Non-local Heat Transport in Alcator C-Mod Ohmic L-mode Plasmas

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1 Non-local Heat Transport in Alcator C-Mod Ohmic L-mode Plasmas C. Gao 1, J.E.Rice 1, H.J. Sun 2,3, M.L.Reinke 1, N.T.Howard 1, D. Mikkelson 4, A.E.Hubbard 1, M.Chilenski 1, J.R.Walk 1, J.W.Hughes 1, P.Ennever 1, M.Porkolab 1, A.E.White 1, C.Sung 1, L.Delgado- Aparicio 4,S.G. Baek 1, W.Rowan 5, M.W. Brookman 5, M.Greenwald 1 R.S.Granetz 1, S.W. Wolfe 1, E.S. Marmar 1 and C-Mod Team 1 1 MIT Plasma Science and Fusion Center 2 WCI Center for Fusion Theory, NFRI, Daejeon, Korea 3 SWIP, Chengdu, China 4 Princeton Plasma Physics Laboratory 5 Institute for Fusion Studies, The University of Texas at Austin

2 Introduction and Motivation Plasma core rotation reversal is correlated with transition from linear ohmic confinement (LOC) regime to saturated ohmic confinement (SOC) regime through density/collisionality. This transition can be characterized by a change in turbulence* Non-local transport is usually referred to fast response (compared with energy diffusion time) in a region of plasma which is distant from the perturbation. This response can be either opposite or same polarity with the perturbation. In this poster, we will define non-locality to be the phenomena with fast response and opposite polarity The non-locality disappears at higher density / higher collisionality. This may connect physics of rotation reversal and LOC/SOC transition. A unifying ansatz: transport dominated by trapped electron modes (TEM) below some critical collisionality and by ion temperature gradient (ITG) modes above the critical collisonality, explains these transient observations * Rice J.E. et al 2011 Phys. Rev. Lett Chi Gao APS-DPP Denver, CO Nov 11-15,

3 Nonlocal Transport and Energy Confinement are Correlated The critical density for non-local effect exists for multiple machines. Collisionality might be a unifying variable The non-local effect seems to be connected to energy confinement If the transients of non-local transport, energy confinement and momentum transport follows the same mechanics? Turbulence change from TEM to ITG? critical density for non-local effect density at confinement saturation v n e qr Rice et al., PoP, 2012 Chi Gao APS-DPP Denver, CO Nov 11-15,

4 Experimental Setup Experimental Setup Multi-Pulse Laser Blow-off (LBO) System CaF 2 is used to introduce edge cooling X-ray Imaging Spectroscopy System Ion temperature and rotation profile measurement Electron Cyclotron Emission Electron temperature profiles with high time resolution Thomson Scattering Electron temperature and density profiles Turbulence measurements: PCI, Reflectrometry, TCI, CECE, GPI Plasma Parameters: Toroidal field: 5.2T Plasma current: 0.8MA, 1.1MA Averaged density: x10 20 m -3 Chi Gao APS-DPP Denver, CO Nov 11-15,

5 Cold Pulse in LOC and SOC Plasmas In low density LOC plasmas, core electron temperature immediately (non-local effect) increases in response to edge cooling. Core T e peaks in ~ 10 ms, much shorter than energy confinement time ~ 23 ms. In high density SOC plasmas, core electron temperature decreases with edge cooling. The cold response evolution time (~ 30 ms) is comparable with energy confinement time ~ 27ms. Cold pulse time Cold pulse time LOC SOC n e = m 3 τ E ~ 23 ms n e = m 3 τ E ~ 27ms Chi Gao APS-DPP Denver, CO Nov 11-15,

6 Ion Temperature and Plasma Rotation Ion temperature response is similar to T e with slower time scale. Plasma rotates in co-current direction in LOC; counter-current direction in SOC LOC SOC n e = m 3 n e = m 3 Chi Gao APS-DPP Denver, CO Nov 11-15,

7 Non-local effect is Correlated with Rotation Reversal Density ramp-up experiments demonstrate that the non-locality is correlated with rotation reversal. LOC SOC Chi Gao APS-DPP Denver, CO Nov 11-15,

8 Correlation of Energy Confinement, Non-local Effect Polarity and Rotation Direction LOC-SOC, nonlocal-local and rotation transitions are correlated via density/collisionality Chi Gao APS-DPP Denver, CO Nov 11-15,

9 Nearly Linear Relation of Edge Cooling and Central Heating The central electron temperature responses almost linearly to edge cooling. Central ΔT e is larger than edge ΔT e Central relative amplitude ~ 2-6% Edge relative amplitude ~ 15%-35% The central ion temperature also responds (close to) linearly to edge cooling. Chi Gao APS-DPP Denver, CO Nov 11-15,

10 Transport Model of Non-Local Effect For LOC plasmas, the prompt increase of central electron temperature indicates a sudden and global reduction of core heat transport. Simulation result agrees well with measured data. Core temperature Electron diffusivity Edge temperature Chi Gao APS-DPP Denver, CO Nov 11-15,

11 Core Density Fluctuation is Suppressed during Cold Pulse For LOC plasmas, density fluctuations are found to be suppressed by cold pulse injections. This suppression seems to be localized in the core PCI fluctuation (core channel) Reflectrometer fluctuation (r/a ~ 0.8) From PCI, khz 1.6 ms averaging Chi Gao APS-DPP Denver, CO Nov 11-15,

12 Heat Propagation of Sawtooth Crash Shows Confinement Improvement after Cold Pulse Injection in LOC Plasmas Time-to-peak from soft X-rays before and after cold pulse injection shows similar reduction in heat transport Before: After : t p ep 3r ~ 8 t 2 p : time-to-peak ep ep ~ 7.83 m ~ 5.13 m s 2 1 s 2 1 Diffusivity is reduced by ~ 30% after cold pulse injection Consistent with the reduction of local electron heat transport *Callen J D and Jahns G L 1976 Phys. Rev. Lett Chi Gao APS-DPP Denver, CO Nov 11-15,

13 Global Fluid Model of Non-Local Effect This can also be modeled by adding an inward pinch term in the heat flux equation. That is, heat transport is not purely diffusive during cold pulse The amplitude of Te from cold pulse modulation experiment is in favor of the pinch model Chi Gao APS-DPP Denver, CO Nov 11-15,

14 phase [ ] amplitude [ev] phase [ ] amplitude [ev] Amplitude and Phase Profiles of Modulation Experiments For LOC plasmas, amplitude increases towards the plasma center, which contradicts pure diffusive local transport. The inversion radius (where electron temperature begins to increases) is near the q=1.5 flux surface, which is close to rotation reversal radius For SOC plasmas, the amplitudes decreases towards plasma center. Transport is more diffusive like LOC SOC n e = m 3 n e = m 3 Chi Gao APS-DPP Denver, CO Nov 11-15,

15 Linear Gyrokinetic Simulation to Characterize the Turbulence TEM to ITG transition as a unifying assumption for energy confinement saturation, rotation reversal and disappearance of non-locality At r/a = 0.5, both LOC and SOC plasmas are ITG mode dominant At r/a = 0.75, LOC is TEM dominant, SOC is ITG mode dominant Real Frequency Growth Rate *Computer simulations using GYRO were carried out on the MIT PSFC parallel AMD Opteron/Infiniband cluster Loki. Power balance and profile calculations were performed using TRANSP on PPPL Unix cluster. Chi Gao APS-DPP Denver, CO Nov 11-15,

16 Growth Rate of Most Unstable Mode: a L Ti, a L n scan The sensitivity scan at r/a = 0.75 shows that LOC plasma is TEM dominant and SOC plasma is ITG dominant LOC SOC TEM TEM ITG ITG n e = m 3 n e = m 3 Chi Gao APS-DPP Denver, CO Nov 11-15,

17 Possible Explanation for Non-local Effect: Turbulence Spreading * The core plasma responds almost immediately (< 5ms), which cannot be explained by local model of heat transport Turbulence propagation (also called avalanching ) and spreading is proposed to be the key for non-local phenomena Simple model suggests turbulence propagates at a velocity of Dγ 1/2, here D ~ ρ D Bohm is turbulent diffusivity, and γ is turbulent growth rate. Take C-Mod parameters (ρ ~0.01, D Bohm ~50m 2 s 1 )and use the result from linear Gyro-kinetic simulation (where γ ~ 20kHz): V ~ m 2 s s 1 1/2 ~ 100 m s τ = a V = 0.22 ~2 ms 100 This value is consistent with our observation (<5 ms) * Garbet X et al 1994 Nucl. Fusion * Sun H J et al 2011 Nucl. Fusion Chi Gao APS-DPP Denver, CO Nov 11-15,

18 Summary Non-local heat transport is observed with a density threshold The density threshold is similar to LOC-SOC transient density and rotation reversal density, which indicates non-local effect is correlated with energy confinement and momentum transport Transport analysis and fluctuation measurements show a reduction of core heat transport during cold pulse Linear GYRO simulations suggest that at r/a = 0.75, TEM is dominant in LOC plasma, while ITG mode is dominant in SOC plasmas. Sensitivity scan shows the dominance discrepancy Chi Gao APS-DPP Denver, CO Nov 11-15,

19 Backups Chi Gao APS-DPP Denver, CO Nov 11-15,

20 There are some issues before further analyzing the data Sawtooth activities need to be removed GSVD T e and n e profiles with high time resolution (~ 2 ms) Thomson scattering (T e, n e ): ~ ms ECE(T e ): ~ 10μs TCI and RF reflectrometer (n e ): ~ μs Chi Gao APS-DPP Denver, CO Nov 11-15,

21 Sawtooth Removal by GSVD Generalized Sigular Value Decomposition Valid and self-consistent method to remove sawtooth oscillations from transient plasmas with multichannel measurements (Dudok de Wit et al., PoP, 1998) U(x,t): signals before the perturbation Y(x,t): signals after the perturbation U x, t = AαV = α k A k t V k x K k=1 K Y x, t = BβV = β k B k t V k x k=1 α m 2 + β m 2 = 1 A m A n = B m B n = σ mn Sawtooth activity could be removed by ~ 80% Chi Gao APS-DPP Denver, CO Nov 11-15,

22 Sawtooth Removal by GSVD Example of GSVD applied to LOC plasmas Raw ECE data After GSVD Chi Gao APS-DPP Denver, CO Nov 11-15,

23 T e profiles with high resolution Same methodology with quickfit (Yunxing Ma) Sawtooth regime (fi): 0<r/a<1.5/q 95 Parabolic function centered at magnetic axis Transport regime (fc): 1.5/q 95 <r/a<1 Polynomial fitting (3 rd order by default) Connection regime Hyperbolic function Outliers removed automatically No edge details GPC/GPC2 calibration is necessary Chi Gao APS-DPP Denver, CO Nov 11-15,

24 T e profiles with high resolution Example of T e profiles during a cold pulse event (1.0 s) Cold pulse at t = 1.0 s Chi Gao APS-DPP Denver, CO Nov 11-15,

25 n e profiles with high resolution TCI data was used for inverted density profile Sensitive to boundary condition and limited by # of working channels Boundary density was estimated using scalings from fast scanning probes Luke et al., Ph.D. thesis, 1994 Now density profile near LCFS is available from RF reflectometer(lau, thesis). This could improve the inversion of density profile Chi Gao APS-DPP Denver, CO Nov 11-15,

26 n e profiles with high resolution Matrix to be inverted: A wi S n e (x) = Y TCI Y RF 0 TCI A: path length matrix w: weighting factor of RF reflectrometer I: unit matrix S: smoothness matrix Y TCI : line integrated density from TCI Y RF : density profile from RF reflectrometer RF reflect Possible issues: Assume density outside the LCFS is a flux quantity RF reflectrometer location uncertainty Chi Gao APS-DPP Denver, CO Nov 11-15,

27 n e profiles with high resolution Comparison with Thomason profiles (fits and normal quickfit) Line integrated densities match Density profiles match, except for near magnetic axis and out of LCFS Chi Gao APS-DPP Denver, CO Nov 11-15,

28 Growth Rate of Most Unstable Mode: a L Ti, a L T e scan The sensitivity scan at r/a = 0.75 shows that LOC plasma is TEM dominant and SOC plasma is ITG dominant LOC SOC TEM TEM ITG ITG n e = m 3 n e = m 3 Chi Gao APS-DPP Denver, CO Nov 11-15,

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