Reduced energetic particle transport models enable comprehensive

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Presentation transcript:

Reduced energetic particle transport models enable comprehensive time-dependent tokamak simulations PPPL Notable 2018: M. Podestà1, N.N. Gorelenkov1, C.S. Collins2, W.W. Heidbrink3, L. Bardóczi2,4, V. Duarte1, G.J. Kramer1, E.D. Fredrickson1, M. Gorelenkova1, D. Kim1, D. Liu3, F.M. Poli1, M.A. Van Zeeland2, R.B. White1 and NSTX-U and DIII-D Teams 1Princeton Plasma Physics Laboratory, Princeton University, Princeton, NJ USA 2General Atomics, P. O. Box 85608, San Diego, CA USA 3Department of Physics and Astronomy, University of California Irvine, Irvine CA USA 4Oak Ridge Associated Universities, Oak Ridge, TN USA 2018 IAEA Fusion Energy Conference Ahmedabad, Gujarat, India October 22 – 27, 2018 Work supported by the U.S. Department of Energy, Office of Science, Office of Fusion Energy Sciences under contract numbers DE-AC02-09CH11466 and DE-FC02-04ER54698. NSTX-U at Princeton Plasma Physics Laboratory and DIII-D at General Atomics are DOE Office of Science User Facilities

Verified, validated energetic particle (EP) models are required in integrated tokamak simulations EPs (alphas, NB ions, RF tails) provide main source of heating, momentum, current drive in burning plasmas But: EPs drive instabilities, instabilities affect EPs This work: reduced EP transport models being developed, validated for time-dependent predictive simulations NSTX-U #204202 RSAEs TAEs kink fishbones NB power [MW] *AE: Alfvén Eigenmode Modeled NB driven current classical model A frequency [kHz] model B [kA/m2] 4/4/2019 Reduced EP transport models for integrated simulations (M. Podestà, IAEA-FEC 2018)

Layout Overview of main modeling tools Summary of results Future work & conclusions 4/4/2019 Reduced EP transport models for integrated simulations (M. Podestà, IAEA-FEC 2018)

Layout Overview of main modeling tools Summary of results Future work & conclusions 4/4/2019 Reduced EP transport models for integrated simulations (M. Podestà, IAEA-FEC 2018)

TRANSP code is the main platform for Integrated Simulations NUBEAM module accounts for (neo)classical EP physics Includes scattering, slowing down, atomic physics TRANSP (main) NUBEAM step k TRANSP (main) Classical EP physics: apply scattering, slowing down; update sources May be inaccurate if EP transport is enhanced by instabilities 4/4/2019 Reduced EP transport models for integrated simulations (M. Podestà, IAEA-FEC 2018)

With instabilities, additional physics is required for quantitative simulations NUBEAM module accounts for (neo)classical EP physics Includes scattering, slowing down, atomic physics TRANSP (main) NUBEAM step k TRANSP (main) Classical EP physics: apply scattering, slowing down; update sources Ad-hoc EP diffusivity: e.g. adjusted to match neutron rate Ad-hoc transport models: often unphysical -> no predictive capabilities! 4/4/2019 Reduced EP transport models for integrated simulations (M. Podestà, IAEA-FEC 2018)

apply scattering, slowing down; update sources Kick and RBQ-1D reduced models address EP transport in time-dependent integrated simulations NUBEAM module accounts for (neo)classical EP physics Includes scattering, slowing down, atomic physics TRANSP (main) NUBEAM step k TRANSP (main) Classical EP physics: apply scattering, slowing down; update sources Phase-space resolved reduced EP models: ‘kick’, RBQ-1D New physics-based models enable predictive capabilities Podestà PPCF 2014, PPCF 2017; Gorelenkov NF 2018 4/4/2019 Reduced EP transport models for integrated simulations (M. Podestà, IAEA-FEC 2018)

Constants of Motion variables are used to describe resonant wave-particle interaction Each orbit characterized by: Wave stability (drive): E, energy Pz~mRvpar-qY, canonical momentum m~vperp2/B, magnetic moment Complex orbits in real space translate in simple trajectories in phase space Resonant interactions obey simple rule: w=2pf : mode frequency n : toroidal mode number R. B. White, Theory of toroidally confined plasmas, Imperial College Press (2001) 4/4/2019 Reduced EP transport models for integrated simulations (M. Podestà, IAEA-FEC 2018)

Constants of Motion variables are used to describe resonant wave-particle interaction Each orbit characterized by: Wave stability (drive): E, energy Pz~mRvpar-qY, canonical momentum m~vperp2/B, magnetic moment Complex orbits in real space translate in simple trajectories in phase space Resonant interactions obey simple rule: w=2pf : mode frequency n : toroidal mode number Define transport matrix(es) for NUBEAM: p(DE,DPz |E,Pz,m) “Conditional probability that a particle at (E,Pz,m) receives kicks DE, DPz from wave-particle interaction” Podestà PPCF 2014, PPCF 2017 4/4/2019 Reduced EP transport models for integrated simulations (M. Podestà, IAEA-FEC 2018)

RBQ-1D and kick models distill physics of wave-particle interaction for its inclusion in p(DE,DPz) Both models use mode structure, damping rate from MHD codes, e.g. NOVA/NOVA-K Input: thermal profiles, equilibrium RBQ-1D based on resonance-broadened quasi-linear theory for wave-particle interaction: Use “diffusive transport” approximation -> gaussian p(DPz | E,Pz,m) 1D: transport along canonical momentum Pz dominates Computationally efficient Gorelenkov NF 2018 4/4/2019 Reduced EP transport models for integrated simulations (M. Podestà, IAEA-FEC 2018)

Perturbation from NOVA code Kick model: particle-following ORBIT code used to infer transport matrix numerically Initialize test particles uniformly in phase space Perturbation from NOVA code Podestà PPCF 2017 4/4/2019 Reduced EP transport models for integrated simulations (M. Podestà, IAEA-FEC 2018)

Perturbation from NOVA code Kick model: particle-following ORBIT code used to infer transport matrix numerically Initialize test particles uniformly in phase space Track energy, momentum variations (kicks) at fixed time intervals Perturbation from NOVA code Podestà PPCF 2017 4/4/2019 Reduced EP transport models for integrated simulations (M. Podestà, IAEA-FEC 2018)

Perturbation from NOVA code Kick model: particle-following ORBIT code used to infer transport matrix numerically Initialize test particles uniformly in phase space Combine DE, DPz from same (E,Pz,m) phase space bin into p(DE,DPz ) Track energy, momentum variations (kicks) at fixed time intervals p(DE,DPz ) Perturbation from NOVA code Podestà PPCF 2017 4/4/2019 Reduced EP transport models for integrated simulations (M. Podestà, IAEA-FEC 2018)

Perturbation from NOVA code Kick model: particle-following ORBIT code used to infer transport matrix numerically Initialize test particles uniformly in phase space Combine DE, DPz from same (E,Pz,m) phase space bin into p(DE,DPz ) Repeat for all (E,Pz,m) bins to infer 5D matrix -> input for NUBEAM: p(DE,DPz |E,Pz,m) Track energy, momentum variations (kicks) at fixed time intervals rms energy change p(DE,DPz ) localized resonances Perturbation from NOVA code Podestà PPCF 2017 4/4/2019 Reduced EP transport models for integrated simulations (M. Podestà, IAEA-FEC 2018)

Models can be used for both interpretive and predictive simulations Interpretive runs: To validate EP models, analyze actual discharges Use experimental info to set DE, DPz E.g. based on neutron rate, internal measurements of mode amplitude classical TRANSP run increase kicks measured Podestà PPCF 2017 4/4/2019 Reduced EP transport models for integrated simulations (M. Podestà, IAEA-FEC 2018)

Models can be used for both interpretive and predictive simulations Interpretive runs: To validate EP models, analyze actual discharges Use experimental info to set DE, DPz E.g. based on neutron rate, internal measurements of mode amplitude reduced input from experiment Predictive runs: To optimize/explore new scenarios Use saturation condition to set DE, DPz Impose drive = damping vs time classical TRANSP run increase kicks drive from NUBEAM or RBQ-1D damping from NOVA-K measured Main limitation: Can be only as good as damping rate estimates! Many practical cases lie in between ‘fully interpretive’ & ‘fully predictive’ Podestà PPCF 2017 4/4/2019 Reduced EP transport models for integrated simulations (M. Podestà, IAEA-FEC 2018)

Layout Overview of main modeling tools Summary of results: from validation/analysis to predictions Single-mode scenarios NTM only: single dominant mode, few resonances in EP phase space AEs only: many modes of same type, many resonances Multi-mode scenarios AEs + fishbones + kinks: multiple types of modes, many resonances Example of predictive capabilities Future work & conclusions complexity 4/4/2019 Reduced EP transport models for integrated simulations (M. Podestà, IAEA-FEC 2018)

DIII-D discharge with large NTM provides a good test bed for EP transport models NTMs destabilized by step-up in NB power Dominant 2/1 in this case Large NTM amplitude causes EP confinement degradation Clear drop in neutron rate DIII-D #170247 NB power [MW] neutron rate [au] magnetic fluctuations frequency [kHz] NTMs 2/1 Heidbrink NF 2018 Bardóczi PoP 2017 Poli NF 2017 Bardóczi PPCF 2018 (submitted) time [ms] 4/4/2019 Reduced EP transport models for integrated simulations (M. Podestà, IAEA-FEC 2018)

Interpretive analysis reproduces experiment, matches direct measurements of NTM island width Kick “interpretive” run: Scale kicks to match measured neutrons Mode amplitude related to wisland Inferred NTM island width agrees with measured wisland from ECE a posteriori check, validation Path towards ‘predictive’ simulations with wisland from Modified Rutherford Equation Heidbrink NF 2018 Bardóczi PPCF 2018 (submitted) 4/4/2019 Reduced EP transport models for integrated simulations (M. Podestà, IAEA-FEC 2018)

Analysis gives reasonable agreement with phase-space resolved diagnostics Kick “interpretive” run: Scale kicks to match measured neutrons Mode amplitude related to wisland Inferred NTM island width agrees with measured wisland from ECE a posteriori check, validation Path towards ‘predictive’ simulations with wisland from Modified Rutherford Equation Favorable comparison with phase- space resolved data (FIDA) Acceptable for co-passing, good for counter-passing Key exercise for model validation Ad-hoc diffusion would give same drop for co/cntr Heidbrink NF 2018 Bardóczi PPCF 2018 (submitted) FIDA brightness 4/4/2019 Reduced EP transport models for integrated simulations (M. Podestà, IAEA-FEC 2018)

Kick & RBQ-1D successfully benchmarked for scenario with multiple unstable AEs AEs selected based on experimental data from ECE, Mirnov coils Amplitudes inferred around t=800ms Adjusted vs time to match measured neutron rate Gorelenkov NF 2018 4/4/2019 Reduced EP transport models for integrated simulations (M. Podestà, IAEA-FEC 2018)

Successful comparison with phase-space resolved data (FIDA, NPA) validates models Simulation can also reproduce dynamic response to NB modulation Less favorable comparison with FIDA using updated calibration Need to work closely with experimentalists Retaining phase space resolution is critical for validation Heidbrink PoP 2016 4/4/2019 Reduced EP transport models for integrated simulations (M. Podestà, IAEA-FEC 2018)

Towards predictive simulations: need estimate of unstable spectrum, saturated amplitudes NSTX-U #204202 Need estimate for relative AE amplitudes: Use saturation condition (drive=damping) to infer AE amplitudes vs time Then, rescale fishbone & kink amplitudes to match measured neutron rate No damping available (yet) TAEs RSAEs TAEs fishbones kink NB power [MW] neutron rate [au] 4/4/2019 Reduced EP transport models for integrated simulations (M. Podestà, IAEA-FEC 2018)

Analysis provides assessment of role of different instabilities on EP transport, NB driven current NSTX-U #204202 NB density AEs and fishbones/kinks cause comparable drop in neutrons Fishbones, kinks are mostly responsible for NB ion density depletion AEs have larger effect on NB ion energy redistribution Synergy between modes is observed, e.g. in total EP losses 4/4/2019 Reduced EP transport models for integrated simulations (M. Podestà, IAEA-FEC 2018)

Layout Overview of main modeling tools Summary of results Future work & conclusions 4/4/2019 Reduced EP transport models for integrated simulations (M. Podestà, IAEA-FEC 2018)

Reduced-physics EP transport models enable quantitative, time-dependent tokamak simulations Verification & Validation being extended for kick & RBQ-1D Extend RBQ to 2D (canonical momentum & energy) Reduced models enable efficient simulations retaining (most of) the relevant EP physics Including predictive capabilities (ITER & beyond) Phase-space resolution is required to move beyond ad-hoc models Critical for heating, current drive, thermal transport Goal: develop framework to streamline TRANSP analysis including effects of instabilities on EPs 4/4/2019 Reduced EP transport models for integrated simulations (M. Podestà, IAEA-FEC 2018)

Backup 4/4/2019 Reduced EP transport models for integrated simulations (M. Podestà, IAEA-FEC 2018)

Reasonable agreement also found for scenario with multiple unstable Alfvén Eigenmodes TAEs frequency [kHz] Heidbrink PoP 2016 Collins PRL 2016 Collins NF 2017 RSAEs classical Mix of Toroidal and Reversed-shear AEs observed Large neutron deficit indicates substantial fast ion transport measured 4/4/2019 Reduced EP transport models for integrated simulations (M. Podestà, IAEA-FEC 2018)

Predictive analysis (AEs) results generally agree within +/-15% with interpretive simulations Relative difference from interpretive simulations: NSTX, NSTX-U and DIII-D database However: in some cases, predictive runs fail to reproduce experiments! Predicted AE spectrum differs from experiment Key role of damping rate from MHD codes Affects inferred AE saturation amplitude More validation is required to assess model limitations, missing physics interpretive kick model 4/4/2019 Reduced EP transport models for integrated simulations (M. Podestà, IAEA-FEC 2018)

Predictive analysis: test kick model on challenging NSTX-U discharge Examples from NSTX-U scenario Transition from co- to counter-TAEs as NB ion density profile becomes flat or hollow Complex scenario, simulations are challenging Most quantities evolve in time, not suitable for “single-time-slice” analysis Podestà NF 2018 4/4/2019 Reduced EP transport models for integrated simulations (M. Podestà, IAEA-FEC 2018)

Predictive analysis recovers overall properties of measured instabilities Reproduces main features of the experiment Reproduces transition co- to counter-TAEs Capture time evolution of unstable modes, spectrum, … co-TAEs only co- and cntr-TAEs 4/4/2019 Reduced EP transport models for integrated simulations (M. Podestà, IAEA-FEC 2018)

Successful comparison with phase-space resolved data (FIDA, NPA) Retaining phase space resolution is important Localized resonances result in “fine structures” in fast ion distribution, profiles Comparison with FIDA: phase space resolution crucial for validation Agreement extends to response to NB modulation 4/4/2019 Reduced EP transport models for integrated simulations (M. Podestà, IAEA-FEC 2018)