# Plasma Performance and Operational Space without ELMs in DIII-D

C. Paz-Soldan  General Atomics, San Diego, California 92186-5608, USA
Department of Applied Physics & Applied Mathematics, Columbia University, New
York, New York 10027, USA<EMAIL_ADDRESS>the DIII-D team

###### 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
(Rev. Mod. Phys. s), quiescent H-mode (QH, including wide-pedestal variant),
improved confinement mode (I-mode), enhanced D-alpha H-mode (EDA-H),
conventional 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: Rev. Mod. Phys. , QH, and Neg-D. Absolute performance (volume-averaged
pressure $\left<p\right>$, confinement time $\tau$, and triple product
$\left<p\right>$$\tau$) also discriminates no-ELM regimes and is found to rise
linearly with $IaB$ (a metric for the magnetic configuration strength, the
product of current $I$, minor radius $a$, and field $B$ that has units of
force), and also benefits from tolerance to power. The highest normalized
performance using the metric $\left<p\right>$$\tau/IaB$ is found in QH and
Rev. Mod. Phys. regimes. Focusing on ITER-shaped no-ELM plasmas, Q=10 at 15 MA
scaled global performance is met with two out of four considered metrics, but
only thus far at high torque. Though comparable QH and Rev. Mod. Phys.
performance is found, the pedestal pressure ($p_{ped}$) is very different.
$p_{ped}$ in Rev. Mod. Phys. plasmas is relatively low, and the best
performance is found with a high core $\left<p\right>$ fraction alongside high
core rotation, consistent with an ExB shear confinement enhancement. $p_{ped}$
of QH plasmas is significantly higher than Rev. Mod. Phys. , and QH
performance does not correlate with core rotation. However, the highest QH
$p_{ped}$ are found with high carbon fraction. While normalized performance of
Neg-D plasmas is comparable to QH and Rev. Mod. Phys. plasmas, the absolute
confinement of Neg-D is lower, owing to low elongation and low $p_{ped}$
achieved thus far. Considering integration with electron cyclotron heating
(ECH), the operational space for Rev. Mod. Phys. and QH plasmas narrow, while
that for EDA-H plasmas open, and the high $p_{ped}$/$\left<p\right>$ 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 highlighted
ELMing plasmas 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.

††preprint:

##  I 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 Zohm1996 ; Leonard2014 . Above a threshold size, the ELM not
only impacts the integrity and lifetime of plasma-facing components
Loarte2003a ; Federici2003 ; Dux2011 ; Pitts2013  but also imposes limits on
the tokamak operating space (and achievable plasma performance) by driving
excessive material influx to the plasmaKallenbach2005 ; Beurskens2014 ;
Kim2018 . Developing scenarios and techniques to mitigate or eliminate the ELM
is thus a topic of well-recognized importance in the fusion community.
Addressing the ELM challenge has also motivated significant actuator
investment in upcoming fusion-grade tokamak projects such as ITER Loarte2014 ;
Maingi2014 ; Garofalo2020 .

In mid-scale tokamaks with carbon walls (such as DIII-D) the operating space
is not generally limited by the ELM. As such scenario development work often
proceeds without enforcing a constraint on ELM virulence. Peak plasma
performance in DIII-D is found in ELMing plasmas Lazarus1997 ; Luce2003 ;
Snyder2019 . 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 in DIII-D. These regimes are
described in Sec. I.1 and summarized in Tab. 1. Though detailed studies of
individual no-ELM regime access, sustainment, and performance against various
parametric dependencies abound (see Tab. 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.

Regime | AUG | C-Mod | DIII-D | EAST | JET | JT-60U | KSTAR | DB Color
---|---|---|---|---|---|---|---|---
EDA-H | Gil2020, | Greenwald2000, | Mossessian2003, | Sun2019, |  Stober2005, †∗ | N/A | N/A |
I-mode |  Ryter1998, † Happel2017, ,Ryter2017, | Whyte2010, | Marinoni2015, | Liu2020b, |  Andrew2004, †∗ | N/A | N/A |
Neg-D | Happel2020, | N/A | Austin2019, | N/A | N/A | N/A | N/A |
QH |  Suttrop2003, † | N/A | Greenfield2001, | Qian2020IAEA, |  Suttrop2005, † | Sakamoto2004, | Lee2020, |
Rev. Mod. Phys. |  Nazikian2016IAEA, ,Suttrop2018, | N/A | Evans2004, | Sun2016, | N/A | N/A | Jeon2012, |
Table 1: No-ELM regime access in MA-class conventional tokamaks. †: access
prior to metal wall installation. ∗: non-stationary or ambiguous access. DB
Color indicates the icon color used in subsequent figures, with L-modes also
shown in magenta.

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 Sec. I.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-factorFenstermacher2013 ). 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. 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.

###  I.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 Refs.
Oyama2006, ; Evans2015, ; Viezzer2018, . In alphabetical order, the regimes
are the:

  * •

The Enhanced D-alpha H-mode (EDA-H) Greenwald1997 ; Greenwald1999a ;
Greenwald2000 , a regime possessing a fully formed density and temperature
pedestal, typified by a “quasi-coherent mode” electro-magnetic fluctuation in
the $\mathcal{O}$(100 kHz) range that drives additional transportLaBombard2014
; Golfinopoulos2018 .

  * •

The Improved energy confinement mode (I-mode) Ryter1998 ; Whyte2010 ;
Hubbard2016 , a regime with a temperature but not a density pedestal, and
improved energy confinement but not particle confinement as compared to L-mode
levels Hubbard2017 . A 100 kHz range “weakly-coherent mode” coupled to a
geodesic acoustic mode (GAM) is ubiquitously observed that drives additional
transportCziegler2013 ; Manz2015 .

  * •

Operation with a Negative Triangularity plasma shape (Neg-D)Moret1997 ;
Camenen2007 ; Austin2019 ; Marinoni2019 . Neg-D plasmas have an L-mode edge
(no or only partial pedestal) but the shaping yields improved core turbulent
transport Merlo2015  and suppresses the H-mode transition to powers well above
that expected by established scalings Marinoni2020IAEA ; Martin2008 .

  * •

The Quiescent H-mode (QH)Greenfield2001 ; Burrell2001 , a regime with fully
formed density and temperature pedestal. QH plasmas are typified by either a
coherent electromagnetic “edge-harmonic oscillation” (EHO)Chen2016 ; Wilks2018
; Pankin2020  or an incoherent “broadband MHD” oscillationGuo2015  both in the
$\mathcal{O}$(10s kHz) range that drive additional transport. A recently
emphasized broadband MHD QH variant, the wide-pedestal QH-modeBurrell2016 ;
Chen2020  is also included. 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 Ernst2016 ; Ernst2018IAEA .

  * •

ELM suppression via Resonant Magnetic Perturbations (Rev. Mod. Phys.
)Evans2004 ; Evans2006 ; Jeon2012 ; Kirk2013c ; Kirk2015 ; Sun2016 ;
Suttrop2018 . Application of $\approx$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 Waelbroeck2009 ; Nazikian2015
; Hu2019 ; Fitzpatrick2020a ; increased turbulent fluctuation levels directly
arising from field penetration McKee2013 ; Lee2016 ; Lee2019 ; increased
turbulence arising indirectly from penetration-induced changes to the radial
electric field structure Sung2017b ; Taimourzadeh2019 ; or a combination of
these effects. The additional transport has also been proposed to be due to
mechanisms such as neoclassical effects Callen2012b ; Huijsmans2015  or
localized peeling-ballooning instabilities driven by 3D equilibrium
modifications Bird2013 ; Willensdorfer2017 ; Ryan2019 ; Kim2020a  which do not
require significant field penetration.

For completeness the default Low-confinement L-mode is also included in the
study, though it is not listed in Tab. 1. Note all no-ELM regimes are subject
to enhanced edge transport, either via enhanced turbulent fluctuations
(L-mode, Neg-D, QH, Rev. Mod. Phys. ), (quasi-)coherent fluctuations (EDA-H,
I-mode, QH), or imposed laboratory-frame non-axisymmetry (Rev. Mod. Phys. ).
Furthermore only Neg-D and Rev. Mod. Phys. 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 Evans2013 ; Daly2013 ).

###  I.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:

  1. 1.

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 Oyama2006 ; Viezzer2018 ; Xu2019 ,
and to ELMs mitigated via RMPs or high-frequency pellet pacing Loarte2014 .

  2. 2.

Intervals must be stationary, as defined by the rate of rise of the average
density ($\left<n_{e}\right>$) being below $1.5\times 10^{19}/s$. 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.

  3. 3.

Intervals must at least 300 ms long (about two energy confinement times,
$\tau$). Longer durations (up to several seconds) are utilized if stationary
conditions are maintained.

  4. 4.

All main control parameters (shape, $I$, $B$) must be fixed during the
interval. All intervals either fix total 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.

  5. 5.

The plasma cross-section or near-SOL 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 100700 (c. 2000) Reis1996
; Bozek1999 . Some discharges prior to shot 127300 (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 Burrell2001  and
early low triangularity Rev. Mod. Phys. discharges Evans2006a .

  6. 6.

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.

###  I.3 Caveats

Several caveats of this study deserve up front mention:

  1. 1.

DIII-D experimental run-time awarded to explore some regimes (namely Rev. Mod.
Phys. 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.

  2. 2.

This caveat concerns the completeness of the database, which was assembled
through a combination of manual and automated techniques. Automated techniques
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.

  3. 3.

ELMs were often present in discharges preceding (or following) the selected
time interval. As such, the presented time intervals may not be accessible
without ELMs earlier in the discharge evolution. As such they might not be
realizable in a tokamak that cannot tolerate any ELMs. The fully formed
pedestal regimes (QH, Rev. Mod. Phys. , EDA-H) are especially prone to
spurious ELMs, while the no or partial pedestal regimes (Neg-D, I-mode,
L-mode) are robustly without ELMs.

  4. 4.

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.

  5. 5.

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.

###  I.4 Structure of Paper

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

Figure 2: 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 $q_{95}$. (b) elongation
($\kappa$) and absolute average triangularity ($\left|\delta_{avg}\right|$),
(c) total power ($P_{tot}$) to injected torque ($T_{inj}$), dash-dot lines
indicate approximate range accessible to the NBI system, (d) ratio of line-
average density to the Greenwald density ($\left<n_{e}\right>$/$n_{G}$) and
ratio of net power (subtracting core radiative losses) to scaled L-H threshold
power ($P_{net}/P_{LH08}$), (e) edge collisionality ($\nu_{e}^{*}$) and edge
safety factor ($q_{95}$), (f) $T_{inj}$ and $q_{95}$. 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.

##  II Operational Space

Stationary plasmas without ELMs are found only in a subset of the accessible
DIII-D operating space. Figure 2 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).

#### Plasma current ($I$) and toroidal field ($B$):

Operating space in terms of $I$ and $B$ is shown in Fig. 2(a). This most basic
representation already reveals important features. Rev. Mod. Phys. plasmas are
found only in a narrow range of $q_{95}$ from 3-4, owing to well known
resonant window requirements Evans2008 ; Suttrop2018 ; Hu2020b , though other
devices have found Rev. Mod. Phys. resonant windows in different ranges of
$q_{95}$ In2019 ; Sun2016 . Note Rev. Mod. Phys. plasmas at $q_{95}$=7
reported in Ref. Fenstermacher2008  are found to have small residual ELMs and
thus do not meet the criteria discussed in Sec. I.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 $q_{95}$ just above 2 Piovesan2014 ; Hanson2014 . 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 Greenwald2000 ;
Hubbard2017 ; Gil2020 .

#### Plasma shaping:

The DIII-D shaping flexibility as manifest in the no-ELM operating space is
shown in Fig. 2(b), represented as absolute average triangularity
($\left|\delta_{avg}\right|$) and elongation ($\kappa$). QH plasmas are found
to operate over a wide range of shapes, including the most strongly shaped
plasmas. Rev. Mod. Phys. plasmas are not tolerant of the strongest shapes
Shafer2020IAEA . Neg-D plasmas are systematically weak in shape, possessing
either low $\kappa$ or $\left|\delta_{avg}\right|$, owing to their poor fit to
the DIII-D vacuum vessel cross-section. Weak shapes (low
$\left|\delta_{avg}\right|$ and $\kappa$) 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.

#### Input power ($P_{tot}$) and injected torque ($T_{inj}$):

DIII-D can access to a wide range of powers ($P_{tot}$) and torques
($T_{inj}$), as shown in Fig. 2(c). $P_{tot}$ is defined as $P_{aux}$ \+
$P_{OH}$, where $P_{aux}$ is auxiliary heating power (NBI and ECH) and
$P_{OH}$ is ohmic heating power (with $P_{OH}$$<$2 MW). Several notable
features can be found. First, no stationary plasma without ELMs has been
observed while injecting the maximum balanced ($T_{inj}$=0) power, with QH
plasmas coming the closest. L-mode plasmas are less frequently found at high
$P_{tot}$, with notable examples being high radiation fraction ($f_{rad}$)
plasmas and limited plasmas (circle symbols). Rev. Mod. Phys. plasmas are not
tolerant of significant counter-NBIMoyer2017 ; PazSoldan2019a , but do exist
over a wide range of $P_{tot}$. Neg-D plasmas have uniquely accessed the
maximum $P_{tot}$, and as will be discussed have thus far not found a core MHD
limit.

#### Power normalized to scaled LH threshold power Martin2008
($P_{net}/P_{LH08}$) and Greenwald density Greenwald1988
($\left<n_{e}\right>$/$n_{G}$):

Tolerance of a no-ELM regime to net exhausted power ($P_{net}$) is partially
set by H-mode threshold physics, as is the virulence of any ELMs encountered
Eich2017 ; Knolker2018 . $P_{net}$ is defined as $P_{tot}$-$P_{rad}$, where
$P_{rad}$ here is radiated power inside the separatrix. Fig. 2(d) shows that
high $P_{net}$ L-mode plasmas are exclusively found at low
$\left<n_{e}\right>$/$n_{G}$, with ELMing H-mode obtained at higher density.
EDA-H and I-mode regimes are found at intermediate
$\left<n_{e}\right>$/$n_{G}$ but at low $P_{net}/P_{LH08}$. Rev. Mod. Phys.
and QH plasmas are able to access high $P_{net}/P_{LH08}$, and are uniquely
limited by core MHD as opposed to the return of the ELM. Rev. Mod. Phys.
plasmas exhibit a strict upper limit in pedestal-top density and thus
$\left<n_{e}\right>$/$n_{G}$ Evans2006a ; Petrie2011 ; PazSoldan2019 . QH
plasmas can access higher $\left<n_{e}\right>$/$n_{G}$ than Rev. Mod. Phys.
plasmas, owing to their improved compatibility with strong shapes and current-
limited pedestals at high density Solomon2014 ; Garofalo2015a ; Solomon2016 ,
though in Sec. VI the ability of high $\left<n_{e}\right>$/$n_{G}$ 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 $P_{net}/P_{LH08}$ and
$\left<n_{e}\right>$/$n_{G}$.

#### Edge collisionality ($\nu_{e}^{*}$) and safety factor ($q_{95}$):

Plasma regimes without ELMs are known to occupy distinctive points in the
pedestal (or edge) collisionality ($\nu_{e}^{*}$) and edge safety factor
($q_{95}$)Oyama2006 ; Viezzer2018 . Indeed the no-ELM regimes found in DIII-D
are well-separated by these parameters, as shown in Fig. 2(e). Rev. Mod. Phys.
and QH plasmas are found below $\nu_{e}^{*}$ of about 1, while all other
regimes are at higher $\nu_{e}^{*}$. As discussed in Fig. 2(a), Rev. Mod.
Phys. plasmas are only found at low $q_{95}$ on DIII-D, and EDA-H are only
found at high $q_{95}$. I-mode is only observed thus far at intermediate
$q_{95}$ $\approx$ 4\. Other regimes are observed over a range of $q_{95}$. In
DIII-D, low $\nu_{e}^{*}$ access is found together with high
$P_{net}/P_{LH08}$, whereas a reactor can be expected to operate with low
$P_{net}/P_{LH08}$ and low $\nu_{e}^{*}$, as will be further discussed in Sec.
VII.

#### Torque ($T_{inj}$) and safety factor ($q_{95}$):

While less emphasized in the literature, DIII-D no-ELM plasmas clearly exhibit
limitations in simultaneous operation of low $T_{inj}$, low $q_{95}$, and low
$\nu_{e}^{*}$. This is likely the edge stability regime expected in ITER, with
the important caveat that extrapolating $T_{inj}$ depends on what rotation-
dependent mechanism is of interest Garofalo2011 . As shown in Fig. 2(f), Rev.
Mod. Phys. plasmas match $q_{95}$ and $\nu_{e}^{*}$ Wade2015 , but find the
return of the ELM at low $T_{inj}$ Moyer2017 ; PazSoldan2019a . QH plasmas so
far have matched two of low $\nu_{e}^{*}$, $q_{95}$, and $T_{inj}$, but not
all three together owing to the onset of core MHD or the ELM Garofalo2015a .
This finding has motivated extensive DIII-D experimentation to understand low
$\nu_{e}^{*}$ \+ $q_{95}$ \+ $T_{inj}$ limits and their extrapolation
Garofalo2020 , and this regime will soon be accessible in the world research
program as new capabilities come online Stober2020 ; Shirai2017 . Note the low
$q_{95}$ & low $T_{inj}$ limit is not found for the high $\nu_{e}^{*}$
regimes, though even these have not been demonstrated at high power or
pressure ($\beta_{N}$$>$1.2). L-mode plasmas suffer a return to ELMing H-mode
at higher $\beta_{N}$, while Neg-D has not yet been attempted in this low
$q_{95}$ \+ $T_{inj}$ part of parameter space. Access to low $q_{95}$
(specifically high $I$) and high $P_{tot}$ will be shown in the next section
to strongly impact the achievable performance without ELMs in DIII-D.

##  III 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 Sec. V.

Figure 4: (a) Troyon core stability space in terms of toroidal beta
($\beta_{T}$) and normalized current ($I/aB$), dash-dot lines indicate
constant normalized pressure ($\beta_{N}$). Confinement quality factors (b)
$H_{L89}$ and (c) $H_{H98y2}$ as a function $\beta_{N}$, with dash-dot lines
at a constant product of $H$ and $\beta_{N}$. Dashed lines indicate ITER 15 MA
Q=10 targets.

###  III.1 Normalized Performance

Discussion of normalized performance begins with global stability. The Troyon
stability diagram Troyon1984  shown in Fig. 4(a) indicates the normalized
current ($I/aB$), pressure normalized to toroidal field ($\beta_{T}$), and
concurrently the normalized beta [$\beta_{N}$=$\beta_{T}$/($I/aB$)]. The
different no-ELM regimes well-separate in this diagram. $I/aB$ access has
already been discussed in relation to Fig. 2(a), with L-mode uniquely
accessing high $I/aB$. The $\beta_{N}$ accessible is clearly higher for QH,
Rev. Mod. Phys. , and Neg-D plasmas owing to the increased tolerance of power
discussed in relation to Fig. 2(c). Peak $\beta_{N}$ of Rev. Mod. Phys. 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 $\beta_{N}$ limit (present
limit $\beta_{N}$ 2.3) and finds confiment is not degraded by raising
$P_{tot}$ Chen2020 . Interestingly, the highest stationary $\beta_{N}$ without
ELMs is found for Neg-D plasmas, despite the expectation of degraded core
stabilityMedvedev2015 . The reason for this is not yet understood, but is
speculated to be related to Neg-D plasmas operating at higher
$\left<n_{e}\right>$/$n_{G}$ than Rev. Mod. Phys. and QH plasmas, as shown in
Fig. 2(d), which may reduce the pressure peaking instability drive Ferron2005
. It is also clear from Fig. 4(a) that QH and Rev. Mod. Phys. access the
highest $\beta_{T}$, as high $\beta_{N}$ and high $IaB$ are simultaneously
achieved. Accessing high $\beta_{N}$ at high $I/aB$ has not yet been attempted
for the Neg-D regime in DIII-D.

Plasma performance is commonly described in terms of the confinement quality
‘H-factors’, defined as the ratio of the measured energy confinement time
($\tau$=$W/$$P_{tot}$, 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
($H_{H98y2}$IPBch2 ), and L-mode plasmas ($H_{L89}$Yushmanov1990 ). Note that
as no-ELM plasmas are often found at low $\left<n_{e}\right>$/$n_{G}$ [See
Fig. 2(d)], the fast ion content is sometimes not negligible, motivating
presentation of both $H_{L89}$ (which includes fast ion pressure) and
$H_{H98y2}$ (which explicitly removes it). For all cases, fast ion pressure is
evaluated automatically with between-shot codess using the formulas presented
in Ref. Heidbrink1994 .

The performance against these H-factors for the database described in Sec. II
is shown in Fig. 4(b,c), plotted against $\beta_{N}$. As can be seen, these
axes are also effective to separate the no-ELM regimes. Furthermore a good
correlation exists between H-factor and $\beta_{N}$ across all regimes,
despite widely varying $P_{tot}$. This correlation is consistent with
$P_{tot}$ being overly penalized in the confinement scalings. Considering each
regime, L-mode plasmas are found at low normalized performance, Rev. Mod.
Phys. and QH plasmas are found at higher H-factor and $\beta_{N}$, while
I-mode and EDA-H plasmas are found at an intermediate level of normalized
performance. Neg-D plasmas span a wide range of performance, from L-mode like
(low H and $\beta_{N}$) to normalized performance on par or better than Rev.
Mod. Phys. and QH regimes (high H and $\beta_{N}$). The highest H-factors are
uniquely found for QH plasmas.

Figure 6: Absolute plasma performance in the DIII-D tokamak without ELMs,
represented by: (a) average pressure ($\left<p\right>$) and confinement time
($\tau$), with dash-dot lines at constant triple product
($\left<p\right>$$\tau$). (b) Triple product $\left<p\right>$$\tau$ referenced
to $IaB$, showing an increasing trend. (c) $\left<p\right>$$\tau$ normalized
to $IaB$ referenced to $T_{inj}$, with dashed lines referencing fusion gain Q
values at 15 MA in ITER.

###  III.2 Absolute Performance

Absolute performance has long been measured in terms of Lawson’s triple
productLawson1957  [$\left<p\right>$$\tau$, where $\left<p\right>$ is the
volume averaged pressure $W$/(1.5*volume)]. Triple product decomposed into
constituent $\left<p\right>$ and $\tau$ is shown in Fig. 6(a). No-ELM regime
separation is again found. QH and Rev. Mod. Phys. plasmas both reach high
$\left<p\right>$$\tau$ with a roughly equal mix of $\left<p\right>$ and
$\tau$, while EDA-H and I-mode plasmas emphasize $\tau$ over $\left<p\right>$,
and Neg-D plasmas emphasize $\left<p\right>$ over $\tau$. Note that most NBI
heated DIII-D plasmas have $T_{i}/T_{e}>1$, but $\left<p\right>$ 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 Rev.
Mod. Phys. . The discrepant view of Neg-D in normalized performance (Fig. 4)
and absolute performance (Fig. 6) 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
$\left<p\right>$$\tau$ without ELMs on DIII-D is found in Rev. Mod. Phys.
plasmas, a surprising result given the significant pedestal degradation
encountered in Rev. Mod. Phys. plasmas. These high $\left<p\right>$$\tau$ Rev.
Mod. Phys. plasmas feature near-threshold RMP current values or below-
threshold values employing hysteresis, sometimes using active RMP current
feedback control Laggner2020 . The role of the pedestal will be further
explored in Sec. IV.

As described in Ref. Snyder2019 , an effective normalization for
$\left<p\right>$$\tau$ is $IaB$, the product of the plasma current ($I$),
minor radius ($a$), and toroidal field ($B$). $IaB$ has units of force (MN),
and is a simple metric for the strength of the tokamak magnetic configuration.
As shown in Fig. 6(b), peak $\left<p\right>$$\tau$ tends to rise linearly with
$IaB$, supporting the value of $IaB$ as a normalization parameter for
$\left<p\right>$$\tau$ as will be soon introduced. The DIII-D tokamak (with
its present divertor baffling) is capable of $IaB$ of around 2.5 MN by
operating full-field strongly shaped plasmas (high $\kappa$ and
$\Delta_{avg}$) at high $I$. Without ELMs however, $IaB$ is found to not
exceed around 2 MN (excepting L-mode). This indicates a straightforward path
to raise $\left<p\right>$$\tau$ 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 $q_{95}$) and strong shapes presented
in Sec. II.

Supported by the trends of $\left<p\right>$$\tau$ with $IaB$ shown in Fig.
6(b), for the subsequent sections the main metric to consider plasma
performance will be $\left<p\right>$$\tau/IaB$. This metric is meant to show
the quality of fusion performance across a range of $T_{i}$, 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 Ref. Snyder2019  to yield
comparable $\left<p\right>$$\tau/IaB$, despite very different $I$, $a$, and
$B$. Further discussion of the $\left<p\right>$$\tau/IaB$ metric, alongside
comparison to other metrics can be found in Appendix A.

$\left<p\right>$$\tau/IaB$ is now plotted against $T_{inj}$ in Fig. 6(c). A
clear distinction is seen at low $T_{inj}$, where only QH plasmas are able to
achieve high $\left<p\right>$$\tau/IaB$, consistent with only QH tolerating
high $P_{tot}$ at low $T_{inj}$ [shown in Fig. 2(c)]. All other regimes
(except Neg-D, which has not been explored) are limited by the ELM at low
$T_{inj}$ and high $P_{tot}$. Performance of Neg-D plasmas in terms of
$\left<p\right>$$\tau/IaB$ is below QH and Rev. Mod. Phys. plasmas for all
$T_{inj}$, possibly due to the weak shaping or to the absence of a pedestal.
Finally, use of $\left<p\right>$$\tau/IaB$ allows for a comparison of
performance scaled to ITER Q=10 at 15 MA, namely $\left<p\right>$$\tau/IaB$
$\approx$ 5.5Snyder2019 . While Sec. V 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.

Figure 8: Gain metrics meant to estimate ITER performance for discharges with
ITER-like plasma shapes. Gain factors based on Ref. Luce2005  for (a) L-mode
confinement ($H_{L89}$) and (b) H-mode confinement ($H_{H98y2}$) plotted
against $T_{inj}$. (c) Gain factor based on Ref. Peeters2007 , allowing
comparison to the $P_{aux}$ available in ITER, showing many datapoints
inaccessible with ITER’s $P_{aux}$.

###  III.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 $\left|\delta_{avg}\right|$=0.4-0.6,
$\kappa$=1.7-1.95 Aymar2001 . 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 $T_{inj}$,
highlighting the special challenge of achieving both ELM control and high
performance with relatively small external momentum input in ITER Garofalo2020
. Extrapolating $T_{inj}$ depepends on what rotation-dependent mechanism is of
interest, but attempting to match the dimensional rotation in ITER yields an
ITER-equivalent torque of $\approx$ 0.5 Nm Garofalo2011 . Section VI will
discuss other integration constraints that apply to all burning plasmas,
including ITER. For all metrics considered the Rev. Mod. Phys. and QH plasma
performance will be clearly superior to other regimes, though this is largely
due to the unique tolerance of Rev. Mod. Phys. and QH plasmas to low $q_{95}$
(15 MA-equivalent in ITER) and high $P_{tot}$ in DIII-D.

Plasma fusion gain factors $G_{L89}$=$H_{L89}$$\beta_{N}$/$q_{95}$2 and
$G_{H98y2}$=$H_{H98y2}$$\beta_{N}$/$q_{95}$2 presented in Refs. Luce2004 ;
Luce2005  are presented in Fig. 8(a)-(b) against $T_{inj}$. Both G-factors are
the product of what was shown in Fig. 4(b,c), but now divided by the square of
the normalized current ($q_{95}$). The G-factors prescribe a target value for
ITER Q=10 operation at any current. Both Rev. Mod. Phys. and QH plasmas are
found to reach the ITER Q=10 target in terms of $G_{H98y2}$ but fall just
short for $G_{L89}$. Peak performance of both QH and Rev. Mod. Phys. plasmas
thus far achieved is lower at low $T_{inj}$. As seen in Fig. 2(c,f) no Rev.
Mod. Phys. plasma exists at $T_{inj}$$<$2 Nm, and Rev. Mod. Phys. plasma
performance will be shown in Sec. IV to correlate with rotation. QH results in
Fig. 8 are not reflective of a confinement degradation with rotation Ernst2016
but rather highlight the two different $q_{95}$ QH plasma populations shown in
Fig. 2(f). The high $T_{inj}$ population is at low $q_{95}$ and high G-factor,
but encounters limits as $T_{inj}$ is reduced, while the $T_{inj}$=0
population is at high $q_{95}$ and lower G-factor. Optimization between these
two $q_{95}$ populations has not yet been given serious effort, and is
highlighted as a valuable experimental direction for QH plasmas. The G-factors
of Fig. 8(a,b) and $\left<p\right>$$\tau/IaB$ [shown in Fig. 6(c)] are found
to be largely co-linear (not shown), with the main discriminant being
$q_{95}$. High $q_{95}$ plasmas are prejudiced in $G_{L89}$/$G_{H98y2}$ as
compared to $\left<p\right>$$\tau/IaB$, consistent with low $q_{95}$ (high
$I$) being over-rewarded in the G-factors. This accounts for differences at
$T_{inj}$=0, where as shown in Fig 2(f) only L-mode plasmas have thus far
accessed low $q_{95}$ and $T_{inj}$=0 without ELMs. Also worth noting is that
the best performing $T_{inj}$=0 plasmas of Fig 6(c) are in strongly-shaped
plasmas, thus they are excluded from Fig. 8. Comparison of $G_{L89}$ to
$\left<p\right>$$\tau/IaB$ is discussed in Appendix A.

As presented in Ref. [Peeters2007, ], a limitation of $G_{L89}$/$G_{H98y2}$ is
that no consideration is given to whether the level of auxiliary heating
($P_{aux}$) required to reach a given performance level is available in ITER.
Simply put, operation at higher $\beta_{N}$ can overcome insufficient H-factor
to reach comparable fusion performance only if there is sufficient $P_{aux}$
to reach the stated $\beta_{N}$. This consideration gave rise to an alternate
G-factor ($G_{alt}$=$H_{H98y2}$3/$\beta_{N}$$q_{95}$2), different from
$G_{H98y2}$ by the ratio ($H_{H98y2}$/$\beta_{N}$)2, which emphasizes
confinement more than pressure and generally favors lower $P_{aux}$ discharges
with still moderate H-factor. Note at constant heating power $\beta_{N}$
$\propto H$, and all discussed G-factors are degenerate.

The $G_{alt}$ formulation allows simultaneous consideration of the expected
fusion gain (Q), expected fusion power ($P_{fus}$), and the heating power
($P_{aux}$) required to achieve this performance, as shown in Fig. 8(c). The
curved dash-dot lines indicate curves of constant ratio of required $P_{aux}$
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 $P_{aux}$, but they do not reach Q=10. A large number of
datapoints lie well above the available $P_{aux}$ line, but comparison with
Fig. 8(a,b) indicate these are all at high $T_{inj}$ ($>$ 2 Nm). Looking at
$T_{inj}$ $<$ 2 Nm, only QH plasmas come close to Q=10 performance and only
below 500 MW of $P_{fus}$, though $q_{95}$ optimization may improve on these
results in the future. If the high $T_{inj}$ limit is relaxed, many discharges
extrapolate to extremely high fusion gain in ITER, including surprisingly
ignition. Comparison to ELMing plasmas is given in Sec. V.

##  IV Core and Pedestal Correlations with No-ELM Plasma Performance

Figure 10: (a) Pedestal pressure (2$p_{e,ped}$$\approx$$p_{ped}$) contribution
to $\left<p\right>$, (b) dependence of plasma performance (quantified using
$\left<p\right>$$\tau/IaB$) on $p_{ped}$, (c) correlation of $Z_{eff}$ with
$p_{ped}$

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 ($p_{ped}$) 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 $p_{ped}$ (here quoted as
2$p_{e,ped}$ and measured by Thomson scattering) to the volume-average
pressure ($\left<p\right>$) is shown in Fig. 10(a), indicating stark
differences between no-ELM regimes. Naturally, the Neg-D and L-mode regimes
have almost no pressure contribution from $p_{ped}$, owing to their lack of an
edge barrier. The few notable L-mode cases with relatively high $p_{ped}$
operate at very high edge density, which despite the very low edge
temperatures (10s eV) yields a finite pressure. At least in this
representation, the I-mode on DIII-D is barely distinguishable from the
L-mode. Rev. Mod. Phys. , EDA-H, and QH plasmas are found to have
progressively higher $p_{ped}$/$\left<p\right>$. QH plasmas stand alone in the
absolute $p_{ped}$ (2$p_{e,ped}$) observed without ELMs in DIII-D. Comparison
of no-ELM $p_{ped}$ to ELMing regimes appears in Sec. V.

Plasma performance as quantified by $\left<p\right>$$\tau/IaB$ is found to be
largest for Rev. Mod. Phys. and QH plasmas with finite $p_{ped}$, however
within each regime there is no clear correlation of $\left<p\right>$$\tau/IaB$
with $p_{ped}$. This indicates that there are other paths to maximize
performance beyond simply maximizing $p_{ped}$, and also that having near-zero
$p_{ped}$ is a meaningful performance penalty. Prior to moving to other
correlations with performance, it bears noting that the uniquely high no-ELM
$p_{ped}$ observed in QH plasmas is correlated with a uniquely high edge
impurity content (particularly the wide-pedestal QH variant), as shown in Fig.
10(c). Here $Z_{eff}$ inferred from CER 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 $\pm$1 at high $Z_{eff}$), and furthermore other
impurities beyond carbon can contribute to $Z_{eff}$. The $Z_{eff}$ 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 $Z_{eff}$=1 to 0% at $Z_{eff}$=6. As such the level of fuel dilution
in DIII-D at high $Z_{eff}$ is certainly intolerable. It should be noted
however that $Z_{eff}$ in QH plasmas typically exhibit a hollow profile, with
on-axis values typically in the range of 2.5-3.5. Dedicated studies have also
reported favorable core impurity transport in QH plasmas relative to ELMing
plasmas Chen2020 , despite the fact that lower $Z_{eff}$ values are typically
observed in ELMing plasmas (as will shown in Sec. V.

Figure 12: Additional correlations with no-ELM plasma performance
($\left<p\right>$$\tau/IaB$): (a) Carbon impurity content ($Z_{eff}$), (b)
core toroidal rotation ($V_{core}$), (c) total input power ($P_{tot}$).

The carbon issue for QH plasmas is further emphasized in Fig. 12(a) by noting
that the highest performance in QH is found with high pedestal-top $Z_{eff}$
values, unlike the other no-ELM regimes on DIII-D (excepting 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 Grierson2015 ; Chen2020 . 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 $Z_{eff}$ is
the default operating condition Viezzer2019 .

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 Rev. Mod. Phys. plasmas are shown in Fig. 12(b) to have a
strong correlation with the absolute core rotation ($V_{core}$), with only QH
plasmas achieving high $\left<p\right>$$\tau/IaB$ at low rotation (at least
partially due to the larger $p_{ped}$). Considering the relatively narrow
$p_{ped}$ for Rev. Mod. Phys. plasmas shown in Fig. 10, the performance
variations in Rev. Mod. Phys. plasmas are largely due to variations in the
core, whose performance is in turn is highly correlated with $V_{core}$. This
is consistent with an ExB shear turbulent stabilization mechanism giving rise
to high core performance in Rev. Mod. Phys. plasmas, a perhaps unsurprising
hypothesis given similar observations in ELMing regimes on DIII-D Solomon2013
; Ding2020 , although alternate mechanisms impacting the confinement of Rev.
Mod. Phys. plasmas at fixed $T_{inj}$ have also been identified Cui2017 . As
shown in Fig. 12(c), increasing $P_{tot}$ (and $T_{inj}$) to maximal values
does not improve the confinement of Rev. Mod. Phys. plasmas, with an optimum
in performance at $P_{tot}$ $\approx$ 6 MW is found ($P_{net}/P_{LH08}$
$\approx$ 3), similarly to QH plasmas in the database. While ExB shear
confinement improvements are readily found at high $T_{inj}$, their
extrapolation to future reactors such as ITER is challenging owing to their
high moment of inertia as compared to expected $T_{inj}$ valuesGarofalo2011 .
However, recent work for ITER finds some ExB shear turbulent suppression can
be expected despite this unfavorable scalingChrystal2020 .

Interestingly, Neg-D plasma performance is also found to correlate with
$V_{core}$ as well as with $P_{tot}$. The role of ExB shear suppression in the
Neg-D performance enhancement has not yet been assessed experimentally, as
evidenced by Fig. 2(c) the requisite variations in $T_{inj}$ at constant
$P_{tot}$ 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 Merlo2015 , supporting a testable hypothesis that the dependence on
$P_{tot}$ 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 $p_{ped}$ contribution, and also feature high
$Z_{eff}$ at their highest performance. Similarly, I-mode exhibits some
features of Rev. Mod. Phys. and Neg-D plasmas: a strong core contribution and
possible correlation with $V_{core}$ and $P_{tot}$. L-mode plasmas also show
evidence of a $P_{tot}$ and $V_{core}$ correlation, as would be expected for a
regime solely dependent on good core performance.

##  V 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. Roughly in
order of increasing $I/aB$ (decreasing $q_{95}$), representative high-
performance discharges in high $\beta_{P}$ Politzer2005 ; Garofalo2015 ;
Garofalo2018 , high $\ell_{i}$ Ferron2015 , high $q_{min}$Holcomb2014 ;
Ferron2011 , steady-state hybrid Petrie2017 ; Turco2015 , advanced inductive
Luce2003 ; Wade2005 ; Politzer2008a ; Solomon2013 , super H-mode Snyder2019 ;
Knolker2020 , and ITER baseline scenario Doyle2010 ; Luce2014IAEA ;
Luce2018IAEA  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 $\kappa$,
$\left|\delta_{avg}\right|$, and $I$ plasmas precluded by the modern DIII-D
divertor Strait1995b ; Lazarus1996 ; Lazarus1997 . Furthermore, no effort was
made to include low performance ELMing discharges. The ELMing operating space
figure (analogous to no-ELM Fig. 2) is not shown, as ELMing plasmas can
generally be found everywhere in the DIII-D operating space (excepting low
$P_{net}/P_{LH08}$).

Figure 14: Comparison of (a) normalized current ($I/aB$) and pressure
($\beta_{N}$), (b) confinement quality factors for L-mode ($H_{L89}$) and (c)
H-mode ($H_{H98y2}$) against $\beta_{N}$ for ELMing and no-ELM plasmas.

Discussion begins with normalized performance, shown in Fig. 14 (to be
compared with no-ELM Fig. 4). The Troyon stability diagram [Fig. 14(a)] shows
a swath of ELMing datapoints at high $\beta_{T}$ for various $I/aB$, generally
showing many scenario paths to high performance. Stationary discharges at
considerably higher $\beta_{N}$ can be found (up to above $\beta_{N}$=4). Also
notable on the Troyon diagram are ELMing data at $I/aB$=2 ($q_{95}$ $\approx$
2.3), which while stationary for over 0.3 s (thus meeting the inclusion
criteria of Sec. I.2) evolve to tearing instability on a longer timescale.
Normalized confinement quality ($H_{L89}$ and $H_{H98y2}$) are found to be
comparable to the best no-ELM plasmas, but high H-factor is now sustained to
much higher $\beta_{N}$ and occurs over a wide range of scenarios.

Figure 16: Comparison of (a) total pressure $\left<p\right>$ and confinement
time ($\tau$), (b) triple product ($\left<p\right>$$\tau$) and $IaB$, (c)
normalized triple product ($\left<p\right>$$\tau/IaB$) and torque ($T_{inj}$)
for ELMing and no-ELM plasmas.

Improved absolute performance is also found in ELMing plasmas, as shown in
Fig. 16 (to be compared with no-ELM Fig. 6). ELMing plasmas reach higher
$\tau$, higher $\left<p\right>$, and higher $\left<p\right>$$\tau$. The
highest ELMing $\left<p\right>$$\tau$ is found for advanced inductive and
super-H plasmas, which as shown in Fig. 16(b) operate at high $IaB$. Improved
ELMing performance to no-ELM performance is found at all $IaB$. A such,
normalized triple product ($\left<p\right>$$\tau/IaB$) as shown in Fig. 16(c)
is robustly higher by about a third, and meets ITER 15 MA Q=10 levels.
Plotting $\left<p\right>$$\tau/IaB$ against $T_{inj}$ reveals a performance
degradation in ELMing plasmas more severe than no-ELM plasmas [compare to Fig.
6(c)]. The performance at $T_{inj}$=0 quantified by $\left<p\right>$$\tau/IaB$
is actually the same with and without ELMs, though $q_{95}$ is quite
different.

Figure 18: Comparison of (a) pedestal ($p_{ped}$) contribution to
$\left<p\right>$, (b) $p_{ped}$ dependence on $\left<p\right>$$\tau/IaB$, and
(c) impurity content $Z_{eff}$ correlation with $p_{ped}$ for ELMing and no-
ELM plasmas.

The pedestal pressure ($p_{ped}$) contribution to ELMing plasma performance is
summarized in Fig. 18 (to be compared with no-ELM Fig. 10). The pressure
fraction from the pedestal [Fig. 18(a)] is on the high end as compared to no-
ELM plasmas, with $p_{ped}$/$\left<p\right>$ between 2 and 4, and is in a
narrower range than no-ELM plasmas. About 50% higher $p_{ped}$ can be achieved
in stationary ELMing conditions as compared to no-ELM conditions, and a good
correlation with $p_{ped}$ and $\left<p\right>$$\tau/IaB$ is found for ELMing
data as shown in Fig. 18(b). Unlike no-ELM plasmas [Fig. 10(c)], no positive
$p_{ped}$ correlation with $Z_{eff}$ is found for ELMing plasmas, shown in
Fig. 18. Instead, the highest $p_{ped}$ ($>$15 kPa) ELMing plasmas are almost
all found below $Z_{eff}$$<$3\. This is consistent with the hypothesis that
the ELM plays an important role in exhausting impurities.

Figure 20: 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 ($G_{H98y2}$) and (b) L-mode scaling
($G_{H98y2}$) plotted against torque $T_{inj}$, and (c) alternate gain factor
($G_{alt}$) against scaling of fusion power.

The performance of ELMing plasmas within ITER shape constraints is shown in
Fig. 20 (to be compared with no-ELM Fig. 8). Performance measured by $G_{L89}$
[Fig. 20(a)] and $G_{H98y2}$ [Fig. 20(b)] is found to decrease with $T_{inj}$,
as was found with $\left<p\right>$$\tau/IaB$ in Fig. 16(c). Interestingly, at
low/zero $T_{inj}$, the ITER Q=10 criterial is met according to $G_{H98y2}$
but not $G_{L89}$, which falls just short. Exceptionally high
$G_{H98y2}$/$G_{L89}$ discharges are found at high $T_{inj}$, corresponding to
the advanced inductive scenario Doyle2010 . Re-visiting the analysis of Ref.
Peeters2007  for ELMing discharges [Fig. 20(c)] reveals many datapoints that
extrapolate to Q=10 or greater within ITER’s $P_{aux}$ constraints. However,
the high $G_{L89}$/$G_{H98y2}$ datapoints at $T_{inj}$ $<$2 Nm do not meet the
ITER $P_{aux}$ criteria.

##  VI 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 electron cyclotron heating
(ECH) power delivered by high power microwaves to the total power
($P_{ECH}/P_{tot}$), and for divertor dissipation the fraction of radiated
power to total power ($f_{rad}$) and the ratio of the density at the
separatrix to the Greenwald density ($n_{e,sep}$/$n_{G}$). The motivation for
these metrics and how no-ELM plasmas perform against them will now be
described in turn.

Figure 22: Integration with electron heating: (a) operational space in terms
of $P_{ECH}/P_{tot}$ and $P_{tot}$, with dashed lines indicating constant
$P_{ECH}$. (b) Plasma performance ($\left<p\right>$$\tau/IaB$) is found to
fall with increasing $P_{ECH}/P_{tot}$.

###  VI.1 Boundaries and Performance towards 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 Petty1999 ;
Prater2004 ; Kaye2013 ; Howard2016 ; Angioni2017 ; Grierson2018 . DIII-D has
long been equipped with $\approx$ 3 MW of ECH power ($P_{ECH}$) to mimic this
heating channel, though this is a small fraction of the available NBI power
($\approx$ 16 MW). NBI heats ions preferentially and depending on the NBI
configuration can also impart significant $T_{inj}$, rotation, and ExB shear,
as described in Sec. IV. 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 $P_{tot}$ against $P_{ECH}/P_{tot}$ in Fig. 22(a) makes clear the
dominant operational consideration is a reduced access to high $P_{tot}$ at
high $P_{ECH}/P_{tot}$ on DIII-D, entirely due to limited available $P_{ECH}$.
Rev. Mod. Phys. plasmas are observed across the full range of $P_{ECH}$,
though interestingly only at fairly high $P_{tot}$ and low $P_{ECH}/P_{tot}$.
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 $P_{ECH}$, and
they clearly access higher $P_{ECH}/P_{tot}$ (lower $P_{tot}$) Ernst2018IAEA .
For the Neg-D, I-mode, QH, and EDA-H regimes no operational limit in
$P_{ECH}/P_{tot}$ is found if L-mode is avoided. Indeed, the EDA-H in DIII-D
is thus far only identified at high $P_{ECH}/P_{tot}$.

Plasma performance quantified by $\left<p\right>$$\tau/IaB$ is plotted against
$P_{ECH}/P_{tot}$ in Fig. 22(b). The loss of $P_{tot}$ access is clearly
manifest in a reduced $\left<p\right>$$\tau/IaB$. The performance degradation
for Rev. Mod. Phys. plasmas is particularly severe, supporting the
particularly important role of rotation shown in Fig. 12(b). Unlike past QH
results at high $T_{inj}$ Ernst2016 , recent experiments in low $T_{inj}$ QH
plasmas (specifically the wide-pedestal variant at high $q_{95}$) have found a
performance improvement with $P_{ECH}/P_{tot}$ at fixed $P_{tot}$
Ernst2018IAEA . This indicates the higher performance $P_{ECH}/P_{tot}$=0 QH
plasmas are likely benefiting from other factors such as higher $P_{tot}$ or
lower $q_{95}$. Interestingly, against this metric the two regimes found to
have the highest performance are QH and EDA-H, which as shown in Fig. 10(a)
also have the highest fractional $p_{ped}$/$\left<p\right>$. As such, a
relatively strong pedestal is correlated with an improved
$\left<p\right>$$\tau/IaB$ at high $P_{ECH}/P_{tot}$ and low $P_{tot}$. The
observed performance at high $P_{tot}$ and high $P_{ECH}/P_{tot}$ is a highly
relevant and compelling question Ernst2020APS , awaiting increased $P_{ECH}$
to be available in DIII-D and has motivated similar research programs
elsewhere Stober2020 .

Figure 24: Integration with dissipative divertor: (a) comparison of line-
averaged $\left<n_{e}\right>$/$n_{G}$ to separatrix density
$n_{e,sep}$/$n_{G}$, (b) operational space in terms of $f_{rad}$ and
$n_{e,sep}$/$n_{G}$. Plasma Performance measured by $\left<p\right>$$\tau/IaB$
against (c) $n_{e,sep}$/$n_{G}$ and (d) $f_{rad}$, indicating decreasing
performance with increasing divertor compatibility.

###  VI.2 Boundaries and Performance towards 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 Sec. VII.

Access and performance towards divertor integration is presented in Fig. 24,
with limiter plasmas (circle symbols) now excluded. $n_{e,sep}$/$n_{G}$ is now
used as a density metric instead of $\left<n_{e}\right>$/$n_{G}$Goldston2017 .
This is because the interface of the divertor solution to the plasma occurs at
the separatrix (not at the core or pedestal top), though as with $Z_{eff}$ it
is a more challenging measurement with increased experimental uncertainty.
Here $n_{e,sep}$ is extracted from automated hyperbolic tangent fits to the
electron pedestal profiles. Predictions for the required $n_{e,sep}$/$n_{G}$
in a reactor depend sensitively on the divertor geometry and impurity seeding
strategy, but in the case of ITER recent modeling $n_{e,sep}$/$n_{G}$ values
in the range of 0.4-0.7 are used Kukushkin2013 , which is off the chart in
Fig. 24. Considering $n_{e,sep}$/$n_{G}$ in Fig. 24(a) presents an important
distinction between no-ELM regimes. While as shown in Fig. 2(d) several
regimes access high $\left<n_{e}\right>$/$n_{G}$ Garofalo2015a , QH plasmas
uniquely follow a trajectory of low $n_{e,sep}$/$\left<n_{e}\right>$
(consistent with its low-recycling wall operational preference), challenging
prospects for divertor integration in this regime Baylor2005 . Rev. Mod. Phys.
plasmas operate at higher $n_{e,sep}$/$\left<n_{e}\right>$, but still limit to
a similarly low $n_{e,sep}$/$n_{G}$ owing to the low pedestal-top density
($n_{e,ped}$) limit Evans2006 ; Suttrop2018 ; PazSoldan2019a . Only the Neg-D
and EDA-H regimes access relatively high $n_{e,sep}$/$n_{G}$ in DIII-D,
indicating a clear advantage in terms of dissipative divertor integration.
Considering observed plasma performance at high $n_{e,sep}$/$n_{G}$ in Fig.
24(c) the Neg-D regime is superior owing to its unique tolerance of both high
density and high power.

A second dissipative divertor metric is the radiation fraction
($f_{rad}$=$P_{rad}$/$P_{tot}$, where $P_{rad}$ is the total core and divertor
radiated power), as high $f_{rad}$ implies less conducted power for the
divertor first-wall to handle Reinke2017 . Again, extrapolation of this
parameter to a reactor requires specifying the divertor geometry and
$n_{e,sep}$/$n_{G}$, but ITER is expected to require $f_{rad}$ $\approx$ 0.8
with about 0.3 inside the separatrix Shimada2009 . As shown in Fig. 24(b),
I-mode, EDA-H, L-mode, and Neg-D plasmas reach 0.5 $f_{rad}$ or greater, while
Rev. Mod. Phys. and QH plasmas have not yet reached this level with
stationarity at the level defined in Sec. I.2 (higher has been achieved
transiently). Considering observed plasma performance at high $f_{rad}$
($>$0.5) shown in Fig. 24(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 $f_{rad}$ is relatively
underexplored in DIII-D no-ELM studies. There have been some dedicated
attempts in Rev. Mod. Phys. Petrie2011 ; Orlov2018IAEA  with mid-Z radiators
such as Ne and Ar and initial attempts in QH plasmas. The collisionless QH and
Rev. Mod. Phys. 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
$f_{rad}$ at relatively low $n_{e,sep}$/$n_{G}$ 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 devicesHughes2011
, appear to be well-suited to divertor integration, reaching both high
$n_{e,sep}$/$n_{G}$ and high $f_{rad}$, and indeed EDA-H is challenged instead
by pedestal compatibility towards low $\nu_{e}^{*}$ operation Oyama2006 .
I-mode appears comparably attractive in Fig. 24(b), though recent work casts
doubt on its ability to tolerate the impurity seeding needed to increase
$f_{rad}$ Reinke2019 . Advancing Neg-D plasmas towards higher $f_{rad}$ and
$n_{e,sep}$/$n_{G}$ 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.

##  VII Discussion and Conclusions

| EDA-H | I-mode | Neg-D | QH | Rev. Mod. Phys. | Figure
---|---|---|---|---|---|---
High $P_{tot}$ [MW] | 4 | 7 | 15 | 10 | 11 |  2(d)
Low $P_{net}/P_{LH08}$ |  $<$1 | 1 |  $<$1 | 1 | 2 |  2(d)
Low $T_{inj}$ [Nm] | 0 | 0 | 0 | 0 | 2 |  2(c,f)
Low $q_{95}$ | 4.5 | 3.5 |  $<$3 | 3 | 3 |  2(a,e)
Low $\nu_{e}^{*}$ | 3 | 1.5 | 2 |  $<$.1 |  $<$.1 |  2(e)
High $\beta_{N}$ | 1.4 | 1.6 | 3 | 2.7 | 2.5 |  4(a)
Low $Z_{eff}$ | 1.5 | 1.3 | 1.5 |  $>$2 | 1.8 |  12(c)
High $P_{ECH}/P_{tot}$ | .9 | .8 | .9 | .7 | .4 |  22(a)
High $n_{e,sep}$/$n_{G}$ | .25 | .2 | .29 | .15 | .15 |  24(a,b)
High $f_{rad}$ | .7 | .6 | .5 | .4 | .4 |  24(b)
High $\left<p\right>$$\tau/IaB$ |  $<$1.5 |  $<$1.8 |  $<$2.6 |  $<$4.4 |  $<$4.6 |  6(c)
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.

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 Tab. 2. Almost all criteria listed in
Tab. 2 must be simultaneously achieved in an integrated burning plasma
scenario, with few exceptions: perhaps $q_{95}$ need not be so low, perhaps
$\beta_{N}$ or $P_{net}/P_{LH08}$ need not be so high, perhaps $\nu_{e}^{*}$
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 Tab. 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 (Fig. 12) 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.

#### Pedestal-Divertor Integration:

Challenging reactor-relevance of some no-ELM regimes is the well-known
inaccessibility (in present tokamaks) of a high-performance (low
$\nu_{e}^{*}$) pedestal simultaneous with a highly dissipative (high
$n_{e,sep}$ & $f_{rad}$) divertor state. Indeed, a key divergence is found
between high-performance pedestal regimes (QH, Rev. Mod. Phys. ) vs. regimes
that favor dissipative divertors (EDA-H). Connecting these two extremes
requires no-ELM regime study in high $p_{ped}$ conditions, which in principle
enables low $\nu_{e}^{*}$ ($\propto$ $n_{e,ped}$3/$p_{ped}$2) at high
$n_{e,ped}$. The connection of $n_{e,ped}$ to $n_{e,sep}$ is indirect, and
sensitive to the no-ELM regime [as evidenced by Fig. 24(a)] as well as the
opacity of the pedestal to neutral fuelingMordijck2020 . High $p_{ped}$ is
predicted (based on peeling-ballooning stability calculations Snyder2011 ) 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 plasmasHubbard2017  or shape thresholds for Rev.
Mod. Phys. plasmasShafer2020IAEA . As such, pursuing no-ELM regime integration
studies at maximal $p_{ped}$ is highlighted as an important pedestal physics
research direction that motivates upgrades to existing facilities Buttery2019
. 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 $\left<p\right>$$\tau$, low $\nu_{e}^{*}$) with a dissipative divertor
solution (high $n_{e,sep}$ & $f_{rad}$).

#### Extrapolation of Power and the Role of $B$:

A second challenge lies with uncertainty in how to extrapolate $P_{net}$ after
a pedestal is established. $P_{LH08}$-like normalizations
($\propto$$\left<n_{e}\right>$$S$$B$, where $S$ is the plasma surface area)
well-predicts H-mode access, qualitatively consistent with the need for a
critical ExB velocity to trigger the shear-suppression of edge turbulence
Ryter2014 ; Cavedon2020 . However, it is not clear whether this scaling is
appropriate after the pedestal is formed, as opposed to alternate scalings
such as $P_{net}$/$S$ (heat flux), or $P_{net}$/$\left<n_{e}\right>$$S$ (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 $P_{net}$ exists where the EDA-H, I-mode, and L-mode regimes
transition to ELMing H-mode Hughes2011 ; Hubbard2017 ; Martin2008 . This is
troubling for EDA-H and I-mode since regime access is meant to increase
performance and increase the fusion power contribution to $P_{net}$, thus
risking a dynamically unstable situation. Furthermore, much of the EDA-H,
I-mode, and L-mode regimes findings of this study can be linked to the
intolerance to $P_{net}$ of these regimes in DIII-D, where $P_{LH08}$ is only
about 2-3 MW. In contrast, the tolerance of QH, Rev. Mod. Phys. , and Neg-D
plasmas to $P_{net}$ significantly opens their operating domain in many
directions. If $P_{net}/P_{LH08}$ is the relevant power normalization, then
the high $P_{net}$ regimes are clearly overpowered ($P_{net}/P_{LH08}$$\gg$1)
in DIII-D. However, if the relevant normalization is $P_{net}$/$S$, the high
$P_{net}$ 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 $P_{LH08}$ as much as possible, though naturally indirect effects
(such as changes in $\nu_{e}^{*}$) will complicate these studies. Once again,
ITER will provide an excellent platform to resolve these issues as it will
operate at high $P_{net}$/$S$ yet low $P_{net}/P_{LH08}$. Similarly, the mid-
size (low $S$) yet very high-$B$ SPARC tokamakCreely2020  will provide a yet
clearer separation of these competing normalizations, with DIII-D like high
$P_{net}$/$S$ yet ITER-like low $P_{net}/P_{LH08}$.

#### 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 $\nu_{e}^{*}$ (high $p_{ped}$) challenge is
simply abandoned, with the core contribution to $\left<p\right>$ instead
relied on to recover high performance. Questions about how to normalize power
and the importance of $P_{LH08}$ 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 $P_{net}/P_{LH08}$. Emerging work
indicates the H-mode suppression is robust in Neg-D due to MHD ballooning edge
stability considerations Saarelma2020 , supported by the observation of
$P_{net}/P_{LH08}$$>$6 shown in Fig. 2(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
$p_{ped}$. This work shows that considering normalized performance (Fig. 4),
Neg-D plasmas are already comparable to the other no-ELM regimes. Absolute
performance (Fig. 6) is considerably lower, but points to raising $\kappa$ and
$I$ to access high $IaB$, benefitting from the tolerance to $P_{tot}$
expected. Operation at high $I/aB$ and high $P_{tot}$ 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.

## Acknowledgments

This work summarizes and reviews progress over nearly two decades of DIII-D
experimental 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.
Constitutent 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. 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. 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.

##  Appendix A Comparison of Performance Metrics

Figure 26: Comparison of fusion performance metrics, comparing (a) $H_{L89}$
scaling law ($G_{L89}$) against normalized triple product
($\left<p\right>$$\tau/IaB$. The ratio of these metrics is seen to correlate
with (b) the safety factor ($q_{95}$) and (c) the total injected power
($P_{tot}$).

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 $H_{L89}$ scaling law ($G_{L89}$) and
the normalized triple product ($\left<p\right>$$\tau/IaB$). Note a similar
study of $G_{H98y2}$ and $G_{L89}$ (not shown) found no meaningful distinction
between these two performance metrics. In contrast, imporatnt distinctions
between $G_{L89}$ and $\left<p\right>$$\tau/IaB$ are pictured in Fig. 26.
Comparing $G_{L89}$ directly against $\left<p\right>$$\tau/IaB$ in Fig. 26(a),
each regime population is found to be largely co-linear, indicating both
metrics are capturing relative trends well. However, some no-ELM regime
distinction is found. Neg-D plasmas perform very well in $G_{L89}$ as compared
to $\left<p\right>$$\tau/IaB$, but this is merely representative of the
penality in $q_{95}$ to be paid for Neg-D plasmas, which artificially inflates
$G_{L89}$ as it is proportional to $q_{95}^{-2}$, thus further motivating the
use of $\left<p\right>$$\tau/IaB$ throughout this work. Conversely, strongly
shaped QH plasmas are penalized in $G_{L89}$ as compared to
$\left<p\right>$$\tau/IaB$. The ratio of $\left<p\right>$$\tau/IaB$ to
$G_{L89}$ is found to be correlated with $q_{95}$, shown in Fig. 26(b), which
shows the positive effect of strong shape as well as provides evidence that
low $q_{95}$ is over-rewarded in the $G_{L89}$ (and $G_{H98y2}$) scaling laws.
A second correlation with $P_{tot}$ is highlighted, which indicates a
gradually decreasing ratio of $\left<p\right>$$\tau/IaB$ to $G_{L89}$ with
increasing $P_{tot}$, suggesting that high power is over-rewarded in
$G_{L89}$. These findings highlight the value of $\left<p\right>$$\tau/IaB$,
which does not impose a scaling law to interpret the plasma performance but
rather lets the triple product ($\left<p\right>$$\tau$) speak for itself.

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