Quasi-Coherent Fluctuations Limiting the Pedestal Growth on Alcator C–Mod: Experiment and Modeling Ahmed Diallo, PPPL � Presented by J.W. Hughes, MIT PSFC � M. Greenwald, J. Walk, C. Theiler, J. Canik a ,P. Snyder b , R. Churchill, B. LaBombard, M.L. Reinke,T. Golfinopoulos, E. Davis, S-G. Baek, I. Cziegler, L. Delgado-Aparicio*, A. Hubbard, J. Terry, A.White, and the Alcator C-Mod team. � Plasma Science and Fusion Center, MIT, Cambridge, MA, USA. * Princeton Plasma Physics Laboratory, Princeton, NJ, USA. a Oak Ridge National Laboratory, Oak Ridge, TN, USA. b General Atomics, San Diego, CA, USA. October 15, 2014 � IAEA-FEC 2014 � St Petersburg, Russia � EX/3-2 � 1
Objective: Understanding the pedestal structure is crucial for performance prediction of fusion devices • Substantial pedestal heights are critical for achieving high fusion power in ITER � • Link between pedestal height and global confinement well established by current experiments, transport modeling Predicted fusion power vs pedestal temperature � at fixed pedestal density 80 GLF23 800 ITER H-mode TGLF (s- α ) P aux =30 MW 700 TGLF-APS07 n ped =9.0e19 TGLF-09 60 n e (0)/n ped =1.1 600 v φ =0 Pedestal P fus (MW) H-mode 500 P fusion ∼ P 2 40 ped 400 Q=10 P ped , n ped , T ped 300 20 200 L-mode 100 Kinsey Nucl Fus (2011) 0 0.0 0.80 0.85 0.90 0.95 1.00 1.0 2.0 3.0 4.0 5.0 6.0 T ρ =0.95 (keV) Normalized radial coordinate 2
EPED predictive model provides a candidate mechanism for pedestal formation • EPED: pedestal structure set by two key limiting instabilities: • non-local peeling–ballooning modes (PBM) — trigger for edge-localized mode (ELM) • nearly local kinetic ballooning modes (KBM) — regulates transport between ELMs – Combining these two constraints allows prediction of two unknowns, the pedestal height and width. Connor, PoP (1998); Wilson, PoP (2002); � Snyder, PoP (2001); Snyder, NF (2011) 1.0 EPED model Peeling-Ballooning (PB) � Normalized edge current density 20 diagram 0.8 Pedestal Height (p ped , kPa) Predicted 15 0.6 Kink/Peeling PB unstable Unstable Ballooning KBM unstable bl 10 Unstable 0.4 e l b Inter-ELM evolution? a t S n o i t u l 5 o v 0.2 e M L E - r e t n I Paths to ELM 0 0 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0 0.5 1.0 Normalized pressure gradient Pedestal Width ( Δψ N ) 3
EPED predictive model provides a candidate mechanism for pedestal formation • EPED: pedestal structure set by two key limiting instabilities: • non-local peeling–ballooning modes (PBM) — trigger for edge-localized mode (ELM) • nearly local kinetic ballooning modes (KBM) — regulates transport between ELMs – Combining these two constraints allows prediction of two unknowns, the pedestal height and width. Connor, PoP (1998); Wilson, PoP (2002); � Snyder, PoP (2001); Snyder, NF (2011) EPED predictions EPED model compared to experiment 20 Pedestal Height (p ped , kPa) Predicted Hughes, Nuclear Fusion (2013) 15 PB unstable KBM unstable bl 10 e l b Inter-ELM evolution? a t S n o i t u l 5 o v e M L E - r e t n I 0 0.02 0.03 0.04 0.05 0.06 0.07 0.08 Pedestal Width ( Δψ N ) Can we find signatures of pedestal-limiting mechanisms between ELMs? 4
Theory predicts a sensitivity of KBM growth rate to β — observable between ELMs? • Experimental goal: Identify Belli and Candy Phys. Plasmas 17, 112314 (2010) and characterize turbulent Norm. growth rate Cyclone base case fluctuations during the ELM GYRO cycle � • Expected measurable characteristics – Pedestal localized – Intermediate-n and Norm. real freq. electromagnetic mode – Sudden change in growth rate – Ion spatial scale (k ρ s < 1) – Propagates in ion diamagnetic direction. Electron Variations can be captured between ELM cycle 5
Experimental collisionality scans are used to access Type I ELMy H-mode 0 0 4 10 Line − averaged ne [10 20 m -3 ] Line-av. � 8 3 Density 6 2 4 Pedestal � 1 collisionality 2 0 0 0 0.5 1 1.5 0 0.5 1 1.5 EDA 1120815008 ELMy 1120815026 ELMy 1120815026 Time [s] Time [s] 12 EDA 1120815008 vis Dalpha [W/m 2 /sterad] 10 Transition from enhanced D α 8 (EDA) H-mode to ELMy H-mode occurs around 𝝃 *~1 6 4 2 ELMy 1120815026 Dalpha 0 4 6
Radially resolved profiles may be either averaged over ELMs or binned by phase of ELM cycle 1.8 Te Thomson 1120815026 800 − 1128 ms 67 − 100 % ELM cycle Ti (2 mm radial shift) CXRS 1120815025 time = 1.1054 s 1.6 Ti XCS equiv. 1120815026 time = 1.0785 s 1.4 ELMy H-mode Temperature [keV] Temperature [keV] 1.2 Hughes, Nuclear Fusion (2013) 1 0.8 0.6 T i = T e 0.4 0.2 Edge Te from ECE 0 80 82 84 86 88 90 R[cm] • ELM crash induces fast drop in Te and measurable rebuild time • ELM perturbation to density is weaker � Pressure evolution is a test bed for KBM onset 7
Various poloidally separated diagnostics provide edge fluctuation measurements between ELMs LSN - 2MW ICRF heated ELMy discharges ~ B magnetic probe magnetic fm uctuations O-mode Reflectometer Local electron density fm uctuations Gas-Puff Imaging (GPI) Proxy local density fm uctuations Phase-Contrast Imaging (PCI) Line-averaged electrons density fm uctuations Line-integrated electron density fluctuations 8
Quasi-coherent fluctuations (QCF) are observed on phase contrast imaging (PCI) spectrogram ELMy H-mode 600 10 1120815026, ch = 15 (R[m] = 0.687) 1 500 New mode Frequency[kHz] intensity[(10 16 m -2 ) 2 /kHz] 11208156026 time[s] = 1.145 1000 400 800 0.01 Frequency[kHz] R 300 600 200 400 100 0 200 0.7 0.6 D α (AU) D (AU) -10 -5 0 5 10 0.5 0.4 0.3 1.12 1.13 1.14 1.15 1.16 1.17 time[s] PCI provides an estimate the radial component wavevector k R ➠ k θ when mode is edge localized 9
Signatures of the QCF have been observed on gas puff imaging (GPI) between ELMs ELM cycle GPI wave number spectra between ELM 1207 - 1211 ms 1211 - 1215 ms 1215 - 1219 ms 500 1140826025 km /s 400 rad/cm Frequncy[kHz] 300 200 QCF 100 0 -6 -4 -2 0 2 4 6 -6 -4 -2 0 2 4 6 -6 -4 -2 0 2 4 6 • QCF is coherent in frequency and wavenumber • Propagates in the electron direction in the lab frame 10
GPI indicates strong radial localization of QCF Fluctuations in measured intensity (proportional to δ n/n) vs. radius 2.0 nominal LCFS 1.5 1.0 δ I/I 0 (%) Uncertainty in 0.5 LCFS position 0.0 -0.5 88 89 90 91 92 R (cm) QCF radial width ~ 0.5 cm 11
O-mode reflectometry localizes the QCFs to the sub- centimeter scale density pedestal (b) Pedestal top 112 GHz Frequency [kHz] Inter-ELM Electron density 3 (a) 2.5 (c) Steep gradient region 88 GHz Electron Density [10 20 m − 3 ] Frequency [kHz] 2 1.5 112 GHz Steep gradient region 75 GHz (d) 1 88 GHz Frequency [kHz] 75 GHz 0.5 1.2 60 GHz Steep gradient region 60 GHz (e) n e Thomson 1120815026 time = 0.89998 − 1.12 s 0 0 0.2 0.4 0.6 0.8 1 1.2 ψ n Typical pedestal width = 0.5 cm 12 Time [s]
Inter-ELM magnetic (a) Magnetic f uctuations spectrogram Magnetic f uctuations spectrogram fluctuations track the edge electron temperature � • ECE shows prompt drop in Te. (b) 1120815027 Integrated spectral power [200 -500] kHz � • Each ELM event is followed by period of the pedestal-T e increase and then saturation - Similar T e dependence with washboard modes on JET Perez, PPCF 2004 (c) � • Mode turn on is correlated with the pedestal saturation 2.5 (d) 2.3 � 2.1 • β -limit is consistent with the expected KBM 0.26 (e) 2 0 . 2 or microtearing growth rate dependencies 0.18 Diallo, PRL (2014) � 0.14 1.11 1.12 1.13 1.14 1.15 Time [s] 13
Quasi-coherent fluctuations are low k θ and propagate in electron diamagnetic direction (lab frame) Wavenumber Spectrum vs. Time Power weighted spectra 4 Poloidal wavenumber [rad/cm] 1000 1000 1120815027 S(f,k) spectum 30 km/s 0 1120815027 800 800 3 t=1.1259s Frequency [kHz] -1 600 600 2 -2 400 400 -3 200 200 1 -4 -4 -2 -2 -2 -2 0 0 0 2 2 2 4 4 0 Poloidal wavenumber k [rad/cm] 1.11 1.12 1.13 1.14 Time [s] • k θ ρ s = 0.04 , n=10 • Two-point correlation using a double-head magnetic provides the wavenumber and propagation direction 14
Wavenumbers from various diagnostics consistent with field-aligned perturbation 4 3 2 Edge Edge channel channel 1 PCI PCI at top at bottom magnetic GPI probe 0 -0.4 -0.2 0.0 0.2 -0.4 15
Pedestal-localized fluctuations are consistent with an ion mode, localized to E r well E × B velocity 20 1000 1000 S(f,k) spectum 30 km/s 0 1120815027 800 800 t=1.1259s 0 Frequency [kHz] -1 V E × B [km/s] 600 600 − 20 -2 Magnetic probe 400 400 Separatrix − 40 -3 200 200 − 60 -4 -4 -2 -2 -2 -2 0 0 0 2 2 2 4 4 − 2.5 − 2 − 1.5 − 1 − 0.5 0 0.5 Poloidal wavenumber k [rad/cm] r − r lcfs [cm] • Width of pedestal, width of well in radial electric field ~ millimeters • Uncertainty in flux surface mappings between poloidally separated diagnostics is of similar scale! • Ongoing work to obtain accurate mapping of fluctuation radial location onto plasma flow profile • Localization in the deepest part of the E r well would imply fluctuations propagating in the ion direction 16
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