e , with both heat channels contributing to increasing P LH .Collisionally, these transitions are in the Pfirsch-Schluter (PS) regime, and converging to similar P LH independent of isotope and Z eff , as previously observed by Yan et al [28].This convergence is not observed on several other tokamaks however (such as ASDEX Upgrade [9]) and is currently not well understood.Distinguishing all 80 analyzed transitions by neoclassical transport regime using edge ion collisionality (banana, plateau, and PS regimes), one finds that the isotope effect is strongest at low collisionality, and suppressed approaching the PS limit (figure 3).Ion collisionality is approximated as [29]: R, log(Λ i ), and ϵ represent the major radius, Coulomb logarithm, and inverse aspect ratio respectively.The observed P LH vs. Z eff trend reversal from low to high collisionality is consistent with a transition from Trapped Electron Mode/ion temperature gradient (TEM/ITG) turbulence to Resistive Ballooning Mode (RBM) dominated turbulence previously observed in simulations [30].Analogous to density scan simulations including ITG/TEM and RBM modes by Bourdelle, the collisionality at the minimum of P LH is observed to increase with lower Z eff (figure 3).L-H transitions at similar Z eff and collisionality are found to have nearly identical power threshold, independent of m i (hydrogen in △ and deuterium in ⃝) in different collisionality regimes.Two banana regime plasmas with a large difference in L-H threshold were selected for detailed turbulence and gyrokinetic analysis, from an ensemble of eighty transitions where power balance analysis has been performed.These two plasmas were chosen because their shapes, L-mode radial kinetic profiles (n e , T e , T i ), injected NBI torque and q 95 were almost identical.In addition, these plasmas had ITER PFPO-1 relevant density n = 1.6 × 19 m −3 , safety factor q 95 = 3.6, ITER similar shaping, and low neutral beam torque [31].Figure 4 illustrates each plasma's L-mode profiles approximately 10 ms before the L-H transition.The deuterium plasma normalized carbon density gradient was used to infer the core electron density due to the lack of reliable inner core Thomson scattering and reflectometry data.The hydrogen plasma inner core toroidal rotation measurements (Ω C ) were not available.The most substantial difference between these two plasmas, aside from main ion species, was carbon impurity content (Z eff ).Despite such similar profiles, heat fluxes calculated from TRANSP power balance analysis were nearly two times larger in H compared to D. Heat flux uncertainty bands represent the time averaged variation in the 50 ms time interval preceding the L-H transition.Main ion charge exchange analysis indicated T C 6+ = T H/D after correcting impurity measurements for Zeeman and fine-structure effects [32].Review of many L-mode pre-transition profiles similar to figure 4 suggested that nearly identical kinetic profiles (n e , T e , T i ) are a commonality among L-H transitions in deuterium and hydrogen, as observed in previous experiments [4,6,10,[33][34][35].This is believed to be due to the required edge ion pressure profile providing sufficient ⃗ E × ⃗ B shear to trigger a positive feedback turbulence suppression loop [36].As a result, it is hypothesized that the heat flux needed to sustain the pre-transition L-mode radial gradients sets P LH , and causes the isotope effect.Stability analysis using quasilinear thermal fluxes from the gyro-fluid stability code trapped gyro-Landau fluid (TGLF) [37] was undertaken to identify the origin of the large isotopic difference in thermal fluxes.TGYRO simulations, which adjust radial temperature and density gradients to match power balance and TGLF-predicted heat fluxes, were run until convergence to match the experimentally observed heat fluxes by adjusting the T e and T i profiles, holding the n e profile fixed.Converged solutions were obtained after 20 iterations, using an extended perpendicular wavenumber (k θ ρ s ) grid model to capture long wavelength modes.All three TGLF quasilinear saturation rules [38][39][40] with and without electromagnetic effects were tested, with saturation rule 2 most closely matching both experimental temperature gradients and profiles (figure 4 in orange (H) and light blue (D)).Saturation rule 2 builds on previous models by including realistic geometry effects and species dependent Landau averaging.Electromagnetic (EM) corrections, although included in the analysis, were found to contribute negligibly to thermal fluxes, consistent with electrostatic ITG/TEM turbulence.TGLF results predicted nearly identical H and D kinetic profiles, consistent with experimental observations.
Gradient scans in the outer core plasma (ρ = 0.7) were performed to identify the origin of the heat flux difference required to maintain the same profiles in H and D, as shown in figure 5. Scans identified characteristics of ITG turbulence (low k θ ρ s dominant spectra, mode propagation in the ion diamagnetic direction, a critical T i gradient), with a shift in the T i critical gradient observed as the dominant unstable mode feature driving the thermal flux differences.TGLF and CGYRO calculations demonstrate that the difference in carbon content is responsible for the shift in critical ITG gradient, in agreement with database results and predictions of ITG turbulence behavior with impurities [41].Such results are consistent with observations of turbulence suppression with impurity seeding, dubbed the RI-mode, documented extensively at TEXTOR and DIII-D [42,43,44].Changing species from D to H with fixed main ion dilution fraction had no effect on the heat flux levels (yellow line in figure 5), however reduced main ion dilution of the D plasma led to a critical gradient that matches the H-plasma critical gradient (purple vs. red), indicating main ion dilution as the precise origin of this effect.First principles nonlinear (k θ ρ s < 1.1) CGYRO [45] simulations (dots) around the TGLF optimized gradients confirmed reduced model predictions.
To identify if the edge H-mode pedestal forming region contains a similar isotope effect, non-linear (k θ ρ s < 1.1) CGYRO modeling around the deuterium experimental gradients at ρ = 0.9 was undertaken.CGYRO scans reproduced both D electron and ion heat fluxes as shown in blue circles on figure 6 at the (deuterium) experimental conditions.Single changes to CGYRO of m i and n C 6+ (yellow and purple respectively) indicated the presence of two isotope effects: one from main ion dilution (similar to the findings at ρ = 0.7 shown in figure 5) and another from intrinsic m i changes.Changing both m i and n C 6+ (shown in red) allowed matching the observed electron thermal flux in hydrogen, and a near match of the ion thermal flux.Electron non-adiabaticity was determined as the likely origin of the m i mass effect by modifying the parallel electron response time [46,47].In simulations imposing hydrogen main ion mass (red and yellow dots), re-scaling the parallel electron response time to its deuterium value ( √ 2) nearly accounted for the difference in heat fluxes with changing m i in gyro-Bohm heat flux units (Q/Q GBi ).This can be seen in figure 6 with the ⋆ simulations (yellow → m H , red → m H + n C 6+ ), which are converted from gyro-Bohm to experimental heat flux units using Q GBD (not Q GBH ) for direct comparison to deuterium counterparts (purple and blue).
In summary, from a large survey of DIII-D isotope experiments, reduced model transport simulations from TGLF sat.2, and first principles gyrokinetic modeling from CGYRO, differences in carbon content are identified as the likely origin of the observed isotope dependence of the L-H power threshold P LH at low collisionality in the DIII-D tokamak.Ongoing work at DIII-D seeks to possibly reduce P LH via impurity seeding as a test for improving H-mode access during ITER PFPO-1/2.The universality of this isotope effect explanation is indeterminate at this time, however isotopic sputtering and impurity dynamics have also been observed to affect P LH in devices with ITER-like wall materials such as in JET [16][17][18].

Figure 1 .
Figure 1.(a) Contributions to the L-H threshold power vs. time, with Psep in black.The red vertical line and gray shaded region indicate the exact time of L-H transition and time averaging window for calculated quantities.(b) Line-averaged density (n) and Balmer α recycling light emission during a typical L-H transition.

Figure 2 .
Figure 2. Panels (a) and (c) illustrate the observed P LH trend with Z eff at low and high collisionality in hydrogen and deuterium plasmas.Panels (b) and (d) show results of power balance analysis using the TRANSP code.The L-mode separatrix heat fluxes carried by ions (gray) and electrons (violet) for a sample of transitions are shown in panels (b) and (d).

Figure 3 .
Figure 3. P LH vs. edge ion collisionality (ρ = 0.95).Heat map shows low (red) and higher (purple) Z eff , and symbol shapes indicate plasma species (△ for H and ⃝ for D).Solid lines are parabolic fits to shown data for a narrow range of Z eff .Vertical dashed lines divide collisionality into neoclassical transport regimes (banana, plateau, and Pfirsch-Schluter).

Figure 4 .
Figure 4. L-mode profiles and gradients approximately 10 ms before L-H transition for hydrogen (red) and deuterium (blue) plasmas at DIII-D vs normalized radius ρ.Dots are raw experimental data.Heat flux profiles are from TRANSP power balance analysis, with the time-averaged variation in heat flux as error bands.Orange and light blue (H, D) stars indicate TGLF flux matching solutions to T i and Te using sat.rule 2.

Figure 5 .
Figure 5. Scan of normalized T i gradient at ρ = 0.7 vs. ion heat flux.Solid lines (closed circles) indicate the TGLF (CGYRO) calculated thermal fluxes.The vertical dashed line indicates the flux matching gradient for both D and H experimental heat fluxes (blue and red horizontal lines).Simulations in blue and red are from deuterium and hydrogen conditions shown in figure 4. Yellow and purple data are based on deuterium, but with reduced m i and main ion dilution respectively.

Figure 6 .
Figure 6.Nonlinear CGYRO simulations at ρ = 0.9 around deuterium experimental gradients (blue vertical lines).Panels (a), (c) show electron heat flux, and (b), (d) ion heat flux.Panels (a), (b) illustrate a density length scale scan, and (c), (d) a T i gradient scan.Horizontal lines with shaded region indicate the power balance heat fluxes and uncertainty (blue → D, red →H).Yellow and red ⋆ illustrate simulations with hydrogen main ion mass and parallel electron response time rescaled to deuterium values.