Exploring Negative Triangularity Through Modeling and Experiment

A.O. Nelson, C. Paz-Soldan, H. Wilson, S. Guizzo, S. Freiberger, �L. Rondini, M. Pharr, N. Logan, C. Hansen

with

J. Parisi, X. Zhang, H. Anand, W. Wehner �and the DIII-D NT Team

APPLIED PHYSICS AND

APPLIED MATHEMATICS

WITH MATERIALS SCIENCE & ENGINEERING

COLUMBIA 丨 ENGINEERING

The Fu Foundation School of Engineering and Applied Science

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This talk will run through Columbia activities under DE-SC002272

1. Brief highlights from the DIII-D NT campaign
2. Assessment of H-mode inhibition for NT plasmas
1. Computational exploration
2. Validation on DIII-D dataset
1. Ongoing efforts to realize NT on MAST-U
1. Initial performance scoping
2. Development of vertical control algorithms
1. Scoping of NT reactor performance
1. MANTA
2. Highly radiative NT scenarios
1. Bonus: Highlights from Columbia efforts on resistive stability

A.O. Nelson / NSTX-U Results Review / PPPL July 25th, 2023

2

DIII-D NT campaign achieved high performance without ELMs

• DIII-D completed dedicated NT campaign in Jan/Feb 2023
• Tiles installed on the outer wall allowed for high power, diverted plasmas
• Highlights include:
• Robust ELM-free operation
• Simultaneous access to � H₉₈>1, β_N>2.5 and q₉₅<3
• Dissipative edge solution obtained with� divertor detachment
• Reliable MHD and vertical stability
• Greenwald fractions of f_GW≲2

A.O. Nelson / NSTX-U Results Review / PPPL July 25th, 2023

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Infinite-n ballooning mode gives upper bound for NT edge

• BALOO is used to model infinite-n ballooning stability in NT edge
• Access to 2^nd stability closed at δ < δ_crit
• δ_crit depends primarily on geometry through local magnetic shear

​

• This sets an upper bound on the NT pedestal below* the PB limit

[A.O. Nelson et al 2022 Nucl. Fusion 62 096020]

A.O. Nelson / NSTX-U Results Review / PPPL July 25th, 2023

4

DIII-D NT plasma consistent with ideal ballooning limit

• During DIII-D campaign, no ELM were encountered past δ ≲ -1.5
• Agrees exactly with closure of the 2^nd stability limit

​

• High power, high performance, �detachment all compatible �with ELM-free operation

A.O. Nelson / NSTX-U Results Review / PPPL July 25th, 2023

5

ELM-free NT scenarios should also be accessible in STs!

• Aspect ratio changes the critical δ at which 2^nd stability access is closed
• In STs, δ_crit is lower
• In STs, ballooning limit for p_ped is lower

​

• On NSTX-U and MAST-U, preliminary modeling shows that the access to �2^nd stability region can be closed!

​

• STs can typically also access H-modes�in the 1^st stability region…
• Does this still apply in NT?

[Nelson et al 2022 NF 62 096020]

A.O. Nelson / NSTX-U Results Review / PPPL July 25th, 2023

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Scoping NT plasmas on MAST-U: coli constraints satisfied

• Conservative options available with reduced current limits �
• On right:
• I_p = 0.6 MA
• δ = -0.1
• no coil at more than 70% of real limit�
• Further optimization for initial test possible

7

Full orbit calculations show enhanced f_gc in MAST-U NT

• Orbit tracking simulations show
• small enhancement in f_trapped with NT
• large enhancement in f_g.c. with NT

​

• Effect strongest at edge:�almost 40% g.c. trapped!�
• Has a less destabilizing effect on turbulence… � …linked to confinement� improvement!

Work done by students L. Rondini and S. Freiberger

A.O. Nelson / NSTX-U Results Review / PPPL July 25th, 2023

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STEP scan shows increasing performance in NT

decreasing triangularity

fixed heating power

Work done by graduate student �H. Wilson

A.O. Nelson / NSTX-U Results Review / PPPL July 25th, 2023

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Vertical stability still an open question for NT reactors

• NT plasmas typically subject to larger vertical instability growth rates

​

• Evident on DIII-D campaign with unoptimized coil sets
• Dataset used to validate TokSys

​

• Using new software (TokaMaker) to explore options for NT reactors
• Non-conformal wall significantly improves vertical stability
• Coil sets can be �optimized to �increase control

[A O Nelson et al 2023 PPCF 65 044002]

Work done by undergraduate student S. Guizzo

A.O. Nelson / NSTX-U Results Review / PPPL July 25th, 2023

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Development of control schemes on MAST-U is ongoing

• Initial experiments scheduled for mid-September!
• Start with low current, Ohmic plasmas
• World first SNT!

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• Goals:
• Achieve NT on MAST-U
• Test NT vertical stability on STs
• Measure basic confinement dependence

​

• Working closely with GA team to develop NT shape controllers for MAST-U
• Control simulations based in TokSys
• Significant help from H Anand, W Wehner

A.O. Nelson / NSTX-U Results Review / PPPL July 25th, 2023

11

CU+MIT graduate students teamed up to design MANTA

• Large aspect ratio, low elongation, and NT reduces physics and technology risks

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• Variable fusion power at constant, manageable divertor power exhaust

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• Pulsed, but constant electricity production > 50 MWe & Q_electrical>1

​

• Tritium breeding beyond �sufficient for operation and �inventory (TBR ≳ 0.9)

​

• Overnight cost < $5B

A.O. Nelson / NSTX-U Results Review / PPPL July 25th, 2023

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STEP enables for self-consistent core modeling + radiators

​

​

• STEP allows for integrated modeling of arbitrary devices by connecting utility codes:
• CHEF: heating and current drive
• CHEASE: equilibria
• TGYRO: transport and profiles (variable SAT rules)

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• Implementing edge model!
• EPED for PT
• BALOO for NT (+gkped??)

​

• Exploring the use of radiators!
• Validate modeling with high f_rad DIII-D
• Extend analysis to MANTA and other�future machines

Work done by graduate student �H. Wilson

radiator: Ne

A.O. Nelson / NSTX-U Results Review / PPPL July 25th, 2023

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Looking forward: using gkped to determine edge constraints

• What physics actually sets the NT edge profiles?
• Use gk_ped to investigate the role of �gyrokinetic instabilities (KBM, ETGs, etc.) �in limiting NT edge T & n gradients
• Validate with data from DIII-D, MAST-U

​

• How does NT (and reduced 2^nd stability limit)�interact with increased β in STs?
• Is NT performance enhanced or hindered�by ST operation?
• Prediction and validation for SMART

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• How does NT physics scale towards reactors?
• Assembling international database for comparison with modeling!

[Courtesy of J. Parisi]

ballooning critical pedestal

A.O. Nelson / NSTX-U Results Review / PPPL July 25th, 2023

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High ITER coil tilting/shifting risk and CC extrapolability

Predicting correction current extrapol- ability from low power scenarios to IBS

Work done by graduate student �M. Pharr

Shifting + tilting PF, CS coils within tolerances and using linear poloidal mode coupling physics (GPEC) to find dominant resonant error field

A.O. Nelson / NSTX-U Results Review / PPPL July 25th, 2023

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– Backup Slides –

​

A.O. Nelson / NSTX-U Results Review / PPPL July 25th, 2023

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In single gyrokinetic study, KBMs limit NT ST performance

• In NT, second stability window DNE → core is ballooning unstable
• Strong KBMs that limit transport → reduced β limit!

​

• Turbulence challenges reduced at high field

R. Davies, et. al., (2022)

PPCF, 64 105001

A.O. Nelson / NSTX-U Results Review / PPPL July 25th, 2023

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DIII-D NT armor

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DIII-D ELM-free phenomenology robust across database

A.O. Nelson / NSTX-U Results Review / PPPL July 25th, 2023

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More NT pulling coils on MAST-U than DIII-D

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DIII-D Neg-D compares well with other no-ELM scenarios

Core:

• High pressure and confinement due to turbulence reduction
• Vertical stability is generally worse

​

Edge:

• Exhaust integration could be alleviated
• H-mode and ELMs avoided through MHD?

C. Paz-Soldan, (2021)

PPCF 63 083001

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Triangularity modifies local shear to close 2^nd stability!

• Local shear defined as:

[A.O. Nelson et al 2022 Nucl. Fusion 62 096020]

A.O. Nelson / NSTX-U Results Review / PPPL July 25th, 2023

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Increased local shear in bad curv. prevents 2^nd stability

• Local shear strong function of geometry�
• When peak of shear profile ventures into the bad curv. region, access to 2nd stability is lost!

​

• This forces a LFS zero-crossing � -> destabilizing

[A.O. Nelson et al 2022 Nucl. Fusion 62 096020]

A.O. Nelson / NSTX-U Results Review / PPPL July 25th, 2023

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For stability, squareness cannot be too high or too low

• Medium squareness needed for 2^nd stability access

​

• Still a strong function of 𝛿!

​

• Similar to�old DIII-D experiments

[A.O. Nelson et al 2022 Nucl. Fusion 62 096020]

A.O. Nelson / NSTX-U Results Review / PPPL July 25th, 2023

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STEP code used to predict performance on MAST-U

• STEP allows for integrated modeling of arbitrary devices by connecting utility codes:�
• CHEF: heating and current drive

​

• CHEASE: equilibria

​

• TGYRO: transport and profiles� (variable SAT rules)

​

• Edge not yet modeled! � (here we force L-mode)

A.O. Nelson / NSTX-U Results Review / PPPL July 25th, 2023

25

MAST-U heating contributions chosen to model NBI source

• Arbitrary heating profiles creating in CHEF to mimic ST NBI�
• Heating amplitude adjusted to reach convergence with TGYRO

A.O. Nelson / NSTX-U Results Review / PPPL July 25th, 2023

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Difficult to converge TGYRO on stronger NT shapes

decreasing triangularity

decreasing electron heatflux

fixed heating power

A.O. Nelson / NSTX-U Results Review / PPPL July 25th, 2023

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