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Plasma performance and operational space without ELMs in DIII-D

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Published 18 June 2021 © 2021 IOP Publishing Ltd
, , Citation C Paz-Soldan and the DIII-D Team 2021 Plasma Phys. Control. Fusion 63 083001DOI 10.1088/1361-6587/ac048b

0741-3335/63/8/083001

Abstract

A database of DIII-D plasmas without edge-localized modes (ELMs) compares the operating space and plasma performance of stationary no-ELM regimes found in conventional tokamaks: ELM suppression with resonant magnetic perturbations (RMPs), quiescent H-mode (QH, including wide-pedestal variant), improved confinement mode (I-mode), enhanced D-alpha H-mode (EDA-H), conventional low-confinement mode (L-mode), and negative triangularity L-mode (Neg-D). Operational space is documented in terms of engineering and physics parameters, revealing divergent constraints for each regime. Some operational space discriminants (such as pedestal collisionality) are well known, while others, such as low torque & safety factor, or high power & density, are less commonly emphasized. Normalized performance (confinement quality and normalized pressure) also discriminate the no-ELM regimes and favor the regimes tolerant to power in DIII-D: RMP, QH, and Neg-D. Absolute performance (volume-averaged pressure , confinement time τ, and triple product ) also discriminates no-ELM regimes and is found to rise linearly with IaB (a metric for the magnetic configuration strength, the product of current I, minor radius a, and field B that has units of force), and also benefits from tolerance to power. The highest normalized performance using the metric is found in QH and RMP regimes. Focusing on ITER-shaped no-ELM plasmas, Q = 10 at 15 MA scaled global performance is met with some metrics (, ), but not others (, ), and only thus far at high torque (βN is normalized pressure, H89,98 is the confinement quality by scaling law, and q95 is the safety factor). Though comparable QH and RMP performance is found, the pedestal pressure (pped ≈ 2 pe,ped) is very different. pped in RMP plasmas is relatively low, and the best performance is found with a high core fraction alongside high core rotation, consistent with an ExB shear confinement enhancement. pped of QH plasmas is significantly higher than RMP, and QH performance does not correlate with core rotation. However, the highest QH pped are found with high carbon fraction. While normalized performance of Neg-D plasmas is comparable to QH and RMP plasmas, the absolute confinement of Neg-D is lower, owing to low elongation and low pped achieved thus far. Considering integration with electron cyclotron heating, the operational space for RMP and QH plasmas narrow, while that for EDA-H plasmas open, and the high pped/ regimes (EDA-H and QH) preserve the highest performance. Only the EDA-H, Neg-D, and L-mode scenarios have approached divertor-compatible high separatrix density conditions, with Neg-D preserving the highest performance owing to its compatibility with both high power and density. Comparison to ELMing plasmas highlighted in the literature finds a clearer pedestal correlation to plasma performance, but also reveals that the peak performance of plasmas without ELMs is significantly lower in DIII-D, owing to limits in operational space accessed so far without ELMs.

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1. Introduction and motivation

A grand challenge for the tokamak approach to fusion energy production is the achievement of a high-performance fusion core integrated with a boundary solution compatible with available first-wall materials. A key issue at this interface is the edge-localized mode (ELM), an instability arising from edge gradients which if uncontrolled delivers an impulsive heat and particle load to the first-wall [1, 2]. Above a threshold size, the ELM not only impacts the integrity and lifetime of plasma-facing components [36] but also imposes limits on the tokamak operating space (and achievable plasma performance) by driving excessive material influx to the plasma [79]. Developing scenarios and techniques to mitigate or eliminate the ELM is thus a topic of well-recognized importance in the fusion community. This importance is further highlighted by noting that the ITER tokamak was designed around the type-I ELMing H-mode regime, though later work led to the expectation that an unmitigated type-I ELM will be intolerable at high plasma current. Thus, some degree of ELM control is essential to achieve the ITER mission [1012], a premise that has consequently motivated significant actuator investment for ITER. Looking beyond ITER, the ELM problem becomes yet more severe, leading to an expectation that the ELM must be completely eliminated in DEMO-class tokamak reactors [13].

In contrast, the operating space of mid-scale tokamaks with carbon walls (such as DIII-D) is not generally limited by the ELM. As such scenario development work in this class device often proceeds without enforcing a constraint on ELM virulence. Peak plasma performance in DIII-D is found in ELMing plasmas [1416]. This is perhaps natural, as the ELM is a pressure-limiting instability. In parallel, several regimes without ELMs have been discovered and advanced—all of which can be accessed and sustained in DIII-D. These regimes are described in section 1.1 and summarized in table 1. Though detailed studies of individual no-ELM regime access, sustainment, and performance against various parametric dependencies abound (see table 1), little work exists in the literature to allow systematic comparison of the performance and access of the various no-ELM regimes against both each other and their ELMing counterparts.

Table 1. No-ELM regime access in MA-class conventional tokamaks. : access prior to metal wall installation. *: non-stationary or ambiguous access. Color indicates the icon color used in subsequent figures, with L-modes also shown in magenta.

RegimeAUGC-ModDIII-DEASTJETJT-60UKSTARColor
EDA-H[17][18][19][20][21] N/AN/A 
I-mode[22] [23], [24][25][26][27][28] N/AN/A 
Neg-D[29]N/A[30]N/AN/AN/AN/A 
QH[31] N/A[32][33][34] [35][36] 
RMP[37], [38]N/A[39][40]N/AN/A[41] 

This work is thus motivated to fill this gap and more fundamentally to understand key stationary plasma performance drivers with a no-ELM constraint. The DIII-D tokamak has nearly two decades of experience in accessing and understanding the various stationary no-ELM regimes listed in section 1.1. Notwithstanding this, no comparative study has been reported that directly compares the observed operating space and plasma performance achieved thus far in each regime (beyond reporting the normalized confinement quality H-factor [42]). At a minimum, this work seeks to provide documentation of what has been achieved in DIII-D and what gaps remain, using easily evaluated metrics that can be compared between tokamaks. A related goal of this study is to facilitate comparative assessment of no-ELM plasma performance (in DIII-D and beyond), moving beyond simply reporting the H-factor. Additionally, a goal is to provide relative assessment of gaps to a viable reactor scenario for all no-ELM regimes, both in terms of performance and integration. To give a specific example, results will be presented alongside fusion gain and scenario integration targets for ITER. An investigation of the possible performance penalty associated with removing the ELM is also desired, here achieved by comparing the performance of ELMing and no-ELM plasmas. A final goal is to provide a foundation from which future extensions of this work to other tokamaks can be performed. As will be discussed, extrapolation to reactor conditions is best achieved by considering the combined experience of several tokamaks, as present-day devices can each only reach a subset of the expected operating conditions of a reactor.

1.1. Stationary tokamak operating regimes without ELMs

The no-ELM regimes considered in this work are briefly described in this section. It is not within the scope of this work to present a detailed discussion of the pedestal stability, micro-turbulence modes, and resultant understanding of each no-ELM regime. This task is well-covered in [4345]. In alphabetical order, the regimes are:

  • the enhanced D-alpha H-mode (EDA-H) [18, 46, 47], a regime possessing a fully formed density and temperature pedestal, typified by a 'quasi-coherent mode' electro-magnetic fluctuation in the (100 kHz) range that drives additional transport [48, 49];
  • the improved energy confinement mode (I-mode) [22, 25, 50], a regime with a temperature but not a density pedestal, and improved energy confinement but not particle confinement as compared to low-confinement mode (L-mode) levels [51]. A 100 kHz range 'weakly-coherent mode' coupled to a geodesic acoustic mode is ubiquitously observed that drives additional transport [52, 53];
  • operation with a negative triangularity plasma shape (Neg-D) [30, 5456]. Neg-D plasmas have an L-mode edge (no or only partial pedestal) but the shaping yields improved core turbulent transport [57] and suppresses the H-mode transition to powers well above that expected by established scalings [58, 59];
  • the quiescent H-mode (QH) [32, 60], a regime with fully formed density and temperature pedestal. QH plasmas are typified by either a coherent electromagnetic 'edge-harmonic oscillation' [6163] or an incoherent 'broadband magneto-hydrodynamic (MHD)' oscillation [64] both in the (10 s kHz) range that drive additional transport. A recently emphasized broadband MHD QH variant, the wide-pedestal QH-mode [65, 66] is also included in this population. As compared to standard QH plasmas, wide-pedestal QH-modes are found to have more favorable access and performance qualities at low torque and with dominant electron heating [67, 68];
  • ELM suppression via resonant magnetic perturbations (RMPs) [3841, 6971]. Application of ≈0.1% non-axisymmetric fields from nearby coils maintain a fully formed pedestal yet prevent the ELM, but only in narrow 'resonant windows' of the edge safety factor. Additional transport is provided by: parallel transport across macroscopic pedestal-top magnetic islands arising from a large degree of island formation [7275]; increased turbulent fluctuation levels directly arising from field penetration [7678]; increased turbulence arising indirectly from penetration-induced changes to the radial electric field structure [79, 80]; or a combination of these effects. The additional transport has also been proposed to be due to mechanisms such as neoclassical effects [81, 82] or localized peeling-ballooning instabilities driven by 3D equilibrium modifications [8386] which do not require significant field penetration.

For completeness the default L-mode is also included in the study, though it is not listed in table 1. Note all no-ELM regimes are subject to enhanced edge transport, either via enhanced turbulent fluctuations (L-mode, Neg-D, QH, RMP), (quasi-)coherent fluctuations (EDA-H, I-mode, QH), or imposed laboratory-frame non-axisymmetry (RMP). Furthermore only Neg-D and RMP impose well-defined design considerations on the tokamak: the former dictates the overall tokamak shape, and the latter requires inclusion of nearby non-axisymmetric coils (as is planned for ITER [87, 88]). QH and RMP may additionally benefit from rotation profile control actuators, though this is still an area of active study.

1.2. Criteria for inclusion in database

This work presents a study of specific intervals within DIII-D plasmas. In order to define the intervals used to populate this database, several selection criteria were applied, enumerated here.

  • (a)  
    Intervals must not have ELMs of any type. This excludes even some regimes where the ELM may be benign. However, as extrapolation of ELM heat loads is a challenging topic, this can be considered the most stringent criteria for a viable ELM solution. Future work may expand this study to candidate benign ELM regimes, such as the 'grassy-ELM' regime [43, 45, 89], and to ELMs mitigated via RMPs or high-frequency pellet pacing [10].
  • (b)  
    Intervals must be stationary, as defined by the rate of rise of the average density () being below 1.5 × 1019 s−1. This threshold is somewhat arbitrary but is functionally effective for DIII-D, with little dependence in key metrics seen below this value. This criteria also served to exclude ELM-free phases and the very high mode [90].
  • (c)  
    Intervals must be at least 300 ms long (about two energy confinement times, τ). Longer durations (up to 2 s) are utilized if stationary conditions are maintained.
  • (d)  
    All main control parameters (shape, I, B) must be fixed during the interval. All intervals either hold input power constant, modulate fixed input power, or regulate fixed pressure via power modulation. Gas or density may evolve, according to the stationarity condition described above. Discharges with ramping down B to increase the off-axis current drive are excluded.
  • (e)  
    The plasma cross-section or near scrape-off layer must not interfere with present day divertor baffles, allowing present-day discharge reproduction in principle. This limited the study to DIII-D shot numbers above 100 700 (c. 2000) [91, 92]. Some discharges prior to shot 127 300 (c. 2005) are incompatible with the present-day lower DIII-D divertor and thus are excluded. This criteria only excluded very early high-elongation QH plasmas [60] and early low triangularity RMP discharges [93].
  • (f)  
    The main ion species must be deuterium.

All datapoints in all figures come with a shot number in small font, enabling single discharges to be followed throughout this paper.

1.3. Caveats

Several caveats of this study deserve up front mention.

  • (a)  
    DIII-D experimental run-time awarded to explore some regimes (namely RMP and QH) vastly exceeds that awarded to others (namely EDA-H, I-mode, and Neg-D). Further, efforts in some regimes have been more focused on plasma performance than others, and high-performance is more commonly pursued in ELMing regimes. In addition, the specifics of the DIII-D tokamak (such as covariance of torque and power at high power) can selectively limit performance and access in ways that are not generic. Simply, this is a snapshot of ongoing work on a single tokamak, and with a sampling bias.
  • (b)  
    This caveat concerns the completeness of the database, which was assembled through a combination of manual and automated techniques. Automated techniques (namely structured query language database searches) were useful in identifying discharges near limits of (easily definable) engineering parameters. However, owing fundamentally to the difficulty of robustly separating a stationary no-ELM state from either small-ELM plasmas or transient ELM-free states, the bulk of the database compilation was done manually. This included consulting with relevant experts, compiling existing single-regime databases, surveying the published literature, and re-analyzing sessions targeting a specific operational direction. As such, while a best effort was made, it is impossible to guarantee that a relevant discharge was not missed.
  • (c)  
    ELMing conditions were often (but not always) present preceding or following the selected no-ELM time interval. As such, some presented time intervals may not be accessible without ELMs earlier in the discharge evolution, and these conditions might not be realizable in a tokamak that cannot tolerate any ELMs. The fully formed pedestal regimes (QH, RMP, EDA-H) are prone to spurious ELMs, while the no or partial pedestal regimes (Neg-D, I-mode, L-mode) are robustly without ELMs.
  • (d)  
    Long-time scale equilibrium evolution toward instability (due to for example current profile relaxation or wall condition evolution) is not precluded with the chosen minimum interval length.
  • (e)  
    Correlation is not causation, a statement which is especially salient when considering a database study. No trends observed in the database should be considered causal based on these findings alone. Further, apparent correlations in the database can contradict controlled scans which isolate variation to a single parameter.
  • (f)  
    A general word of caution must be expressed regarding extrapolation of results from a mid-scale tokamak. For reasons described throughout the text, these results do not directly map to burning plasma conditions. Notwithstanding this, the results shown provide ample inspiration for future targeted experiments (emphasizing model validation) and also highlight key gaps for further multi-machine study.

1.4. Structure of paper

The structure of this paper is as follows: the basic operating space of stationary no-ELM plasmas is discussed in section 2. The achieved plasma performance (as measured by a variety of metrics) is then presented in section 3. Correlations with plasma performance in each regime are given in 4. A comparison of no-ELM to ELMing plasma performance then follows in section 5, repeating key figures including high performance ELMing plasma datapoints. No-ELM plasma integration considerations with electron heating and dissipative divertor are then shown in section 6. Discussions and conclusions follow in section 7. Appendix A compares performance metrics against each other.

2. Operational space

Stationary plasmas without ELMs are found only in a subset of the accessible DIII-D operating space. Figure 1 presents the no-ELM operational space against a variety of parameters. In some axes, the operating space is defined by the return of the ELM, while in others, it is defined by hardware, and for some regimes it is simply unexplored. Consideration of the operating space is essential as it directly relates to the achievable absolute plasma performance (though not necessarily the normalized performance).

Figure 1. Refer to the following caption and surrounding text.

Figure 1. DIII-D no-ELM operational space in terms of basic machine and plasma parameters: (a) Toroidal current (I) and toroidal magnetic field (B), dash-dot lines indicate approximately constant q95, (b) elongation (κ) and absolute average triangularity (), (c) total power (Ptot ) to magnitude of net injected torque (Tinj ), dash-dot lines indicate approximate range accessible to the NBI system, (d) ratio of line-average density to the Greenwald density (/nG ) and ratio of net power (subtracting core radiative losses) to scaled L-H threshold power (), (e) edge collisionality () and edge safety factor (q95), (f) Tinj and q95. ITER baseline targets are indicated if applicable. In these and all figures, different colors/symbols are used for each regime. Limiter plasmas are given a circular symbol.

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2.1. Plasma current (I) and toroidal field (B)

Operating space in terms of I and B is shown in figure 1(a). This most basic representation already reveals important features. RMP plasmas are found only in a narrow range of q95 from 3 to 4, owing to well known resonant window requirements [38, 94, 95], though other devices have found RMP resonant windows in different ranges of q95 [40, 96]. Note RMP plasmas at q95 = 7 reported in [97] are found to have small residual ELMs and thus do not meet the criteria discussed in section 1.2. QH plasmas are found across a wide range of I and B. L-mode plasmas are in principle found for all I and B, with only a subset presented. Notable are L-mode discharges operating with q95 just above 2 [98, 99]. The less explored regimes of EDA-H, Neg-D, and I-mode have as yet only been observed in a subset of I & B operational space, though DIII-D findings with EDA-H and I-mode are consistent with those reported in other devices [17, 18, 51].

2.2. Plasma shaping

The DIII-D shaping flexibility as manifest in the no-ELM operating space is shown in figure 1(b), represented as absolute average triangularity () and elongation (κ). QH plasmas are found to operate over a wide range of shapes, including the most strongly shaped plasmas. QH plasmas use the pumped divertor structures at small major radius, imposing a compatibility limit with low . RMP plasmas are not tolerant of the strongest shapes [100], but can be accessed at lower shapes without a pumping requirement [37]. Neg-D plasmas are systematically weak in shape, possessing either low κ or , owing to their poor fit to the DIII-D vacuum vessel cross-section. Weak shapes (low and κ) naturally transition to limiter configurations (indicated by circles). L-mode plasmas in principle can also exist everywhere in this space. Later sections will focus on ITER-like plasma shapes, indicated by dash-dot lines.

2.3. Input power (Ptot ) and magnitude of net injected torque (Tinj )

DIII-D can access to a wide range of powers (Ptot ) and torques (Tinj ), as shown in figure 1(c). Ptot is defined as Paux + POH , where Paux is auxiliary heating power (neutral beam injection (NBI), and electron cyclotron heating (ECH)) and POH is ohmic heating power (with 2 MW). Several notable features can be found. First, no stationary plasma without ELMs has been observed while injecting the maximum balanced (Tinj = 0) power, with QH plasmas coming the closest (Ptot = 7 MW at Tinj = 0 or Ptot = 8 MW at Tinj = 1 Nm). Note nearly all QH plasmas operate with counter-I directed (negative) net torque. L-mode plasmas are less frequently found at high Ptot , with notable examples being high radiation fraction (frad ) plasmas and limited plasmas (circle symbols). RMP plasmas are not tolerant of significant counter-NBI [101, 102], but do exist over a wide range of Ptot . Neg-D plasmas have uniquely accessed the maximum Ptot , and as will be discussed have thus far not found a core MHD limit.

2.4. Power normalized to scaled LH threshold power [59] (Pnet /PLH08 ) and Greenwald density [103] (/nG )

Tolerance of most no-ELM regimes to net exhausted power (Pnet ) as well as the virulence of any ELMs encountered is partially set by H-mode threshold physics [104, 105]. Pnet is defined as Ptot -Prad , where Prad here is radiated power inside the separatrix and varies from ≈0.5 to 2 MW over this database. Radiation will be further discussed in section 6.2. Figure 1(d) shows that high Pnet L-mode plasmas are exclusively found at low /nG , with ELMing H-mode obtained at higher density. EDA-H and I-mode regimes are found at intermediate /nG but at low . RMP and QH plasmas are able to access high , and are uniquely limited by core MHD as opposed to the return of the ELM. The absence of points near = 1 for RMP does not necessarily imply ELMing H-mode is found at lower power, but rather that the regime can return to L-mode away from the scaled PLH08. RMP plasmas exhibit a strict upper limit in pedestal-top density and thus /nG [93, 106, 107]. QH plasmas can access higher /nG than RMP plasmas, owing to their improved compatibility with strong shapes and current-limited pedestals at high density [108110], though in section 6 the ability of high /nG to raise the separatrix density in QH plasmas will be shown to be less favorable. Neg-D plasmas are found to be uniquely able to access high and /nG , indicating the Neg-D regime is decoupled from the usual H-mode threshold considerations at least in the parameter regimes explored so far.

2.5. Edge collisionality () and safety factor (q95)

Plasma regimes without ELMs are known to occupy distinctive points in the pedestal (or edge) collisionality () and edge safety factor (q95) [43, 45]. Collisionality is evaluated at the pedestal-top based on electron profile tanh fits using the formula in [43]. Indeed the no-ELM regimes found in DIII-D are well-separated by these parameters, as shown in figure 1(e). RMP and QH plasmas are found below of about 1, while all other regimes are at higher . As discussed in figure 1(a), RMP plasmas are only found at low q95 on DIII-D, and EDA-H are only found at high q95. I-mode is only observed thus far at intermediate q95 ≈ 4. Other regimes are observed over a range of q95. In DIII-D, low access is found together with high , whereas a reactor can be expected to operate with low and low , as will be further discussed in section 7.

2.6. Torque (Tinj ) and safety factor (q95)

While less emphasized in the literature, DIII-D no-ELM plasmas clearly exhibit limitations in simultaneous operation of low Tinj , low q95, and low . This is likely the edge stability regime expected in ITER, with the important caveat that extrapolating Tinj depends on what rotation-dependent mechanism is of interest [111]. As shown in figure 1(f), RMP plasmas match q95 and [112], but find the return of the ELM at low Tinj [101, 102]. QH plasmas so far have matched two of low , q95, and Tinj , but not all three together owing to the onset of core MHD or the ELM [109]. This finding has motivated extensive DIII-D experimentation to understand low + q95 + Tinj limits and their extrapolation [12], and this regime will soon be accessible in the world research program as new capabilities come online [113, 114]. Note the low q95 & low Tinj limit is not found for the high regimes, though even these have not been demonstrated at high power or pressure ( 1.2). L-mode plasmas suffer a return to ELMing H-mode at higher βN , while Neg-D has not yet been attempted in this low q95 + Tinj part of parameter space. Access to low q95 (specifically high I) and high Ptot will be shown in the next section to strongly impact the achievable performance without ELMs in DIII-D.

3. Plasma performance without ELMs

Plasma performance of DIII-D plasmas without ELMs is now presented using metrics previously proposed in the literature. This section begins with a survey of normalized performance (normalized pressure and confinement quality), then moves to absolute performance without constraints, and finally explores plasma performance within ITER shaping constraints. Comparison of ELMing and no-ELM plasma performance is left to section 5.

3.1. Normalized performance

Discussion of normalized performance begins with global stability. The Troyon stability diagram [115] shown in figure 2(a) indicates the normalized current (I/aB), pressure normalized to toroidal field (βT ), and concurrently the normalized beta [βN = βT /(I/aB)]. The different no-ELM regimes well-separate in this diagram. I/aB access has already been discussed in relation to figure 1(a), with L-mode uniquely accessing high I/aB. The βN accessible is clearly higher for QH, RMP, and Neg-D plasmas owing to the increased tolerance of power discussed in relation to figure 1(c). Peak βN of RMP and QH plasmas are limited by core instability (generally tearing modes), while Neg-D is confinement-limited, and the other regimes by the return of the ELM. Note the wide-pedestal QH variant has not yet found a βN limit (present limit βN 2.3 for Ptot = 5.6 MW and Tinj = 0 Nm) and finds confinement is not degraded by raising Ptot [66]. Interestingly, the highest stationary βN without ELMs is found for Neg-D plasmas, despite the expectation of degraded core stability [116]. The reason for this is not yet understood, but is speculated to be related to Neg-D plasmas operating at higher /nG than RMP and QH plasmas, as shown in figure 1(d), which may reduce the pressure peaking instability drive [117]. It is also clear from figure 2(a) that QH and RMP access the highest βT , as high βN and high I/aB are simultaneously achieved. Accessing high βN at high I/aB has not yet been attempted for the Neg-D regime in DIII-D.

Figure 2. Refer to the following caption and surrounding text.

Figure 2. (a) Troyon core stability space in terms of toroidal beta (βT ) and normalized current (I/aB), dash-dot lines indicate constant normalized pressure (βN ). Confinement quality factors (b) HL89 and (c) HH98y2 as a function βN , with dash-dot lines at a constant product of H and βN . Dashed lines indicate ITER 15 MA Q = 10 targets.

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Plasma performance is commonly described in terms of the confinement quality 'H-factors', defined as the ratio of the measured energy confinement time (τ = W/Ptot , where W is the plasma kinetic stored energy) to expectations of scalings derived from multiple tokamaks. The confinement quality H-factors have been derived for type-I ELMing H-mode plasmas (HH98y2[118]), and L-mode plasmas (HL89[119]). Note that as no-ELM plasmas can be found at low /nG (see figure 1(d)) where the fast ion content is sometimes not negligible, both HL89 (which includes fast ion pressure) and HH98y2 (which explicitly removes it) are presented. For all cases, fast ion pressure is evaluated automatically with between-shot codes using the formulas presented in [120]. Fast ion pressure is not subtracted from the pressures reported in this study.

The performance against these H-factors for the database described in section 2 is shown in figures 2(b) and (c), plotted against βN . As can be seen, these axes are also effective to separate the no-ELM regimes. Furthermore a good correlation exists between H-factor and βN across all regimes, despite widely varying Ptot . This correlation is consistent with Ptot being overly penalized in the confinement scalings. Considering each regime, L-mode plasmas are found at low normalized performance, RMP and QH plasmas are found at higher H-factor and βN , while I-mode and EDA-H plasmas are found at an intermediate level of normalized performance. Neg-D plasmas (which are all in L-mode) span a wide range of performance, from conventional L-mode like (low H and βN ) to normalized performance on par or better than RMP and QH regimes (high H and βN ). The highest H-factors are uniquely found for QH plasmas.

3.2. Absolute performance

Absolute performance has long been measured in terms of Lawson's triple product [121] [, where is the volume averaged pressure W/(1.5*volume)]. Triple product decomposed into constituent and τ is shown in figure 3(a). No-ELM regime separation is again found. QH and RMP plasmas both reach high with a roughly equal mix of and τ, while EDA-H and I-mode plasmas emphasize τ over , and Neg-D plasmas emphasize over τ. Note that most NBI heated DIII-D plasmas have core , but does not separate ion and electron contributions (despite only ions fusing). Some L-mode datapoints occupy the same absolute performance as Neg-D, QH, and RMP. The discrepant view of Neg-D in normalized performance (figure 2) and absolute performance (figure 3) is reflective of the weaker shape and lower I of the Neg-D plasmas created thus far, and perhaps due to the H-factors over-penalizing input power. As can be seen, the highest without ELMs on DIII-D is found in RMP plasmas, a surprising result given the significant pedestal degradation encountered in RMP plasmas. These high RMP plasmas feature near-threshold RMP current values or below-threshold values employing hysteresis, sometimes using active RMP current feedback control [122]. The role of the pedestal will be further explored in section 4.

Figure 3. Refer to the following caption and surrounding text.

Figure 3. Absolute plasma performance in the DIII-D tokamak without ELMs, represented by: (a) average pressure () and confinement time (τ), with dash-dot lines at constant triple product (). (b) Triple product referenced to IaB, showing an increasing trend. (c) normalized to IaB referenced to Tinj , with dashed lines referencing fusion gain Q values at 15 MA in ITER.

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As described in [16], an effective normalization for is IaB, the product of the plasma current (I), minor radius (a), and toroidal field (B). IaB has units of force (MN), and is a simple metric for the strength of the tokamak magnetic configuration. As shown in figure 3(b), peak tends to rise linearly with IaB, supporting the value of IaB as a normalization parameter for as will be soon introduced. The DIII-D tokamak (with its present divertor baffling) is capable of IaB of around 2.5 MN by operating strongly shaped plasmas ( 2.0 or 0.9) at high I and B. Without ELMs however, IaB is found to not exceed around 2 MN (excepting L-mode). This indicates a straightforward path to raise is to develop stationary no-ELM plasmas at the maximum achievable IaB, though this implies overcoming the operational limits associated with high I/aB (low q95) and strong shapes presented in section 2.

Supported by the trends of with IaB shown in figure 3(b), for the subsequent sections the main metric to consider plasma performance will be . This metric is meant to show the quality of fusion performance across a range of Ti , with an advantage of only requiring simple engineering inputs without imposing any scaling relationships. Said differently, this metric is agnostic as to the importance of factors such as plasma shape and density, and rather lets the triple product speak for itself. Note standard type-I ELMing H-mode performance across DIII-D, Alcator C-mod, and JET was found in [16] to yield comparable , despite very different I, a, and B. Further discussion of the metric, alongside comparison to other metrics can be found in appendix A.

is now plotted against Tinj in figure 3(c). A clear distinction is seen at low Tinj , where only QH plasmas are able to achieve high , consistent with only QH tolerating high Ptot at low Tinj (shown in figure 1(c)). All other regimes (except Neg-D, which has not been explored) are limited by the ELM at low Tinj and high Ptot . Performance of Neg-D plasmas in terms of is below QH and RMP plasmas for all Tinj , possibly due to the weak shaping or to the absence of a pedestal. Finally, use of allows for a comparison of performance scaled to ITER Q = 10 at 15 MA, namely 5.5 [16]. While section 5 will show this can be met and exceeded for ELMing plasmas, it is not yet met in DIII-D for stationary plasmas without ELMs, even when ignoring all ITER operational constraints.

3.3. Plasma performance with ITER-like shapes

Plasma performance focusing on ITER-like plasma shapes is now presented, with the ITER shape only loosely specified as = 0.4–0.6, κ = 1.7–1.95 [125]. The goal is to exclude strongly shaped double-null plasmas as well as other scenarios clearly inaccessible to ITER, such as Neg-D. As such only scenarios that in could in principle be realized in ITER are retained. Results are first presented as a function of Tinj , highlighting the special challenge of achieving both ELM control and high performance with relatively small external momentum input in ITER [12]. Extrapolating Tinj depends on what rotation-dependent mechanism is of interest, but attempting to match the dimensional rotation in ITER yields an ITER-equivalent torque of ≈0.5 Nm [111]. It also bears reminding that all QH non-zero Tinj are counter-I directed. section 6 will discuss other integration constraints that apply to all burning plasmas, including ITER. For all metrics considered the RMP and QH plasma performance will be clearly superior to other regimes, though this is largely due to the unique tolerance of RMP and QH plasmas to both low q95 (15 MA-equivalent in ITER) and high Ptot in DIII-D.

Plasma fusion gain factors GL89 = / and GH98y2 = / presented in [123, 126] are presented in figures 4(a) and (b) against Tinj . Both G-factors are the product of what was shown in figures 2(b) and (c), but now divided by the square of the normalized current (q95). The G-factors prescribe a target value for ITER Q = 10 operation at any current. Note G-factors are only as accurate as the confinement scaling laws that underpin them, and their treatment of auxiliary power motivates an alternate G-factor that will be described next. Both RMP and QH plasmas are found to reach the ITER Q = 10 target in terms of GH98y2 but fall just short for GL89. Peak performance of both QH and RMP plasmas thus far achieved is lower at low Tinj . As seen in figures 1(c) and (f) no RMP plasma exists at 2 Nm, and RMP plasma performance will be shown in section 4 to correlate with rotation. QH results in figure 4 are not reflective of a confinement degradation with rotation [67] but rather highlight the two different q95 QH plasma populations shown in figure 1(f). The high Tinj population is at low q95 and high G-factor, but encounters limits as Tinj is reduced, while the net Tinj = 0 population is at high q95 and lower G-factor. Optimization between these two q95 populations has not yet been given serious effort, and is highlighted as a valuable experimental direction for QH plasmas. The G-factors of figures 4(a) and (b) and (shown in figure 3(c)) are found to be largely co-linear (not shown), with the main discriminant being q95. High q95 plasmas are prejudiced in GL89/GH98y2 as compared to , consistent with low q95 (high I) being over-rewarded in the G-factors. This accounts for differences at Tinj = 0, where as shown in figure 1(f) only L-mode plasmas have thus far accessed low q95 and Tinj = 0 without ELMs. Also worth noting is that the best performing net Tinj = 0 plasmas of figure 3(c) are in strongly-shaped plasmas, thus they are excluded from figure 4. Comparison of GL89 to is discussed in appendix A.

Figure 4. Refer to the following caption and surrounding text.

Figure 4. Gain metrics meant to estimate ITER performance for discharges with ITER-like plasma shapes. Gain factors based on [123] for (a) L-mode confinement (HL89) and (b) H-mode confinement (HH98y2) plotted against Tinj . (c) Gain factor based on [124], allowing comparison to the Paux available in ITER, showing many datapoints inaccessible with ITER's Paux .

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As presented in [124], a limitation of GL89/GH98y2 is that no consideration is given to whether the level of auxiliary heating (Paux ) required to reach a given performance level is available in ITER. Simply put, operation at higher βN can overcome insufficient H-factor to reach comparable fusion performance only if there is sufficient Paux to reach the stated βN . This consideration gave rise to an alternate G-factor (Galt = /), different from GH98y2 by the ratio (HH98y2/βN )2, which emphasizes confinement more than pressure and generally favors lower Paux discharges with still moderate H-factor. Note at constant heating power , and all discussed G-factors are degenerate.

The Galt formulation allows simultaneous consideration of the expected fusion gain (Q), expected fusion power (Pfus ), and the heating power (Paux ) required to achieve this performance in ITER based on HH98y2 scaling, as shown in figure 4(c). The curved dash-dot lines indicate curves of constant ratio of required Paux to available power in ITER. There is insufficient power in ITER to realize many of the presented cases, evidenced by the data below the top curved line. Nearly all of the L-mode, EDA-H, and I-mode plasmas can be realized within ITER's available Paux , but they do not reach Q = 10. A large number of datapoints lie well above the available Paux line, but comparison with figures 4(a) and (b) indicate these are all at high Tinj (2 Nm). Looking at 2 Nm, only QH plasmas come close to Q = 10 performance and only below 500 MW of Pfus , though q95 optimization may improve on these results in the future. If the high Tinj limit is relaxed, many discharges extrapolate to extremely high fusion gain in ITER, including surprisingly ignition. Comparison to ELMing plasmas is given in section 5.

4. Core and pedestal correlations with no-ELM plasma performance

The pedestal (or edge) is naturally the key region of interest for understanding access to no-ELM regimes. However, the role of the pedestal in the plasma performance is found to be more nuanced in DIII-D than the simple paradigm of maximizing pedestal pressure (pped ) to maximize fusion performance. Additional correlations of the plasma performance with core rotation, impurity content, and total power are identified for some regimes.

The contribution of the pedestal pressure pped to the volume-average pressure () is shown in figure 5(a), indicating stark differences between no-ELM regimes. Note pped is taken to be 2pe,ped as measured by Thomson scattering, which is a more experimentally reliable parameter and is furthermore the expectation for reactor conditions. Naturally, the Neg-D and L-mode regimes have almost no pressure contribution from pped , owing to their lack of an edge barrier. The few notable L-mode cases with relatively high pped operate at very high edge density, which despite the very low edge temperatures (10 s eV) yields a finite pressure. At least in this representation, the I-mode on DIII-D is barely distinguishable from the L-mode, though in temperature some distinction is found. RMP, EDA-H, and QH plasmas are found to have progressively higher pped /. QH plasmas stand alone in the absolute pped (2pe,ped ) observed without ELMs in DIII-D. Comparison of no-ELM pped to ELMing regimes appears in section 5.

Figure 5. Refer to the following caption and surrounding text.

Figure 5. (a) Pedestal pressure (2) contribution to , (b) dependence of plasma performance (quantified using ) on pped , (c) correlation of Zeff with pped .

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Plasma performance as quantified by is found to be largest for RMP and QH plasmas with finite pped , however within each regime there is no clear correlation of with pped . This indicates that there are other paths to maximize performance beyond simply maximizing pped , and also that having near-zero pped is a meaningful performance penalty. Prior to moving to other correlations with performance, it bears noting that the uniquely high no-ELM pped observed in QH plasmas is correlated with a uniquely high edge impurity content (particularly the wide-pedestal QH variant), as shown in figure 5(c). The high Zeff QH population also features low net Tinj (not shown). Here Zeff inferred from charge exchange recombination measurements of carbon density in the outer core (near the pedestal top), and is a more challenging measurement than others presented in this work. As such a larger experimental uncertainty should be ascribed (say ±1 at high Zeff ), and furthermore other impurities beyond carbon can contribute to Zeff . The Zeff expected in a fusion reactor is sensitive to the divertor strategy and the atomic number (Z) of the selected radiator(s). In DIII-D the dominant impurity is carbon (Z = 6), and the deuterium fuel concentration decreases linearly from 100% at Zeff = 1 to 0% at Zeff = 6. As such the level of fuel dilution in DIII-D at high Zeff is certainly intolerable. It should be noted however that Zeff in QH plasmas typically exhibit a hollow profile, with on-axis values in the range of 3–4 observed even when the edge Zeff ≈5 [127]. Dedicated studies have also reported favorable core impurity transport in QH plasmas relative to ELMing plasmas [66], despite the fact that lower Zeff values are typically observed in ELMing plasmas (as will shown in section 5).

The carbon issue for QH plasmas is further emphasized in figure 6(a) by noting that the highest performance in QH is found in all but one discharge with pedestal-top 4, unlike the other no-ELM regimes on DIII-D (excepting perhaps EDA-H). It is unclear if this correlation has any basis in causality, and past studies focusing on impurity confinement have found reasonably high impurity exhaust for QH plasmas [66, 128]. Understanding and reducing the carbon inventory of QH plasmas (while maintaining high performance) is thus an important research direction already underway, and further motivates the establishment of the QH regime in all-metal tokamaks where low Zeff is the default operating condition [129].

Figure 6. Refer to the following caption and surrounding text.

Figure 6. Additional correlations with no-ELM plasma performance (): (a) carbon impurity content (Zeff ), (b) core toroidal rotation (Vcore ), (c) total input power (Ptot ).

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While carbon content is less of an issue for other no-ELM regimes in DIII-D, other correlations that challenge extrapolation are identified. Neg-D, L-mode, and especially RMP plasmas are shown in figure 6(b) to have a strong correlation with the absolute core rotation (Vcore ), with low Vcore accessed by operating near Tinj = 0 conditions. Only QH plasma achieve high at low rotation (at least partially due to the larger pped ). Considering the relatively narrow pped for RMP plasmas shown in figure 5, the performance variations in RMP plasmas are largely due to variations in the core, whose performance is in turn is highly correlated with Vcore . This is consistent with an ExB shear turbulent stabilization mechanism giving rise to high core performance in RMP plasmas. This hypothesis is perhaps unsurprising given similar observations in ELMing regimes on DIII-D [130, 131], although alternate mechanisms impacting the confinement of RMP plasmas at fixed Tinj have also been identified [132]. As shown in figure 6(c), increasing Ptot (and Tinj ) to maximal values does not improve the confinement of RMP plasmas, with an optimum in performance at Ptot ≈ 6 MW is found ( 3), similarly to QH plasmas in the database. While ExB shear confinement improvements are readily found at high Tinj , their extrapolation to future reactors such as ITER is challenging owing to their high moment of inertia as compared to expected Tinj values [111]. However, recent work for ITER finds some ExB shear turbulent suppression can be expected despite this unfavorable scaling [133]. Extracting the ExB shearing rate for the database and comparing to micro-instability growth rates is beyond the scope of this study.

Interestingly, Neg-D plasma performance is also found to correlate with Vcore as well as with Ptot . The role of ExB shear suppression in the Neg-D performance enhancement has not yet been assessed experimentally, as evidenced by figure 1(c) the requisite variations in Tinj at constant Ptot have yet to be performed. However, the expected mechanism for enhanced confinement in Neg-D plasmas is thought to be directly related to the shape (triangularity and Shafranov shift) giving rise to a reduction in stiffness [57], supporting a testable hypothesis that the dependence on Ptot is more important than ExB shear.

Given the scarcity of EDA-H and I-mode data, any observed correlations may be due to sampling bias. That being said, EDA-H plasmas appear to have some features of QH plasmas: strong pped contribution, and also feature high Zeff at their highest performance. Similarly, I-mode exhibits some features of RMP and Neg-D plasmas: a strong core contribution and possible correlation with Vcore and Ptot . L-mode plasmas also show evidence of a Ptot and Vcore correlation, as would be expected for a regime solely dependent on good core performance.

5. Comparison to plasma performance with ELMs

A logical interlude at this point is to compare the no-ELM plasma performance and core-pedestal correlations discussed in the preceding sections to DIII-D ELMing plasmas highlighted in the literature. This section repeats key figures of these two sections but now including ELMing data points. While less effort was undertaken to ensure the highest performance ELMing pulses were found against all abscissa, the ELMing database consists of highlighted 'trophy' discharges across the breadth of ELMing regimes studied in DIII-D. These discharges exhibited noteworthy plasma performance, either in confinement or pressure. Roughly in order of increasing I/aB (decreasing q95), representative high-performance discharges in high βP [134136], high [137], high [138, 139], steady-state hybrid [140, 141], advanced inductive [15, 130, 142, 143], super H-mode [16, 144], and ITER baseline scenario [145147] are included. This database should not be considered comprehensive in the absolute best of DIII-D ELMing performance, but rather representative of featured high-performance ELMing discharges created since the installation of the divertor baffling structures. Note significantly higher ELMing absolute performance can be found with the higher κ, , and I plasmas precluded by the modern DIII-D divertor [14, 148, 149]. Furthermore, no effort was made to include low performance ELMing discharges. The ELMing operating space figure (analogous to no-ELM figure 1) is not shown, as ELMing plasmas can generally be found everywhere in the DIII-D operating space (excepting low ). The highlighted ELMing discharges span the accessible range of I/aB, IaB, and Ptot operating space, and include both NBI, ECH, and mixed heating plasmas.

Discussion begins with normalized performance, shown in figure 7 (to be compared with no-ELM figure 2). The Troyon stability diagram (figure 7(a)) shows a swath of ELMing datapoints at high βT for various I/aB, generally showing many scenario paths to high performance. Stationary discharges at considerably higher βN can be found (up to above βN = 4). Also notable on the Troyon diagram are ELMing data at I/aB = 2 (q95 ≈ 2.3), which while stationary for over 0.3 s (thus meeting the inclusion criteria of section 1.2) evolve to tearing instability on a longer timescale. Normalized confinement quality (HL89 and HH98y2) are found to be comparable to the best no-ELM plasmas, but high H-factor is now sustained to much higher βN and occurs over a wide range of scenarios.

Figure 7. Refer to the following caption and surrounding text.

Figure 7. Comparison of (a) normalized current (I/aB) and pressure (βN ), (b) confinement quality factors for L-mode (HL89) and (c) H-mode (HH98y2) against βN for ELMing and no-ELM plasmas.

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Improved absolute performance is also found in ELMing plasmas, as shown in figure 8 (to be compared with no-ELM figure 3). ELMing plasmas reach higher τ, higher , and higher . The highest ELMing is found for advanced inductive and super-H plasmas, which as shown in figure 8(b) operate at high IaB. Improved ELMing performance to no-ELM performance is found at all IaB. A such, normalized triple product () as shown in figure 8(c) is robustly higher by about a third, and meets ITER 15 MA Q = 10 levels. Plotting against Tinj reveals a performance degradation in ELMing plasmas more severe than no-ELM plasmas (compare to figure 3(c)). The performance at net Tinj = 0 quantified by is actually the same with and without ELMs, though q95 is quite different.

Figure 8. Refer to the following caption and surrounding text.

Figure 8. Comparison of (a) total pressure and confinement time (τ), (b) triple product () and IaB, (c) normalized triple product () and torque (Tinj ) for ELMing and no-ELM plasmas.

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The pedestal pressure (pped ) contribution to ELMing plasma performance is summarized in figure 9 (to be compared with no-ELM figure 5). The pressure fraction from the pedestal (figure 9(a)) is on the high end as compared to no-ELM plasmas, with pped / between 2 and 4, and is in a narrower range than no-ELM plasmas. About 50% higher pped can be achieved in stationary ELMing conditions as compared to no-ELM conditions, and a good correlation with pped and is found for ELMing data as shown in figure 9(b). Unlike no-ELM plasmas (figure 5(c)), no positive pped correlation with Zeff is found for ELMing plasmas, shown in figure 9. Instead, the highest pped (15 kPa) ELMing plasmas are almost all found below 3. This is consistent with the hypothesis that the ELM plays an important role in exhausting impurities.

Figure 9. Refer to the following caption and surrounding text.

Figure 9. Comparison of (a) pedestal (pped ) contribution to , (b) pped dependence on , and (c) impurity content Zeff correlation with pped for ELMing and no-ELM plasmas.

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The performance of ELMing plasmas within ITER shape constraints is shown in figure 10 (to be compared with no-ELM figure 4). Performance measured by GL89 (figure 10(a)) and GH98y2 (figure 10(b)) is found to decrease with Tinj , as was found with in figure 8(c). Interestingly, at low/zero Tinj , the ITER Q = 10 criterial is met according to GH98y2 but not GL89, which falls just short. Exceptionally high GH98y2/GL89 discharges are found at high Tinj , corresponding to the advanced inductive scenario [145]. Re-visiting the analysis of [124] for ELMing discharges (figure 10(c)) reveals many datapoints that extrapolate to Q = 10 or greater within ITER's Paux constraints. However, the high GL89/GH98y2 datapoints included in this study at 2 Nm do not meet the ITER Paux criteria.

Figure 10. Refer to the following caption and surrounding text.

Figure 10. Comparison of ELMing and no-ELM plasmas in terms of figures of merit for fusion performance isolating discharges with ITER-like plasma shape. (a) Gain factor based on L-mode scaling (GH98y2) and (b) L-mode scaling (GH98y2) plotted against torque Tinj , and (c) alternate gain factor (Galt ) against scaling of fusion power.

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6. No-ELM plasma integration with electron heating and dissipative divertors

Viable tokamak scenarios without ELMs must also be integrated with two essential features of burning plasmas: auxiliary electron heating and a dissipative divertor state. The former models the heating from fusion-produced alpha particles, while the latter is mandatory to manage the heat flux to the material boundary. While sophisticated modeling (of heat flux channels and atomic dissipation) is necessary to define the operating point of a regime against burning plasma requirements, a few simple and robust metrics can be considered. For electron heating, the ratio of ECH power delivered by high power microwaves to the total power (), and for divertor dissipation the fraction of radiated power (here in the core and the divertor) to total power (frad ) and the ratio of the density at the separatrix to the Greenwald density (ne,sep /nG ). The motivation for these metrics and how no-ELM plasmas perform against them will now be described in turn.

6.1. Boundaries and performance toward dominant electron heating

Burning plasmas self-heat through the collisional slowing down of MeV alpha particles, and at this high energy the dominant heat deposition is to the electrons, modifying the plasma turbulent transport properties [150155]. DIII-D has long been equipped with ≈3 MW of ECH power (PECH ) to mimic this heating channel, though this is a small fraction of the available NBI power (≈16 MW). NBI heats ions preferentially (though the ratio depends on the density) and depending on the NBI configuration can also impart significant Tinj , rotation, and ExB shear, as described in section 4. The mix of ion and electron heating required to mimic a burning plasma depends on the detailed kinetic profiles expected in the plasma core.

Plotting Ptot against in figure 11(a) makes clear the dominant operational consideration is a reduced access to high Ptot at high on DIII-D, entirely due to limited available PECH . RMP plasmas are observed across the full range of PECH , though interestingly only at fairly high Ptot and low . This operating range is found to be limited by the return of ELMs at low rotation and pressure, though this threshold has not yet been explored in detail. QH plasmas are also observed across the full range of PECH , and they clearly access higher (lower Ptot ) [68]. For the I-mode, QH, and EDA-H regimes no operational limit in is found if (conventional) L-mode is avoided, and Neg-D also finds no limit. Indeed, the EDA-H in DIII-D is thus far only identified at high .

Figure 11. Refer to the following caption and surrounding text.

Figure 11. Integration with electron heating: (a) operational space in terms of and Ptot , with dashed lines indicating constant PECH . (b) Plasma performance () is found to fall with increasing .

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Plasma performance quantified by is plotted against in figure 11(b). The loss of Ptot access is clearly manifest in a reduced . The performance degradation for RMP plasmas is particularly severe, supporting the particularly important role of rotation shown in figure 6(b). Unlike past QH results at high Tinj [67], recent experiments in low Tinj QH plasmas (specifically the wide-pedestal variant at high q95) have found a performance improvement with at fixed Ptot [68]. This indicates the higher performance = 0 QH plasmas are likely benefiting from other factors such as higher Ptot or lower q95. Interestingly, against this metric the two regimes found to have the highest performance are QH and EDA-H, which as shown in figure 5(a) also have the highest fractional pped /. As such, a relatively strong pedestal is correlated with an improved at high and low Ptot . The observed performance at high Ptot and high is a highly relevant and compelling question [127], awaiting increased PECH to be available in DIII-D and has motivated similar research programs elsewhere [113].

6.2. Boundaries and performance toward dissipative divertor conditions

The final topic discussed is integration with dissipative divertor conditions. This is a uniquely challenging direction for no-ELM regimes at least in present tokamaks, owing to the inability to simultaneously access low collisionality (favorable to access the current-limited pedestal physics of interest) together with high density (favorable to access highly dissipative divertor regimes). Results will be presented here with additional interpretation discussed in section 7.

Access and performance toward divertor integration is presented in figure 12, with limiter plasmas (circle symbols) now excluded. ne,sep /nG is now used as a density metric instead of /nG [156]. This is because the interface of the divertor solution to the plasma occurs at the separatrix (not at the core or pedestal top). As with Zeff , ne,sep /nG is a more challenging measurement with increased experimental uncertainty (here characterized at ±0.03). Here ne,sep is extracted from automated hyperbolic tangent fits to the electron pedestal profiles. Predictions for the required ne,sep /nG in a reactor depend sensitively on the divertor geometry and impurity seeding strategy, but in the case of ITER recent modeling ne,sep /nG values in the range of 0.4–0.7 are used [157], which is off the chart in figure 12. Considering ne,sep /nG in figure 12(a) presents an important distinction between no-ELM regimes. While as shown in figure 1(d) several regimes access high /nG [109], QH plasmas uniquely follow a trajectory of low ne,sep / (consistent with its low-recycling wall operational preference), challenging prospects for divertor integration in this regime [158]. RMP plasmas operate at higher ne,sep /, but still limit to a similarly low ne,sep /nG owing to the low pedestal-top density (ne,ped ) limit [38, 69, 102]. Only the Neg-D and EDA-H regimes access relatively high ne,sep /nG in DIII-D, indicating a clear advantage in terms of dissipative divertor integration. Considering observed plasma performance at high ne,sep /nG in figure 12(c) the Neg-D regime is superior owing to its unique tolerance of both high density and high power.

Figure 12. Refer to the following caption and surrounding text.

Figure 12. Integration with dissipative divertor: (a) comparison of line-averaged /nG to separatrix density ne,sep /nG , (b) operational space in terms of frad and ne,sep /nG . Plasma Performance measured by against (c) ne,sep /nG and (d) frad , indicating decreasing performance with increasing divertor compatibility.

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A second dissipative divertor metric is the radiation fraction (frad = Prad /Ptot , where Prad is the total core and divertor radiated power), as high frad implies less conducted power for the divertor first-wall to handle [159]. Again, extrapolation of this parameter to a reactor requires specifying the divertor geometry and ne,sep /nG , but ITER is expected to require frad ≈ 0.8 with about 0.3 inside the separatrix [160]. As shown in figure 12(b), I-mode, EDA-H, L-mode, and Neg-D plasmas reach 0.5 frad or greater, while RMP and QH plasmas have not yet reached this level with stationarity at the level defined in section 1.2 (higher has been achieved transiently). Considering observed plasma performance at high frad (0.5) shown in figure 12(d), there is no clear separation observed between the EDA-H, I-mode, and L-mode plasmas, and indeed performance is overall severely degraded.

Unlike other axes, it should be noted high frad is relatively underexplored in DIII-D no-ELM studies. There have been some dedicated attempts in RMP [106, 161] with mid-Z radiators such as Ne and Ar and initial attempts in QH plasmas. The collisionless QH and RMP regimes are challenged on these axes by a return of the ELM found at high density and collisionality, which as described may be qualitatively different when extrapolating to a reactor. However, high frad at relatively low ne,sep /nG may be accessible by using efficient high-Z radiators (Xe, Kr, etc), motivating an interesting future experimental direction. EDA-H plasmas, as reported in other devices [162], appear to be well-suited to divertor integration, reaching both high ne,sep /nG and high frad , and indeed EDA-H is challenged instead by pedestal compatibility toward low operation [43]. I-mode appears comparably attractive in figure 12(b), though recent work casts doubt on its ability to tolerate the impurity seeding needed to increase frad [163]. Advancing Neg-D plasmas toward higher frad and ne,sep /nG stands out as a fertile ground for future study, with little experimental data yet also no known mechanism to prohibit robust divertor integration with a relatively high performance core, as will be further discussed.

7. Discussion and conclusions

This work has endeavored to document the observed operational boundaries as well as the plasma performance within those boundaries for stationary plasmas without ELMs in DIII-D. These operational boundaries and their compatibility with various regimes are summarized in table 2. Almost all criteria listed in table 2 must be simultaneously achieved in an integrated burning plasma scenario for ITER or beyond, with few exceptions: perhaps q95 need not be so low, perhaps βN or need not be so high, perhaps need not be low in a Neg-D scenario, etc. However, it can be clearly seen that no regime is yet able to demonstrate comprehensive reactor compatibility. While this table does not detail the observed performance, it is generally found that where access is readily achieved (green color in table 2), relatively high performance (as compared to other no-ELM regimes) is also generally found. It also bears repeating that the identified correlations of performance with carbon content and rotation (figure 6) challenge extrapolability of all regimes and motivate further targeted studies. Also worth noting is that assessment of non-inductive fraction needed for steady-state tokamak operation is not in the scope of this work, largely because extracting the non-inductive fraction is considerably more challenging than the metrics already included. With this as pre-amble, a few salient further issues are now discussed.

Table 2. Operational boundaries and peak performance for no-ELM regimes as observed in DIII-D, with numeric limits included alongside figures from which these values are extracted. Colors qualitatively indicate presently demonstrated access: red for no access, yellow for marginal access, and green for robust access. Access is not necessarily achieved simultaneously.

 EDA-HI-modeNeg-DQHRMPFigure
High Ptot [MW]47151011 1(d)
Low 11 112 1(d)
Low Tinj [Nm]00002 1(c), (f)
Low q95 4.53.5 333 1(a), (e)
Low 31.52 .1 .1 1(e)
High βN 1.41.632.72.5 2(a)
Low Zeff 1.51.31.5 21.8 6(c)
High .9.8.9.7.4 11(a)
High ne,sep /nG .25.2.29.15.15 12(a), (b)
High frad .7.6.5.4.4 12(b)
High 1.5 1.8 2.6 4.4 4.6 3(c)

7.1. Pedestal-divertor integration

Challenging reactor-relevance of some no-ELM regimes is the well-known inaccessibility (in present tokamaks) of a high-performance (low ) pedestal simultaneous with a highly dissipative (high ne,sep & frad ) divertor state. Indeed, a key divergence is found between high-performance pedestal regimes (QH, RMP) vs. regimes that favor dissipative divertors (EDA-H). Connecting these two extremes requires no-ELM regime study in high pped conditions, which in principle enables low (/) at high ne,ped . The connection of ne,ped to ne,sep is indirect, and sensitive to the no-ELM regime (as evidenced by figure 12(a)) as well as the opacity of the pedestal to neutral fueling [164]. High pped is predicted (based on peeling-ballooning stability calculations [165]) to be accessible via large size, high-field, and/or strong shaping. However, the interaction of these engineering parameters with the specifics of each no-ELM regime access criteria may complicate this picture, as seen for example with B thresholds for I-mode plasmas [51] or shape thresholds for RMP plasmas [100]. As such, pursuing no-ELM regime integration studies at maximal pped is highlighted as an important pedestal physics research direction that motivates upgrades to existing facilities [166]. This question also forms a key scientific motivation of the ITER project, whose primary goal will be integrating a high-performance burning plasma core (high , low ) with a dissipative divertor solution (high ne,sep & frad ).

7.2. Extrapolation of power and the role of B

A second challenge lies with uncertainty in how to extrapolate Pnet after a pedestal is established. PLH08-like scalings (, where S is the plasma surface area) well-predicts H-mode access, qualitatively consistent with the need for a critical ExB velocity to trigger the shear-suppression of edge turbulence [167, 168]. However, it is not clear whether this scaling is appropriate after the pedestal is formed, as opposed to alternate scalings such as Pnet /S (heat flux), or Pnet / (heat flux per particle). This question directly relates to the impact of B in the extrapolation of no-ELM regime solutions, and more broadly in how to predict the pedestal transport without ELMs. For example, it is well documented that an upper limit in Pnet exists where the EDA-H, I-mode, and L-mode regimes transition to ELMing H-mode [51, 59, 162]. This is troubling for EDA-H and I-mode since regime access is meant to increase performance and increase the fusion power contribution to Pnet , thus risking a dynamically unstable situation. Furthermore, much of the EDA-H, I-mode, and L-mode regime findings of this study can be linked to the intolerance to Pnet of these regimes in DIII-D, where PLH08 is only about 2–3 MW. In contrast, the tolerance of QH, RMP, and Neg-D plasmas to Pnet over a range of density significantly opens their operating domain in many directions. If is the relevant power normalization, then the high Pnet regimes are clearly overpowered ( 1) in DIII-D. However, if the relevant normalization is Pnet /S, the high Pnet regimes are in-line with expectations in future tokamaks. The key difference between these extremes is thus whether B enters in the normalization of power. These questions motivate dedicated study of no-ELM regimes over as wide a range of B as possible, to decouple the no-ELM regime access from PLH08 as much as possible, though naturally indirect effects (such as changes in ) will complicate these studies. Once again, ITER will provide an excellent platform to resolve these issues as it will operate at high Pnet /S yet low . Similarly, the mid-size (low S) yet very high-B SPARC tokamak [169] will provide a yet clearer separation of these competing normalizations, with DIII-D like high Pnet /S yet ITER-like low .

7.3. Negative triangularity

The above challenges are not resolvable with presently operating tokamaks. Interestingly, the Neg-D regime side-steps the aforementioned integration issues and in principle can achieve fully and unambiguously integrated no-ELM scenarios in mid-scale tokamaks, though likely at the expense of lower absolute performance. The low (high pped ) challenge is simply abandoned, with the core contribution to instead relied on to recover high performance. Questions about how to normalize power and the importance of PLH08 are similarly side-stepped, because there is no desire for H-mode. The only 'access' question is whether H-mode will be robustly avoided, and to what maximum . Emerging work indicates the H-mode suppression is robust in Neg-D due to MHD ballooning edge stability considerations [170], supported by the observation of 6 shown in figure 1(d). The Neg-D regime thus relieves the physics risk from integration issues but increases the burden on the core confinement to achieve sufficiently high plasma performance despite low pped . This work shows that considering normalized performance (figure 2), Neg-D plasmas are already comparable to the other no-ELM regimes. Absolute performance (figure 3) is considerably lower, but points to raising κ and I to access high IaB, benefitting from the tolerance to Ptot expected. Operation at high I/aB and high Ptot is also a compelling direction to further raise normalized performance without ELMs. This work provides ample basis to quantify any future no-ELM scenario achievements in performance and integration, Neg-D or otherwise.

Acknowledgment

This work summarizes and reviews progress over nearly two decades of DIII-D experimental ELM control work. As such, the central acknowledgement is to the many talented individuals comprising the DIII-D team who worked diligently to create the plasmas here documented. To the degree possible, the constituent studies and authors have been recognized via citation. Useful targeted discussions relating to the scope of this study were provided by: P Snyder, D Ernst, M Knolker, A Garofalo, B Grierson, A Jarvinen, F Laggner. Constituent databases incorporated into this study were provided by: T Evans, K Burrell, T Osborne, M Austin. Further discharges of interest were highlighted by: X Chen, T Abrams, D Ernst, J Hughes, A Marinoni, W Solomon. D Ernst improved the impurity concentration analysis in wide-pedestal QH mode discharges.

This material is based upon work 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(s) DE-FC02-04ER54698 and DE-SC0020298. 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.

Data availability statement

The data that support the findings of this study are openly available at the following URL/DOI: https://fusion.gat.com/global/diii-d/dmp.

Appendix A.: Comparison of performance metrics

A short discussion of the observed differences between plasma performance metrics discussed in this work is appended, focusing on the difference between fusion performance metrics based on the HL89 scaling law (GL89) and the normalized triple product (). Note a similar study of GH98y2 and GL89 (not shown) found no meaningful distinction between these two performance metrics. In contrast, important distinctions between GL89 and are pictured in figure A1. Comparing GL89 directly against in figure A1(a), each regime population is found to be largely co-linear, indicating both metrics are capturing relative trends well. However, some no-ELM regime distinction is found. Neg-D plasmas perform very well in GL89 as compared to , but this is merely representative of the penalty in q95 to be paid for Neg-D plasmas, which artificially inflates GL89 as it is proportional to , thus further motivating the use of throughout this work. Conversely, strongly shaped QH plasmas are penalized in GL89 as compared to . The ratio of to GL89 is found to be correlated with q95, shown in figure A1(b), which shows the positive effect of strong shape as well as provides evidence that low q95 is over-rewarded in the GL89 (and GH98y2) scaling laws. A second correlation with Ptot is highlighted, which indicates a gradually decreasing ratio of to GL89 with increasing Ptot , suggesting that high power is over-rewarded in GL89. These findings highlight the value of , which does not impose a scaling law to interpret the plasma performance but rather lets the triple product () speak for itself.

Figure A1. Refer to the following caption and surrounding text.

Figure A1. Comparison of fusion performance metrics, comparing (a) HL89 scaling law (GL89) against normalized triple product (. The ratio of these metrics is seen to correlate with (b) the safety factor (q95) and (c) the total injected power (Ptot ).

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