Measurements of Plasma Turbulence in Tokamaks

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1 Measurements of Plasma Turbulence in Tokamaks Anne White Nuclear Science & Engineering Department MIT Symposium on Laboratory Astrophysics at the CfA Friday, April 26, 2013 With thanks to many people at MIT-PSFC & Alcator C-Mod 4/25/13 1

2 Turbulence in Fluids widely studied, relevant for many systems of interest 4/25/13 2

3 Turbulent flow in plasmas can play key role in many space and astrophysical processes Physics of accretion disks around black holes Physics of Solar Wind Origin of planetary, stellar and cosmic magnetic fields Kinetic Plasma Turbulence Acceleration and propagation of high energy cosmic rays 4/25/13 Alexander Tchekhovskoy 3

4 Magnetic Confinement in Tokamak relies on helical magnetic field (toroidal plus poloidal) Tokamak MagneJc field lines are helical and lie on closed, nested surfaces flux surfaces, Ψ = const. VerJcal B dris averages to zero as parjcle follows helical field Poloidal field from current in the plasma itself. Axisymmetric good confinement 4/26/13 4

5 Measurements Reveal Turbulence in Tokamaks: 1% level, small spatial scale compared to device BES diagnostic measurement locations in tokamak Measurements of density fluctuations Size of Tokamak L ~ 1 m ρ ~ 1 mm Eddy size ~ cm 4/26/13 5

6 Next step for fusion energy research is ITER ITER is an internationally funded experimental tokamak planned to deliver ten times the power it consumes by achieving a burning plasma state. ITER ITER Person for scale Why must ITER be so large? 4/25/13 6

7 Because of turbulence, the next step for international fusion progress is ITER: beat turbulence with size 2 Confinement time scales strongly with size, L! 4/25/13 7

8 Turbulence in Astrophysical Plasmas and Tokamaks can be described by gyrokinetic theory GyrokineJcs is kinejc theory averaged over the fast gyro- mojon (Larmor mojon). Rutherford & Frieman 1968; Taylor & HasJe 1968; Frieman & Chen 1982; Howes et al Low- frequency limit eliminates fast cyclotron Jmescale ω Ω i Anisotropic k k Captures: Finite Larmor radius, Landau resonance, and Collisions Excludes: Fast wave and cyclotron resonance SimulaJons: 5- D DistribuJon FuncJon, mulj- species species, fully electromagnejc, realisjc mass rajo Ion to Electron scale simulajons require millions of CPU hours But can predict transport! 8

9 Tractable nonlinear GK simulations describe the nonlinear saturated state of two important instabilities ITG Ion Temperature Gradient TEM Trapped Electron Mode Long wavelength (kρ < 1.0) Long wavelength (kρ < 1.0) Driven by T i gradient Driven by both n e and T e gradients, and trapped particle resonance Unaffected by collisions Damped by flow shear Drives strong potential, density, and ion temperature fluctuations: Associated with ION HEAT FLUX Propagates in ion diamagnetic flow direction in plasma frame of reference Damped by collisions Damped by flow shear Drives strong potential, density, and electron temperature fluctuations: Associated with ELECTRON HEAT FLUX Propagates in electron diamagnetic flow direction in plasma frame of reference Can co-exist with TEM Can co-exist with ITG 4/25/13 9

10 Can we identify ITG vs TEM turbulence and relate this to a change in energy confinement? Measure density, temperature profiles (so we know about gradient drive for turbulence) Measure rotation profiles (so we know about flow suppression; may or may not be important) Measure turbulence (density and electron temperature fluctuations) Use gyrokinetic theory to predict whether ITG or TEM turbulence is present Assess whether changes in changes in measured turbulence are consistent with ITG/TEM 4/25/13 10

11 Highlight two (of many) tokamak plasma diagnostics used for turbulent transport studies x-ray imaging crystal spectrometer (XICS) Measures radial profiles of Ion temperature and Plasma Flow Correlation Radiometry of Electron Cyclotron Emission (CECE) CECE measures local turbulent fluctuations of electron temperature 4/25/13 11

12 Ion Temperature and Rotation profiles from X-ray imaging crystal spectrometer x-ray line emission from partially ionized, high Z, impurities in fusion plasmas Line broadening effects used to measure ion temperature Doppler effect (line shift) used to find flow velocities Problem with measurements has been lack of spatial resolution line integrated measurements only Recently developed x-ray imaging crystal spectrometers use tomographic techniques to find local flow temperatures and velocities [Bell, RSI 1997, Condrea POP 2000, Reinke RSI 2012] View to plasma through port Three He-like Detectors One H-like Detector He-like Crystal H-like Crystal Sample image from one He-like detector Imaging x-ray spectrometer at MIT tokamak tuned to He-like and H-like argon, T e < 5 kev) Spatially resolving spherically bent crystal detectors 12

13 Electron Cyclotron Emission (ECE) in tokamaks: measure T e with radiometers Emission layer ECE is mm-wave radiation at electron cyclotron frequencies measure ECE to get T e profile measurement in optically thick tokamak plasma Measure ECE at black body intensity, directly related to temperature; Localization provided by known variation in magnetic field 4/25/13 13

14 ECE radiometers have excellent temporal and spatial resolution; but focusing optics needed to measure turbulence Temporal resolution is determined by bandwidth of video amplifier τ int =1/(2B vid ) ~ µsec Radial resolution determined by combination of ECE physics (line broadening) and IF filter bandwidth, B if r ~ 1 cm Poloidal resolution determined by focusing optics of the antenna system; Gaussian beam waist, w 1/e, z ~ 1 cm Plasma cross section Spatial resolution allows for study of ITG/TEM scale fluctuations in plasma 14

15 Correlation ECE is needed to measure broadband low amplitude electron temperature fluctuations Single ECE radiometer channel sensitivity limited by the thermal noise level given by radiometer equation T ~ /T 2B vid B if ~ B if ~ 100 MHz, B vid ~ 1.0 MHz : sensitivity T e /T e > 15 % Standard cross-correlation techniques are used to improve sensitivity to turbulent fluctuations T ~ /T 1 N s 2B vid B if Long time averaging, large N s ~ Sensitivity improves T e /T e > 0.4% Correlation ECE has been used on tokamaks and stellarators W7-AS (Sattler 1994, Hartfuss 1996, Watts 2004), TEXT (Cima 1995, Deng 1998 ), RTP (Deng 2001), Review article (Watts 2007), DIII-D (White 2008), C-Mod (White 2013) A. E. White 52nd APS- DPP Chicago, IL

16 Case Study: Can we identify ITG vs TEM turbulence and relate this to a change in energy confinement? Increase in density in ohmically heated tokamak plasmas exhibits satura;on of energy confinement above a cri;cal density (purple). When confinement ;me saturates, rota;on profile (plasma is intrinsically rota;ng) changes shape from peaked to hollow. LOC SOC Hypothesis in community TEM turbulence is dominant at low densijes, does not drive significant heat flux. But ITG turbulence becomes dominant when density is increased (due to change in Ti gradient drive term) and increases heat flux, thus saturajng the energy confinement Jme. LOC ITG/TEM transijon can also explain change in intrinsic rotajon according to some theories for momentum generajon and transport by turbulence SOC Measured with XICS 4/25/13 16

17 Across the LOC-SOC transition, there is an increase in ion heat flux, consistent with more ITG drive n e ~ n crit LOC SOC SOC LOC 4/26/13 17

18 Across the LOC-SOC transition, there is little change in density fluctuations At first glance, there is now an inconsistency: Heat flux, Q i, increased! But Turbulence amplitude did not So far no clear evidence that ITG is more active in SOC. n e ~ n crit LOC SOC LOC SOC 4/25/13 18

19 Across the LOC-SOC transition, there is significant decrease in electron temperature fluctuations Resolving inconsistency : Reduction of temperature fluctuations indicates transition from TEM to ITG, consistent with increase in Q i. n e ~ n crit LOC SOC LOC SOC Measured with CECE 4/25/13 19

20 Decrease in Electron Temperature Fluctuations Correlated with transition to ITG dominance* Gyrokinetic calculations for growth rate Measurements of temperature fluctuations ITG SOC ITG SOC TEM LOC TEM LOC * Sung Nuclear Fusion submitted; White Phys. Plasmas 2010 & /25/13 20

21 Appears that hypothesis for ITG-TEM transition linked to LOC-SOC transition may be correct Energy confinement time changes may be explained Changes in electron temperature turbulence (first direct measurements) are consistent with gyrokinetic theory predictions for these plasmas Sung Nuclear Fusion submitted First direct measurements supporting ITG/TEM hypothesis for LOC/SOC confinement time change Standard gyrokinetic theory appears to predict reasonably well changes in energy confinement and turbulence But why does plasma rotate spontaneously? Why change? Intrinsic momentum source and momentum transport NOT UNDERSTOOD Standard gyrokinetic theory is valid for high flow (high mach number), and may not be valid for low flow. Frontier for theory and simulations 4/25/13 21

22 Turbulence in tokamak plasmas causes high levels of transport observed in experiments The transport of heat and particles in tokamak plasmas happens more quickly than expected from classical theory tokamak transport is turbulent Controlling turbulence is necessary to control loss of heat and particles from tokamak plasmas Understanding turbulence requires the use of measurements, theory, and simulations Huge progress made in understanding ITG/TEM model X-ray spectrometers and radiometers play key role Diagnosing turbulence in present-day tokamaks is critical for developing transport models that are used to predict the capabilities of future tokamaks, like ITER 4/25/13 22

23 Where can fusion energy research and astrophysics overlap? Development/advancement of gyrokinetic theory and simulation ASTROGK (Greg Howes, Univ. Iowa) used to simulate kinetic turbulence in solar wind New computational methods/algorithms to allow for more efficient coupled ion and electron scale simulations of turbulence Atomic data bases/spectral survey data Transport of high-z impurities is becoming more important as we progress toward fusion reactor (which must use metal walls and metal plasma facing components) Tungsten, Molybdenum, Beryllium, etc. are all materials to be used in reactor Analysis techniques/hardware Development Imaging techniques; X-ray diagnostics Mm-wave and THZ detectors e.g. many astronomy/astrophysics applications use detectors/ electronics to process emission at f > 300 GHz, but only one tokamak (ITER) will have high enough magnetic field for ECE to be relevant in this range 4/25/13 23

24 Extra Slides 4/25/13 24

25 Great success in confining hot plasmas and generating fusion power in Tokamaks Best performance achieved in tokamak (other leading magnetic configuration is stellarator) Exceeded required temperatures and densities for fusion Record ion temperature of 50 kev on TFTR (Neutral Beam heating) at 6 atm central pressure, with central density 1x10 20 m -3 TFTR produced >10MW of D-T fusion power in the early 90 s (bested by JET (UK) later on with 16MW) Problem is confinement time! Need to increase confinement time 4/25/13 25

26 Progress in explaining suppression of ITG/TEM turbulence: flow shear reduces size of eddies Heuristic picture: Sheared flow breaks up turbulent eddies, smaller eddies means smaller diffusive step size Eddies affected By flow shear Eddy Nonlinear Gyrokinetic Simulations and experiments in basic laboratory devices confirm picture [e.g. Lin 1998, Carter 2012] Shear flow can stabilize/reduce transport associated with gradient driven modes (ITG and TEM) Sheared flow can also be source of free energy/turbulence 4/25/13 26 With flow shear Without flow shear

27 When axisymmetry is perfect, toroidal angular momentum is conserved. Tokamaks have near-perfect axisymmetry In tokamaks, there are nearby fixed structures to which momentum could be transfered (unlike astrophysics!) Momentum can only be transfered by non- axisymmetric fields or by parjcles. We know that somejmes non- axisymmetric B- fields arise that transfer momentum (PerturbaJons, Locked modes, Wall modes). Most of the Jme these are absent. Poloidal RotaJon is rapidly damped by the 1/R magnejc field variajon (not symmetric in poloidal direcjon). So why does tokamak plasma spontaneously (intrinsically) rotate? LOC SOC And why under certain condijons, will rotajon direcjon flip? Hypothesis is change from ITG to TEM turbulence* *K.C.Shaing, Phys. Rev. Lett. 86 (2001) 640. B.Coppi, Nucl. Fusion 42 (2002) 1. A.G.Peeters et al., Phys. Rev. Lett. 98 (2007) O.D.Gurcan et al., Phys. Plasmas 14 (2007) T.S.Hahm et al., Phys. Plasmas 14 (2007) /25/13 27

28 Nonlinear GK simulations use experimentally measured Radial profiles as input. Electron density Ion Temperature Electron Temperature Plasma Rotation Nonlinear Gyrokinetic Simulations run only in limited (grey) radial domain (core plasma) Only simulate ion-scale turbulence (ITG and TEM instabilities) In ITG dominant plasmas ion temperature gradient is key drive term plasma rotation gradient is key suppression term 4/25/13 28