simulations of neoclassical tearing modes seeded via
TRANSCRIPT
Simulations of Neoclassical Tearing Modes Seeded via
Transient-Induced-Multimode Interaction
Eric Howell1, Jake King1, Scott Kruger1, Jim Callen2, Rob La Haye3
and Bob Wilcox4
1Tech-X Corporation, 2University of Wisconsin, 3General Atomics, 3Oak Ridge
Virtual Theory and Simulation of Disruptions Workshop
July 19-23, 2021
Work Supported by US DOE under grants DE-SC0018313,
DE-FC02-04ER54698, DE-FG02-86ER53218
Outline
β’ Introduction
β’ Summarize NIMROD developments that enable NTM modeling
β’ Heuristic closures model neoclassical effects
β’ External MP generate seed
β’ Simulations of transient induced NTMs in IBS discharge
β’ MP pulse as surrogate model for MHD transient
β’ Resulting 2/1 grows in two phase (slow and fast)
β’ Slow growth phase sustained by nonlinear 3-wave coupling
β’ Conclusions and Future Work
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NTMs are leading physics cause of disruptions.
β’ Robustly growing NTMs are more likely in ITER and future ATs
β’ Larger ππ΅, small πβ, low rotation
β’ Qualitatively understood β¦
β’ Seeding -> Locking -> Disruption
β’ but key details are missing
β’ Why do some transients seed NTMs but not others?
β’ How do locked NTMs trigger the TQ?
β’ Avoidance requires understanding details
β’ Design NTM resilient scenarios
β’ Evaluate proximity to seeding
β’ Nonlinear simulations help address knowledge gaps
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What makes NTM simulations challenging?
β’ NTMs require linear layer thinner than critical island width: πΏππ < ππ·
β’ Large Lundquist number and large heat flux anisotropy
β’ Bootstrap current is kinetic
β’ Self-consistent modeling requires 5D kinetic closures
β’ We use heuristic closures
β’ NTMs growth slow compared to ELMs and Sawteeth
β’ Modeling multiple MHD transients is not practical
β’ NTMs require seed island for growth
β’ We apply MP to seed generate island
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Outline
β’ Introduction
β’ Summarize NIMROD developments that enable NTM modeling
β’ Heuristic closures model neoclassical stress
β’ External MP generate seed
β’ Simulations of transient induced NTMs in IBS discharge
β’ MP pulse as surrogate model for MHD transient
β’ Resulting 2/1 grows in two phase (slow and fast)
β’ Slow growth phase sustained by nonlinear 3-wave coupling
β’ Conclusions and Future Work
5
Heuristic Closures Model Forces due to Neoclassical Stresses1
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ππ Τ¦π£
ππ‘+ Τ¦π£ β β Τ¦π£ = ββπ + Τ¦π½ Γ π΅ β β β Ξ π
πΈ = β Τ¦π£ Γ π΅ + πΤ¦π½ β1
ππβ β Ξ π
β β Ξ π = πππππ π΅ππ2
π β Veq β Τ¦πΞ
Bππ β Τ¦πΞ2 Τ¦πΞ
β β Ξ π = βπππππ
πππ΅ππ2
Τ¦π½ β Τ¦Jeq β Τ¦πΞ
Bππ β Τ¦πΞ2 Τ¦πΞ
β’ Closures model dominant
neoclassical effects
β’ Bootstrap current drive
β’ Poloidal ion flow damping
β’ Closures use fluid quantities
available in simulations
1T. Gianakon et al., PoP 9 (2002)
Pulsed magnetic perturbations (MP) surrogate model for MHD transient
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β’ External MP generates seed needed for growth
β’ MP applied as a 1ms pulse at boundary
β’ Applied n=1 pulse is designed to excite large 2/1 vacuum
response
β’ MP phase is modulated with flow to minimize screening
π΅π = π΅ππ₯π‘ Γ amp π‘ Γ exp πΞ©π‘
Outline
β’ Introduction
β’ Summarize NIMROD developments that enable NTM modeling
β’ Heuristic closures model neoclassical stress
β’ External MP generate seed
β’ Simulations of transient induced NTMs in IBS discharge
β’ MP pulse as surrogate model for MHD transient
β’ Resulting 2/1 grows in two phase (slow and fast)
β’ Slow growth phase sustained by nonlinear 3-wave coupling
β’ Conclusions and Future Work
8
Simulations are based on a DIII-D NTM seeding study1,2
β’ Simulations use ITER baseline
scenario discharge 174446
β’ ELM at 3396 ms triggers a 2/1 NTM
β’ Mode grows to large amplitude and
locks in ~100ms
β’ High resolution measurements enable
high fidelity kinetic reconstruction
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1La Haye, IAEA-FEC (2020) 2Callen, APS-DPP TI02:00005 (2020)
Simulations initialized with kinetic reconstruction at 3390ms, prior to growth
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Parameters at 2/1
Surface
Simulation Experiment
Lundquist number 2.5x106 7.9x106
Prandtl number 23 11
Ξ€πβ₯ πβ₯ 108
Ξ€ππ πππ + ππ 0.55 0.45
β’ Reconstructed toroidal and poloidal
flows are required for ELM stability
β’ Fix |q0|>1 to avoid 1/1
β’ Normalized parameters are within a
factor of 5 of experiment at 2/1 surface
β’ 2/1 resonant helical flux grows and
decays with initial pulse
β’ Robust growth starting at 10ms
consistent with MRE
β’ MRE: ππ
ππ‘~3.3 ππ/π
β’ Simulation: ππ
ππ‘~3.4 ππ/π
β’ Origin of slow growth phase subject of
the rest of this talk
Multiple phases of 2/1 mode following 1ms MP pulse
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Pulse
Slow Growth
Fast Growth
π΅π πΊ = 0.544 π2/1[πππ]
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β’ Robust 2/1 growth follows sequence of core modes
β’ High-n (3,4,5) core modes grow up around around 5ms
β’ 3/2 takes off when 4/3 reaches large amplitude
β’ 2/1 takes off when 3/2 reaches large amplitude
Simulation involve rich multimode dynamics
Experiment shows two phases of growth and multiple core modes,
but there are differences
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β’ Core mode evolution spans whole discharge
β’ Red: n=1 (1/1 and 2/1)
β’ Yellow: n=2 (3/2)
β’ Green: n=3 (4/3)
Callen, APS-DPP TI02:00005 (2020)
Power analysis quantifies interaction between toroidal modes1
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β’ π β 0 Fourier mode energy is sum of
kinetic energy and magnetic energy
β’ Powers grouped to highlight transfer
between nβs
Linear πππ Γ π΅π +ππΓ π΅ππ β Τ¦π½πβ +
Τ¦π½ππ Γ π΅π + Τ¦π½π Γ π΅ππ β ππβ β βππ β ππ
β
Quasilinear ΰ·¨π0 Γ π΅π + ππ Γ ΰ·¨π΅0 β Τ¦π½πβ
+ απ½0 Γ π΅π + Τ¦π½π Γ ΰ·¨π΅0 πβ ππ
β
Nonlinear ΰ·¨π Γ ΰ·¨π΅πβ Τ¦π½π
β + απ½ Γ ΰ·¨π΅πβ ππ
β
Dissipative -ππ½π2 +
1
π0πβ β Ξ ππ β Τ¦π½π
β β β β Ξ ππ β ππβ
Poynting
Flux ββ β πΈπ Γ π΅π
β
π0
β’ Linear: transfer with n=0 equilibrium
β’ Quasilinear: transfer with n=0
perturbations
β’ Nonlinear: power transfer with nβ 0
perturbations
β’ Dissipative: Collision transfer to n=0
internal energy
β’ Poynting Flux: Conservative
redistribution of energy
β’ Advective: Small
Linear powers are main drivers of n=2 and n=3 growth
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β’ Linear powers quantify transfer with equilibrium fields
β’ Growth results from small imbalance between drives and sinks
β’ n=2 saturation dominated by quasilinear terms
β’ Nonlinear and dissipative terms contribute more to n=3 saturation
Linear and nonlinear powers drive n=1 during slow growth phase
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Pulse
Slow Growth
Robust Growth
β’ Linear power terms are main drive during fast growth phase
β’ Fast growth phase is described by MRE analysis
β’ Small positive QL drive prior to transition to fast growth
Flux surface averaged power density shows radial deposition
β’ During robust growth, linear terms inject power into n=1 near q=2
β’ Poynting flux radially redistributes magnetic energy radially inwards
β’ Linear terms strongly damp n=1 near ππ β 0.6
β’ Small imbalance between PF and linear terms results in power deposition
q=2
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Nonlinear drives deposit energy into n=1 near 6/5 surface at 5ms
β’ Power deposition is driven by 6/5 beating with 7/6
β’ Diss & Linear terms grow with NL drive and damp energy around q=6/5
β’ PF radially redistributes energy injected around q=6/5 to q=2
q=2q=6/5
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Nonlinear power transfer into n=1 has visible impact on mode
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At 8ms n=1 nonlinear power deposition spans a large radius
q=6/5
q=3/2
q=2
q=4/3
q=5/3
β’ Multiple peaks in NL power suggests multiple 3-wave interactions
β’ Largest peaks occur near q=3/2, q=4/3, and q=5/3 surfaces
β’ n=2 power consistent with 3/2
β’ n=3 power indicates 4/3 and 5/3
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Conclusionsβ’ Recent code developments enable NTM modeling in NIMROD
β’ Rich nonlinear dynamics results from the application of MP
β’ 2/1 island grows in two phases
β’ Late in time robust growth is well described by MRE
β’ 2/1 slow growth phase sustained by multiple nonlinear three-wave interactions
β’ Initially, one interaction dominates (n=1,5,6)
β’ Later, multiple interactions are important
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Future workβ’ Continue seeding studies using more
sophisticated pulses
β’ Use n=5+6 MP to better mimic ELMs
β’ Start with existing 3/2 or 4/3 islands
β’ Use model to study other NTM physics:
β’ How do 4/3 and 3/2 modes interact to
seed 2/1?
β’ How do locked modes trigger TQ?
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Preliminary: Saturated(?) 3/2 and
4/3 islands result from n=2 MP
pulse