I-mode and H-mode plasmas at high magnetic fieldand pressure on Alcator C-Mod
A. E. Hubbard,
J. W Hughes, S.-G. Baek, D. Brunner, I. Cziegler1, E. Edlund,
T. Golfinopoulos, M.J. Greenwald, J. Irby, B. LaBombard, Y. Lin, E.S. Marmar,
S. Mordijck2, R. Mumgaard, M.L. Reinke3, J.E. Rice, S. Scott4, P. Snyder5,B. Sorbom, J.L. Terry, C. Theiler6, E. Tolman, J. R. Walk, A.E. White, D.G.
Whyte, T. Wilks, S.M. Wolfe, S.J. Wukitch, and the Alcator C-Mod TeamMIT Plasma Science and Fusion Center
1York Plasma Institute, Univ. of York, UK, 2William & Mary,
3ORNL, Oak Ridge ,TN, USA
4Princeton Plasma Physics Lab, NJ, USA, 5General Atomics, La Jolla, CA
6EPFL, Swiss Plasma Center, Lausanne, Switzerland

Supported by the U.S. Dept. of Energy, Office of Fusion Energy Sciences

Talk I2:005: 44th EPS conference on Plasma Physics, Belfast, June 27, 2017

Outline• Overview of Alcator C-Mod and its main confinement
regimes. Why high B and pressure?
• Extension of regimes to highest field and pressure.
– EDA H-mode.
– ELMy H-mode, ‘Super-H’ exploration.
– I-mode.
• Highlights of pedestal and transition physics.
• Implications for future fusion devices– Extrapolations, open issues, and needed research to resolvethem.
A. Hubbard, EPS 20172

Alcator C-Mod Tokamak:
Compact, high B, high power density••••• Shaped, diverted(similar to ITER).

A. Hubbard, EPS 2017

• Divertor, all PFCs
high Z metal.
― Mostly Mo,
from day 1,some W tests.

R=0.68 m
V ~0.9 m3, S ~7.4 m2
a=0.21 m
B ≤ 8.1 T (LN2 cooled Cu magnets)
Ip ≤ 2.0 MA

All RF heating (no torque or corefueling)• ICRH: 50-80 MHz, ≤ 6 MW
• LHCD: 4.6 GHz, ≤ 1.2 MW

3Alcator C-Mod Tokamak:
Compact, high B, high power density• Shaped, diverted(similar to ITER).

A. Hubbard, EPS 2017

• Divertor, all PFCs
high Z metal.
― Mostly Mo,
from day 1,some W tests.

• R=0.68 m
V ~0.9 m3, S ~7.4 m2• a=0.21 m• B ≤ 8.1 T (LN2 cooled Cu magnets)• Ip ≤ 2.0 MA→ Density limit nG=Ip/𝜋𝜋a2 ≤1.4x1021m-3(Max n e>5x1020 m-3, ne,0 >1021m-3)
All RF heating (no torque or corefueling)• ICRH: 50-80 MHz, ≤ 6 MW
• LHCD: 4.6 GHz, ≤ 1.2 MW→ P/V ≤ 7.4 MW/m3, P/S ≤0.94MW/m2,
PB/R≤ 73 MW-T/m→ Divertor q// ≤ 3 GW/m2 (λq<0.5 mm)4

Confinement physics strongly favors high B to
produce fusion capable devices at smaller size
Lawson criterion: n T τE= p τE sets fusion gain Q=Pfus/Pext.
PowerdensityPfusionS wall

β N 2 2
q*2

RB 4

Options for fusion devices:
1.
2.
3.

At fixed powerβ H 1.3 3
density, aspect p τ E  N 2 R Bq*ratio εIncrease H, βN, decrease q95. Optimize confinement, at stability limits.
Increase R. Increases cost. V ∝ R 3
Increase B. Allows smaller R, away from operational limits.

Alcator program has emphasized the high field approach, especially as new
High T Superconductor magnets make higher B steady state reactors feasible.
• How high can field B, pressure be increased in practice?
• Do physics, trends from lower B tokamaks hold, or are there surprises?
A. Hubbard, EPS 20175

Physical models indicate pedestal, corepressure should increase with BT, Ip.

If pedestal gradientis limited by high-nballooning modes:∇p(max) α Ip2(or ~ BT2 at fixedsafety factor q95)
A. Hubbard, EPS 20176

Physical models indicate pedestal, corepressure should increase with BT, Ip.
Core transport ‘stiffness’

LT= T/ ∇T ≈ const• Stiffness of core T
profiles is widely
observed in tokamaks,
including all C-Mod regimes.
Greenwald NF’97.

Pped∇p(max) α Ip2• Now well understood,
and predicted by GK
modelseg N. Howard I1:10• Implies a minimum
Pedestal pressure, pped isneeded for fusion.
A. Hubbard, EPS 20177•Pedestal limit is not quite that simple.
Set by coupled peeling-ballooning modes.

 If p-b limit is violated, typically get
Edge Localized Modes (ELMs) which
release bursts of pedestal energy.
 Would be a big problem in a fusion device
with high pped.
 Ideally want to operate in a stable region,
just below limits.
A. Hubbard, EPS 2017

Pedestal current

Physical models indicate pedestal pressure
should increase with BT, Ip.

Pedestal pressure gradient8

Physical models indicate pedestal pressure
should increase with BT, Ip.
•

Pedestal limit is not quite that simple.
Set by coupled peeling-ballooning modes.

•

EPED model combines P-B and KBM
constraints to predict height and width.

Snyder PoP09, NF11

A. Hubbard, EPS 20179

Physical models indicate pedestal pressure
should increase with BT, Ip.
•

Pedestal limit is not quite that simple.
Set by coupled peeling-ballooning modes.

•

EPED model combines P-B and KBM
constraints to predict height and width.
It typically still predicts that pedestal
height scales approximately as•

p ped ∝ BT B pol ∝ BT I p
 Should operate at highest BT, Ip.
• C-Mod can match ITER’s BT, Bpol.

5.3 T, fGW=0.8

Can it reach ITER’s predicted pedestal pressure at 15 MA? (90 kPa)A. Hubbard, EPS 2017

Snyder,PEP ITPA
2012
10

C-Mod has explored several
high energy confinement regimes
RegimeELMs?

Stationary?

NO

NO 

YES 

YES

Enhanced Dα (EDA) H-mode

NO

YES

I-modeNO

YES

ELM-free H-mode
ELMy H-mode

Will illustrate each of these regimes with examples at C-Mod’s most typicaloperating field, BT~5.4 T.
•

C-Mod is the only diverted tokamak able to explore these high confinement
regimes at full ITER field.

•

The most efficient ICRH scenario, D(H), can be used in this B range for
f~80 MHz.

A. Hubbard, EPS 201711

ELM-free H-mode•

C-Mod tends to access ELM-free
H-mode in ITER-like shape, atlower q95 and density,– Note P/Pth~ 1-2, at H-mode ne.

•

•

•

This has very high energy
confinement, but also high particle
confinement.
Density and radiation increase,leading to transient H-mode,
radiative collapse.
Some edge mechanism isneeded to increase particle
transport, ‘flush’ impurities!

A. Hubbard, EPS 201712

ELMy H-mode•

Type I ELMy H-mode on
C-Mod is only accessed ina shape with modified(reduced) pressure limits,
at lower ν*.

HughesNF
2013– Power supply limitations
restrict this shape to
Ip < 1 MA.

– Particle transport isprovided by ELMs.
→Stationary density
and radiation.

A. Hubbard, EPS 201713

ELMy H-mode•

Type I ELMy H-mode on
C-Mod is only accessed ina shape with modified(reduced) pressure limits,
at lower ν*.

HughesNF
2013– Power supply limitations
restrict this shape to
Ip < 1 MA.

•
A. Hubbard, EPS 2017

– Particle transport isprovided by ELMs.
→Stationary density
and radiation.
C-Mod validates models at
unique parameters.

14

Enhanced Dα H-mode•••

In EDA H-mode, particle transport
is increased by a continuous
fluctuation, the Quasicoherent(QC) mode.
Gives stationary density, impurity
radiation, WITHOUT Periodic ELMs.
– Need boronization.
Has been routinely achieved over awide range of C-Mod shapes,
plasma parameters

QC
mode

– until 2016 only up to 6.2 T.

•

Access to EDA regime is favoured byhigher ν*, higher q95, ∇p

A. Hubbard, EPS 2017

Greenwald
FST 2007

15

Enhanced Dα H-mode•

An advantage of the EDA regime is that seeding can readily be used toreduce divertor heat flux, while maintaining needed high confinement.
– H98 ≥1 as long as Pnet ≥ Pthresh (at H-mode ne)
Loarte, PoP 2011,
Hughes, NF 2011

A. Hubbard, EPS 201716

I-mode regime has a thermal barrier,without a particle barrier
•
•

•
•

•

H-mode-like temperature pedestal
and energy confinement.
L-mode density pedestal and low
particle confinement.
– Avoids impurity accumulation.
– Unlike C-Mod H-modes, routineboronization is not needed.
ELM-free.
Accessed when ion B×∇B drift isaw ay from the active X-point(which raises L-H power threshold).
Accessible at low ν*, low q95.

A. Hubbard, EPS 2017

Whyte NF 2011, Hubbard IAEA 201217

Particle and energy confinement in
I-mode vs H-mode

Weaker power degradation in I-mode:
τE,Imode~ PL-0.3 vs τITER98p ~ PL-0.7
A. Hubbard, EPS 201718

Outline• Overview of Alcator C-Mod and its main confinement
regimes. Why high B?
• Extension of regimes to highest field and pressure.
– EDA H-mode.
– ELMy H-mode, ‘Super-H’ exploration.
– I-mode.
• Highlights of pedestal and transition physics.
• Implications for future fusion devices– Extrapolations, open issues, and needed research to resolvethem.
A. Hubbard, EPS 201719

EDA H-mode regime extended to 7.8 T••

For 80 MHz ICRH at ~ 8T, need touse D(He3), a lower absorption
scenario, hence lower effective
power is available. ηRF~50-80%.
Obtaining EDA H-modes was achallenge– L-H power threshold:•••

7.8 T EDA H-modes accessed for
Ip =0.7-1.4 MA (q95 ≥ 3.9)
ELM-free H-modes to 1.8 MA(q95=3.1)
ELMy H-modes at 0.9-1 MA.

𝑃𝑃𝑡𝑡𝑡 ~ 𝑛𝑛𝑒𝑒 0.7 𝐵𝐵0.8 𝑆𝑆 0.9 (Martin 2008)– C-Mod Pth at 7.8 T roughly fit
ITPA scaling (E. Tolman, TTF17)– To get EDA H-mode, we need aminimum L-mode target density(n/nG > 0.25).
A. Hubbard, EPS 201720

EDA H-mode at 7.8 T, Ip =1.4 MA.
••

Reached high plasma pressures– Pedestal pressure 30 kPa– Volume average <p> 150 kPa– Central pressure p0 350 kPa.
Usual quasicoherent mode in pedestal,at higher freq, 230- 150 kHz.

A. Hubbard, EPS 2017

q95=3.921

Maximum plasma pressure was obtained in
EDA at 5.7 T, 1.4 MA•

At this intermediate field we could use
more efficient D(H) ICRH, at
r/a=0.2-0.35, still with high Ip =1.4 MA.

– Optimized with strong fueling, N seeding.

••Marmar IAEA 2016

Achieved world record <p> 207 kPa.
No ELMs, near stationary conditions.

A. Hubbard, EPS 201722

High pressure EDA H-mode pedestals are still
below peeling-ballooning stability limit• Typical of EDA H-modes; tend to be at
higher ν*, far from peeling boundary.

Earlier
5.4 T EDA

Could peeling limit, and even higher
pressures, be reached at low ν*,
more like expected ITER pedestals?
A. Hubbard, EPS 201723

EPED predicted peeling limit, higher ppedshould be possible at low ne, high Te• Predictions by P. Snyder,well before experiments.

How to access such low ν*
H-mode pedestals?

Peeling
limitedA. Hubbard, EPS 201724

EPED predicted peeling limit, higher ppedshould be possible at low ne, high Te• Predictions by P. Snyder,well before experiments.

How to access such low ν*
H-mode pedestals?

A. Hubbard, EPS 2017

1.

Start with a hot I-mode,
instead of a cold L-mode!

2.

Shift X-point location to trigger
H-mode (recall I-mode prefers
drift away from X-point).

3.

Modify shape to promote
instabilities, vs ELM-free.

25

Experiments confirmed higher pressure
pedestal, likely at peeling limit.
Hughes,
Snyder
TTF17

Preliminary•

Much higher Tped, Pped than EDA at sameIp (1 MA).
– Pressure close to EDA at 1.4 MA.

•
A. Hubbard, EPS 2017

Then extended regime to Ip=1.4 MA,
record pped 80 kPa.
26

Latest C-Mod H-modes reach 90% of predicted
ITER pressure, extend EPED validation• Majoraccomplishment, fortheory and joint
experiments.
Preliminary• Greatly increases
confidence in ITER
predictions.
– Recall that in early
2000’s, Pped was highly
uncertain, allowing big
range in fusion Q.

Hughes, Snyder TTF17
A. Hubbard, EPS 201727

Outline• Overview of Alcator C-Mod and its main confinement
regimes. Why high B?
• Extension of regimes to highest field and pressure.
– EDA H-mode.
– ELMy H-mode, ‘Super-H’ exploration.
– I-mode.
• Highlights of pedestal and transition physics.
• Implications for future fusion devices– Extrapolations, open issues, and needed research to resolvethem.
A. Hubbard, EPS 201728

I-mode has now been extended to a very
wide range of parameters••

Robust I-mode
operation on C-Mod :– BT 2.8-8 T,– Ip 0.4-1.7 MA,– Density 0.85-2.35
x1020m-3

2015-16

Has also been studied on ASDEX
Upgrade and DIII-D.
Together, I-mode discharges have used
– Heating with ICRH, NBI and/or ECH.
– Mo, W and C PFCs.

A. Hubbard, EPS 2017

Hubbard, Ryter, Osborne NF 2016•

Dimensionlessparameters:–––

q95 2.4-5.4
ν*95 0.06-5.4
ρ* 0.0026-0.006
29

8 T I-modes exhibit typical features• Example with 7.8 T,
1.35 MA, (q95= 3.7), PRF=4.7 MW:
•
•
•
•
•
WCM

Central Te to 7.3 keV,
Volume averaged <P> to 1.4 atm (0.14MPa).
H98=1, assuming ηRF=80%.
No ELMs
Weakly Coherent Mode at 350 kHz (again
higher than at lower Ip and BT).

•A. Hubbard, EPS 2017

Up to 450 kHz at 1.7 MA.

30

Power range for I-mode widens withincreasing magnetic field••

In contrast to L-H scalings,
L-I power threshold has at most aweak dependence on BT.
P(L-I)/ne~ BT0.26.
− Uncertainties in Ploss at 8 T.

•••

Maximum power for I-mode does
increase with BT.
− NO discharges at 7.8-8 T had I-Htransitions, up to 5 MW available
ICRF power (Ptot/S ≤ 0.63 MW/m2)

More range to stay robustly in I-mode at higher B, avoiding H-mode.
Consistent with experience on lower B tokamaks.

A. Hubbard, EPS 201731

I-mode pedestals have much higher
T, lower density than EDA H-mode•

Comparison of discharges with 7.8 T, 1.35
MA, Ploss ~ 4.4 MW.

•

I-mode has– Steep Te gradient, Tped~1 keV (also Ti)
Low ν*=0.15, ρ*=0.0033– L-mode density profile.

A. Hubbard, EPS 2017•

EDA has highest pressure, but is high ν*.

•

Pedestals in both regimes are MHD stable,
Explains lack of ELMs; regulated bycontinuous fluctuations.

•

Scope to increase further; pressure at 8 T
was limited only by input power.
32

Outline• Overview of Alcator C-Mod and its main confinement
regimes. Why high B?
• Extension of regimes to highest field and pressure.
– EDA H-mode.
– ELMy H-mode, ‘Super-H’ exploration.
– I-mode.
• Highlights of pedestal and transition physics.
• Implications for future fusion devices– Extrapolations, open issues, and needed research to resolvethem.
A. Hubbard, EPS 201733

Pedestal turbulence and flows are key toregimes without ELMs.
EDA H-mode:••

Sharp suppression of turbulence at L-H
transitions, rapid formation of bothdensity and temperature pedestals.
Followed by appearance of QC mode.
New highly detailed mirror Langmuirprobe measurements show that QCM:
– spans LCFS region with a mode width of~ 3mm– drives transport directly across LCFS
– is an electron drift-wave withinterchange drive and EM
contributions

A. Hubbard, EPS 2017

LaBombard PoP 201434

Pedestal turbulence and flows are key toregimes without ELMs.
I-mode:
•

•
•

•
•

Reduction in mid-freq turbulence,correlated with χeff, formation of
only a temperature pedestal.
Weakly Coherent Mode – broad
fluctuation at few 100 kHz
Fluctuating flow at GAM frequency(10’s of kHz). Important inbroadening WCM.
Both WCM and GAM likely drive
particle transport
Consistent results on C-Mod (Cziegler
PoP 2013) and AUG (Manz NF 2015).

A. Hubbard, EPS 2017

For details, seeCziegler P5:175(Friday).
35

Transfer from turbulence to zonal flows is 2x lower with
B×∇B away from X-pt, opening an I-mode power window••

L-H transition occurs when energy transfer rate into ZF exceeds turbulent drive.
[AUG Manz PoP12, DIII-D Yan PRL14, C-Mod Cziegler PoP 14,NF15]
Transfer rate in the configuration with B×∇B away from X-pt(“unfavourable”) is only half the rate towards X-pt (“Favourable”)=>higher H-mode threshold! Opens up a power window for I-mode.
In I-mode, energy goes
into both Zonal Flowsand GAMs.
I. Cziegler, YorkPRL 118 (2017) 105003
For details see
P5:175 (Friday).

A. Hubbard, EPS 201736

Er wells in both H-mode and I-mode
In 5.4 T field range, Er follows same
trends as energy confinement:• L-mode has little Er, ~ 20 kV/m.
• EDA H-mode, I-mode both havesignificant Er wells, ~ 50-100 kV/m.

A. Hubbard, EPS 201737

Er wells in both H-mode and I-mode
In 5.4 T field range, Er follows same
trends as energy confinement:• L-mode has little Er, ~ 20 kV/m.
• EDA H-mode, I-mode both havesignificant Er wells, ~ 50-100 kV/m.
••

ELMy H-mode ~100-150 kV/m.
ELM-Free H-mode has deepest
wells: in some cases 200-300 kV/m.

A. Hubbard, EPS 201738

Outline• Overview of Alcator C-Mod and its main confinement
regimes. Why high B?
• Extension of regimes to highest field and pressure.
– EDA H-mode.
– ELMy H-mode, ‘Super-H’ exploration.
– I-mode.
• Highlights of pedestal and transition physics.
• Implications for future fusion devices– Extrapolations, open issues, and needed research to resolvethem.
A. Hubbard, EPS 2017

39

C-Mod experience confirms high pressure athigh field, current, in a compact tokamak•••

Average pressures often
exceeded those of larger,
lower B, tokamaks(RJET >4 RC-Mod).

Similar <p>, trends for all confinement regimes (EDA H-mode, I-mode….)
Each regime has different advantages, issues.

A. Hubbard, EPS 201740

C-Mod experience confirms high pressure athigh field, current, in a compact tokamak••

Average pressures often
exceeded those of larger,
lower B, tokamaks(RJET >4 RC-Mod).
<p>max~Ip2 to ~1 MA, but
was limited by heating power
at higher currents.
– With more RF power, at 120
MHz, much higher <p> likely
possible••

Similar <p>, trends for all confinement regimes (EDA H-mode, I-mode….)
Each regime has different advantages, issues.

A. Hubbard, EPS 201741

H-mode: Pedestals, thresholds at 5-8 T
closely follow trends from lower B.

•
•
•
•

P(L-H) follows ITPA scaling.
EDA access possible at higher ne, power.
H-mode pedestal limits follow EPED predictions, to 90% of ITER Pped.
No surprises!
We can confidently use prior multi-device scalings,
and our present models, to project to high field DT tokamaks.

Examples: Assuming H98=1, project to• R= 1.65 m(~AUG, DIII-D), B=12 T•

Pfus=50-100 MW (Q=2-3.6)

ARC*: R=3.3 m(~JET), B=9.2 T, I=12 MA

Pfus=525 MW (Q~13)*B. Sorbom, FED 100 (2015)
A. Hubbard, EPS 201742

I-mode: Pedestals and thresholds trends

with field, up to 8 T, are favourable for high B
Surprise: P(L-I) increases weakly with BT.

••

Upper range of power increases with BT,
making I-mode regime much more robust at
5-8 T than 2-3 T.
Confinement remains high (H~1).
No ELMs or impurity accumulation.
Simple projections indicate I-mode may beaccessible in ITER, ARC, and could bemaintained to full fusion power.

••

BUT: We do not yet have as much experience with I-mode.
•

Multi-device scalings of thresholds, τE, density range are needed for
confident extrapolation. ITPA activity, including several EU tokamaks.
Experiments at larger size (JET, JT60-SA) will be especially valuable.

A. Hubbard, EPS 201743

Some of the remaining issues and questions
Much work remains for understanding, and extrapolation to a fusion reactor.
For all regimes.
• How to handle high divertor heat loads? Require advanced divertors• Sustainment of plasma current, at high density.
H-mode:• Can EDA H-mode still be accessed at needed high temperatures?
• How to fuel plasmas with high SOL density? Will pedestals change?
I-mode:• Confinement scaling. Why are particle and energy transport separated?
At what power, pressure may pped, τE saturate?
• Threshold scaling. Dependence on B vs normalized parameters?
• How high in density can the regime be extended?
• Heat footprint? How can it be integrated with a detached divertor solution?
A. Hubbard, EPS 201744

Conclusions• C-Mod results have demonstrated the expected strong
improvement in plasma pressure at high field and current.
– We have developed two stationary, quiescent, high confinement regimes, EDA
H-mode and I-mode and are making good progress on pedestal physics.
– Each confinement regime, also ELM-free H-mode and ELMy H-mode, has been
extended to BT=8 T. Some to 1.8 MA.
– Highest pressure of any tokamak, <p>=207 kPa, po=450 kPa, was achieved in
EDA H-mode at 5.7 T, 1.4 MA.
– Highest pedestal pressure, pped=80 kPa, in a low ν* H-mode validates the EPED
model to 90% of ITER prediction.
– L-H thresholds agree with ITPA scalings to 8 T.
– I-mode threshold trends with B are very favourable for high field tokamaks.

• C-Mod has established a strong design basis for future highfield, compact, burning tokamaks for fusion energy.
A. Hubbard, EPS 201745