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

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Turbulence in Fluids widely studied, relevant for many systems of interest

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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

• Acceleration and propagation of high energy cosmic rays

Kinetic Plasma Turbulence www.physics.uiowa.edu

Alexander Tchekhovskoy www.cfa.harvard.edu

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Magnetic Confinement in Tokamak relies on helical magnetic field (toroidal plus poloidal)

●  Poloidal field from current in the plasma itself.

●  Axisymmetric – good confinement

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  

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Measurements Reveal Turbulence in Tokamaks: 1% level, small spatial scale compared to device

Size of Tokamak

L ~ 1 m

ρ ~ 1 mm Eddy size ~ 0.5-1.0 cm

Measurements of density fluctuations

BES diagnostic measurement locations in tokamak

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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?

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Because of turbulence, the next step for international fusion progress is ITER: beat turbulence with size

Confinement time scales strongly with size, L!

2

•  GyrokineJcs  is  kineJc  theory  averaged  over  the  fast  gyro-­‐moJon  (Larmor  moJon).  

–  Rutherford  &  Frieman  1968;  Taylor  &  HasJe  1968;                Frieman  &  Chen  1982;  Howes  et  al.  2006  

•  Low-­‐frequency  limit  eliminates  fast  cyclotron  Jmescale    ω  ≪  Ωi  

•  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  

Turbulence in Astrophysical Plasmas and Tokamaks can be described by gyrokinetic theory

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Tractable nonlinear GK simulations describe the nonlinear saturated state of two important instabilities

ITG TEM Ion Temperature Gradient Trapped Electron Mode Long wavelength (kρ < 1.0) Long wavelength (kρ < 1.0) Driven by Ti gradient Driven by both ne and Te gradients,

and trapped particle resonance

Unaffected by collisions Damped by collisions Damped by flow shear Damped by flow shear Drives strong potential, density, and ion temperature fluctuations: Associated with ION HEAT FLUX

Drives strong potential, density, and electron temperature fluctuations: Associated with ELECTRON HEAT FLUX

Propagates in ion diamagnetic flow direction in plasma frame of reference

Propagates in electron diamagnetic flow direction in plasma frame of reference

Can co-exist with TEM Can co-exist with ITG

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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

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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

Highlight two (of many) tokamak plasma diagnostics used for turbulent transport studies

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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]

• Imaging x-ray spectrometer at MIT tokamak tuned to He-like and H-like argon, Te < 5 keV)

• Spatially resolving spherically bent crystal detectors

View to plasma through port

H-like Crystal

He-like Crystal

Three He-like Detectors

One H-like Detector

Sample image from one He-like detector

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Electron Cyclotron Emission (ECE) in tokamaks: measure Te with radiometers

Emission layer

measure ECE to get Te 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

ECE is mm-wave radiation at electron cyclotron frequencies

ECE radiometers have excellent temporal and spatial resolution; but focusing optics needed to measure turbulence

Plasma cross section

• Temporal resolution is determined by bandwidth of video amplifier τint=1/(2Bvid) ~ µsec

• Radial resolution determined by combination of ECE physics (line broadening) and IF filter bandwidth, Bif ∆r ~ 1 cm

• Poloidal resolution determined by focusing optics of the antenna system; Gaussian beam waist, w1/e,

∆z ~ 1 cm

Spatial resolution allows for study of ITG/TEM scale fluctuations in plasma

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Correlation ECE is needed to measure broadband low amplitude electron temperature fluctuations

A.  E.  White  52nd  APS-­‐DPP  Chicago,  IL  2010  

• Single ECE radiometer channel sensitivity limited by the thermal noise level given by radiometer equation

• Standard cross-correlation techniques are used to improve sensitivity to turbulent fluctuations €

T~/T ≥ 2Bvid

Bif

€

T~/T ≥ 1

Ns

2Bvid

Bif

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)

Bif ~ 100 MHz , Bvid ~ 1.0 MHz : sensitivity Te/Te > 15 %

Sensitivity improves Te/Te > 0.4% ~

~

Long time averaging, large Ns

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•  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.  

•  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.  

–  ITG/TEM  transiJon  can  also  explain  change  in  intrinsic  rotaJon  according  to  some  theories  for  momentum  generaJon  and  transport  by  turbulence  

SOC

LOC

Case Study: Can we identify ITG vs TEM turbulence and relate this to a change in energy confinement?

SOC LOC

Measured with XICS

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Across the LOC-SOC transition, there is an increase in ion heat flux, consistent with more ITG drive

ne~ ncrit

SOC LOC SOC

LOC

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Across the LOC-SOC transition, there is little change in density fluctuations

SOC LOC

ne~ ncrit

SOC LOC

At first glance, there is now an inconsistency: Heat flux, Qi, increased! But Turbulence amplitude did not …So far no clear evidence that ITG is more active in SOC.

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Across the LOC-SOC transition, there is significant decrease in electron temperature fluctuations

ne~ ncrit

SOC LOC SOC LOC

Resolving inconsistency : Reduction of temperature fluctuations indicates transition from TEM to ITG, consistent with increase in Qi.

Measured with CECE

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Decrease in Electron Temperature Fluctuations Correlated with transition to ITG dominance*

Gyrokinetic calculations for growth rate

ITG

TEM

ITG

TEM

Measurements of temperature fluctuations

*Sung Nuclear Fusion submitted; White Phys. Plasmas 2010 & 2013

SOC

LOC

SOC

LOC

•  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…

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Appears that hypothesis for ITG-TEM transition linked to LOC-SOC transition may be correct

•  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

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Turbulence in tokamak plasmas causes high levels of transport observed in experiments

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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

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Extra Slides

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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 1x1020 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

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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

• 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

With flow shear Without flow shear

Eddy

Eddies affected By flow shear

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•  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?    

•  And  why  under  certain  condiJons,  will  rotaJon  direcJon  flip?  Hypothesis  is  change  from    ITG  to  TEM  turbulence*  

When axisymmetry is perfect, toroidal angular momentum is conserved. Tokamaks have near-perfect axisymmetry

*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) 265003. O.D.Gurcan et al., Phys. Plasmas 14 (2007) 042306. T.S.Hahm et al., Phys. Plasmas 14 (2007) 072302.

SOC

LOC

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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