Presented at PPPL, Princeton, NJ May 20, 2008

Presented at PPPL, Princeton, NJ

May 20, 2008

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Measurements of Core Electron Temperature Fluctuations

A. E. White

University of California-Los Angeles, Los Angeles, California, USA

L. Schmitz,a) W.A. Peebles,a) T.A. Carter,a) G.R. McKee,b)

C. Holland,c M.E. Austin,d) K.H. Burrell,e) J. Candy,e)

J.C. DeBoo,e) E.J. Doyle,a) M.A. Makowski,f) R. Prater,e) T.L. Rhodes,a) M.W. Shafer,b) G.M. Staebler,e) G.R. Tynan,c)

R.E. Waltz,e)G. Wanga) and the DIII-D Team,e)

a)University of California-Los Angeles, Los Angeles, California, USA

b)University of Wisconsin-Madison, Madison, Wisconsin, USAc)University of California-San Diego, La Jolla, California, USA

d)University of Texas, Austin, Texas, USAe)General Atomics, P.O. Box 85608, San Diego, California,

USAf)Lawrence Livermore National Laboratory, Livermore,

California, USA

1

Both Electron Temperature and Density Fluctuations Provide Information about Physics of Turbulence and Transport• Several types of instabilities may contribute to electron heat and particle transport in the tokamak

– Ion temperature gradient (ITG) mode ( < 1), – Trapped electron mode (TEM) ( < 2 ) – Electron temperature gradient (ETG) mode ( > 2 )

•Core electron temperature and density fluctuations both contribute to energy transport flux (Liewer 1985, Wootton 1990, Ross 1992)

•Measurements of Te probe physics of non-Boltzmann electron response, in particular, trapped electrons

– Turbulence models: electron heat and particle transport result from non Boltzmann (non-adiabatic) electrons

–Trapped electrons destabilize ITG mode, drive TEM unstable

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2

• Time history of Te/Te during single discharge reveals changes in amplitude in L-mode, H-mode and Ohmic plasmas

• Electron temperature fluctuations, Te/Te, and density fluctuations, ñ/n, have similar spectra, amplitudes and increase with radius

• GYRO predicts Te/Te ~ ñe/ne, consistent with observations. GYRO/synthetic diagnostics do not fully reproduce increase in fluctuation level with radius.

• Electron Cyclotron Heating (ECH) during beam heated L-mode plasmas results in increased Te/Te, but not ñ/n

Summary of Results

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SSB receiver with two channel filter bank

4

•Emission in non-overlapping frequency bands

•Separated by less than turbulence correlation length

•Cross-correlate signals to measure RMS amplitude and spectrum

∆f1

∆f2

Correlation Electron Cyclotron Emission (CECE) Diagnostic Measures Local, Low-k Electron Temperature Fluctuations

∆f2∆f1

110 MHz

250 MHz

• The thermal noise feature is broadband in frequency •The temperature fluctuation feature can be measured (~ 100 ms average) in cases of moderate filter overlap when Bsig< Bvid

•MHD modes (Bsig<< Bvid ) often observed in a single radiometer channel

The Thermal Noise is Uncorrelated When Intermediate Frequency Filter Bandwidths Do Not Overlap

Beam Emission Spectroscopy (BES) Diagnostic Measures Local Density Fluctuations at Same Radius as CECE

• Measurement locations separated toroidally and vertically

• CECE and BES measure turbulence on Ion Temperature Gradient (ITG) and Trapped Electron mode (TEM) scales

k 1.8 cm 1

kr 2 cm 1

kr 4 cm 1

CECE

BES n/n

Te/Te

~

~

6

1.2 cm

0.9 cm

k 3 cm 1

Outline

• Temporal evolution of electron temperature fluctuations

• Comparison between electron temperature and density fluctuations in beam heated L-mode plasmas

• Comparison with nonlinear simulations

• Comparison of electron temperature and density fluctuations in ECH experiment

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Temperature Fluctuations Are Measured in L-mode, H-mode and Ohmic Plasmas in a Single Discharge

r/a = 0.74

• Shot parameters

– Ip = 1 MA– BT = 2.1 T, – 2.5 -10 MW beam power– upper single null

• Measure Te/Te at r/a = 0.75

– Early L-mode 700-900 ms – Stationary L-mode 1400-1600 ms– ELM-free H-mode 1895-1930 ms– Ohmic 3700-3900 ms

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• Typical cross-power spectra of Te/Te at r/a = 0.75

– Spectrum broadens and narrows in response to Doppler shifts due to changing ExB rotation

– Normalized fluctuation levels in Ohmic (1%) are lower than L-mode (1.5%) at same radius

– H-mode temperature fluctuations are below sensitivity limit (0.5%, 35 ms)

H-mode results are consistent withQH-mode experiments, a factor 5 reduction has been observed at same radius (Schmitz, PRL 100, 035002,(2008))

Spectra Evolve in Time, with Large Reduction in Te/Te After L-H Transition

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VExB = 2.4 km/sec

VExB = 7.1 km/sec

VExB =6.5 km/sec

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VExB = 4.1 km/sec

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Outline

• Temporal evolution of temperature fluctuations

• Comparison between temperature and density fluctuations in beam heated L-mode plasmas

• Comparison with linear and nonlinear simulations

• Comparison of temperature and density fluctuations in

ECH experiment

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The Profile of Temperature Fluctuations in L-mode Is Compared to the Profile of Density Fluctuations

1300-1700 ms used in analysis

Use series of repeat discharges tomeasure profiles of Te/Te and n/n

Stationary, sawtooth-free L-mode.

ne ~ 2.5 x 10 19 m-3

Te ~ 450 eVTi ~ 500 eV

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• 2nd Harmonic ECE is far from being cut-off by RH wave

• Plasma is optically thick ( )in region of interest

• Density fluctuations will not contribute to temperature fluctuation signal

CECE and BES diagnostics scanned between 0.3 < r/a < 0.9

Plasma Profiles, Plasma Frequencies, and Optical Depth in L-mode Plasma of Interest

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Temperature and Density Fluctuations Have Similar Spectraand Normalized Fluctuation Amplitude Profiles

–Shot 128915– r/a = 0.74

–Data averaged 1300-1700 ms– Spectra Integrated 40-400 kHz

•Te/Te and n/n measured between 0.3< r/a < 0.9

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Outline





ECH experiment

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• Comparisons between profiles of two fluctuating fields and nonlinear gyrokinetic simulations provide unique and challenging tests of the turbulence models

– GYRO is an initial value, Eulerian (Continuum) 5-D gyrokinetic transport code

– Local simulations include real geometry, drift-kinetic electrons, e-i pitch-angle collisions, realistic mass ratio

and equilibrium ExB flow, electromagnetic effects

– Take experimental profiles (Te, Ti, ne, Er) as input

~Compare Measured Te/Te and ñ/n With Results From Local, Nonlinear GYRO Simulations

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Synthetic Diagnostics That Model the BES and CECE Sample Volumes are Used to Spatially Filter the Raw GYRO Data

BES PSF

CECE PSF

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CECE sample volume: Antenna pattern and natural linewidth

BES sample volume: Collection optics, neutral beam/sight-line geometry, neutral beam cross-section intensity and the finite atomic transition time of the collisionally excited beam atoms [Shafer RSI 2006)

CECE Sample

volumes

BESsample volumes

- Radial extent causes symmetric attenuation of all wavenumbers

(Bravenec, RSI 1995)

(McKee, PRL 2000)

•CECE sample volume extended vertically (∆r ~ 1 cm, ∆z ~ 3.5 cm)

•BES sample volume extended radially (∆r ~ 2 cm, ∆z ~ 1.5 cm)

r/a =0.5

r/a =0.5

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Shapes of BES and CECE Sample Volumes Result In Different Filtering of the High Frequencies

•In measurements, Doppler shift dueto ExB plasma rotation dominates Observed spectrum of fluctuations

- Poloidal extent causes more attenuation of higher wavenumbers

f ~ k

GYRO (40-400 kHz)

ne/ne = 0.33+-0.007

Experiment (40-400 kHz)

n/n = 1.1+-0.2%

GYRO (40-400 kHz)

Te/Te = 0.5+-0.02


Te/Te = 1.5+-0.2%

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~

~

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At r/a = 0.75 GYRO Underestimates the Experimental Fluctuation Levels

TemperatureFluctuations

DensityFluctuations

•Temperature Fluctuations

•Density Fluctuations

(Te/Te)2/kHz

(ne/ne)2/kHz~

~

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At r/a = 0.5 GYRO Shows Reasonable Agreement With Experimental Fluctuation Levels

GYRO (40-400 kHz)

ne/ne = 0.56+0.008 %


n/n = 0.55+-0.12%

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GYRO (40-400 kHz)

Te/Te = 0.66+-0.2 %


Te/Te = 0.4+-0.2%~

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•Temperature Fluctuations

•Density Fluctuations

(ne/ne)2/kHz~

(Te/Te)2/kHz~

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• At r/a = 0.5, • At r/a = 0.75,

• Common result:

(RMS level) 2

GYRO Predicts Te/Te and ne/ne are Similar in Amplitude but Radial Profile Trend is not Reproduced

• Te/Te ~ ne/ne, consistent with experiment

• At r/a = 0.5, reasonable quantitative agreement

• Trend that fluctuation levels increase with radius not reproduced

EXP GYRO

EXP GYRO

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• GYRO flux-tube simulation at r/a = 0.5 has good quantitative agreement with experiment

– fluctuation levels– energy fluxes

– GYRO predicts Te drives 80% of energy transport ne drives 20% of energy transport

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GYRO Predicts Temperature Fluctuation Contribution to Energy Flux at r/a = 0.5

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Outline





ECH experiment

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Experiment Using Local ECH to Change Local Te Gradient and Turbulence Drives

• Baseline discharge with beam heating only– Ip = 1 MA, – BT = 2.0 T, – 2.5 MW of co-injected beam power– Inner wall limited

• Compare to discharge with additional EC heating at r/a ~ 0.17

Times used in analysis 1500-1700

ms

– Density is held constant –Heat fluxes and heat diffusivities increase

– TGLF indicates increase in TEM growth rate

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• The correlation reflectometer shows no change in correlation length of electron density fluctuations

Increases in Heat Flux and TEM Growth Rate Correlate With Increase in Te/Te, but ñ/n Does Not Change

BES : n/n stays the sameNB only 1.2+-0.2%NB + ECH 1.2+-0.2%

CECE : Te/Te increases by 50%NB only 1.0+-0.2%NB + ECH 1.5+-0.2%

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• Change in spectral shape due to dominant Doppler shift

– Reduction in Er with ECH causes spectra to shift to lower frequencies

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• Time history of Te/Te during single discharge reveals changes in amplitude in L-mode, H-mode and Ohmic plasmas

• Electron temperature fluctuations, Te/Te, and density fluctuations, ñ/n, have similar spectra, amplitudes and increase with radius

• GYRO predicts Te/Te ~ ñe/ne, consistent with observations. GYRO/synthetic diagnostics do not fully reproduce increase in fluctuation level with radius.

• Electron Cyclotron Heating (ECH) during beam heated L-mode plasmas results in increased Te/Te, but not ñ/n

Summary of Results

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Future Work

Simultaneous measurements of multiple fluctuating fields improve understanding of turbulence and transport, provide the opportunity for challenging comparisons with nonlinear gyrokinetic simulations

• GYRO predicts phase between Te and ne, measure phase between Te and ñe using CECE and reflectometry (Haese 1997)

• Dimensionless parameter scans and comparison of Te/Te and n/n

• Simulations of results where Te/Te and ñ/n respond differently to ECH

• Flux-matched profiles, TGLF transport model (J. E. Kinsey POP May, 2008 )

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BACK-UP SLIDES

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Notes of Definition of Point Spread Function for BES and CECE The point spread function PSF is used to calculate the synthetic fluctuation signal corresponding to a diagnostic centered at (R0,Z0) from the ŅunfilteredÓ real-space fluctuation fields calculated by a simulation using the following convolution:

fsynthetic R0 ,Z0 ,t dRdZ R R0,Z Z0 fsim R,Z, t

dRdZ R R0 ,Z Z0

For the BES system, is calculated by the UW-Madison group and taken as a given input. For the CECE diagnostic, we specify a model form as

CECE exp 12

R R0

LR

2

Z Z0

LZ

2

where LR = 0.25 cm, and Lz = (3.8/4) cm, based on the 1 cm radial 1/e**2 diameter and 3.8 cm vertical 1/e**2 diameter provided by Anne. So we can write

CECE exp 8R R0

1 cm

2

Z Z0

3.8 cm

2

So for example, with Z=Z0, we find = 1/e**2 at R-R0 = 0.5 cm (giving the 1 cm radial diameter). Likewise, we obtain = 1/e**2 with Z-Z0 = 1.9 cm for R=R0.

Generic PSF Convolution Integral and CECE PSF model as Asymmetric Gaussian

BES PSF

r/a = 0.5 predicted to be ITG-dominant

ei

ExB

ITG TEM

ks

Linear growth rate

ITG is dominant Instability at Long Wavelengths, r/a = 0.5

GYRO Transport Fluxes

i

e

Linear Growth Rate

ITG is dominant instability at Low-k, TEM dominant at Higher-k, at r/a = 0.75

ei

ExB

ITG TEM

ks

Linear Growth Rate

ks

e

i

GYRO Transport Fluxes

Local GYRO Simulations Match the Experimental Heat Diffusivities Well at r/a = 0.5, not at r/a = 0.75

Electron heat diffusivity

Ion heat diffusivity

GYRO GYRO

Experiment

Experiment

Use TGLF to Calculate Flux-Matched Profiles

Disagreements with experimental fluctuation levels motivate future workwith simulations and experiments

• TGLF (Trapped gyro-Landau-fluid) code used for linear stability

analysis

• ITG mode (fREAL < 0) is fastest growing mode for long wavelengths in CECE range

–Te associated with ITG mode

• Linear growth rate of fastest growing mode (TEM) peaks at ~ 0.7

• Transport fluxes peak at longer wavelengths, ~ 0.2 at r/a = 0.75

Growth Rate of Most Unstable Mode Increases With Radius, Consistent With Measured Fluctuations

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Core Te/Te Reduction in Quiescent H-mode Experiments Suggests Contribution to Qturb

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•Flow shear stabilization is not expected to suppress the dominant ITG mode in L-mode

•In QH-mode, TEM mode are dominant

•EXB shearing rate is found to exceed the calculated linear growth rate

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•The magnetized plasma radiates as a black body from an optically thick emission layer with the ECE intensity proportional to the electron temperature

–Emission at harmonics of the cyclotron frequency, , originates at a particular frequency determined by B-field strength

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

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

T~

/T

2

BvidBif

Bif ~ 110 MHz , Bvid ~ 2.5 MHz : sensitivity Te/Te > 15%

qB /m

T~

/T

2

1

Ns

BvidBif

Ns 2tBvid

Sensitivity improves Te/Te > 0.2%

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Correlation Radiometry Needed for Measurements of Turbulent Temperature Fluctuations from ECE

•Past Work: TEXT (Cima 1995, Deng 1998 ), W7-AS (Sattler 1994, Hartfuss 1996, Watts 2004), RTP (Deng 2001), DIII-D (Rettig 1997, Schmitz 2008)

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k 1.8 cm 1

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CECE Gaussian Optics Provide Small Spot-Size Needed for Turbulence Measurements

CECE is sensitive to long wavelength fluctuations of electron temperature

Laboratory tests:

94 GHz incident beam focused using parabolic mirror

The beam agrees well with a Gaussian spatial profile.

Small spot-size makes turbulence measurements possible

1/e2 power diameter

Radial Extent of CECE Sample Volume is Determined by the Natural Linewidth, with Small Corrections From Filter Width

G(s) I(s)(s)exp( )

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•Natural linewidth of the emission layer is given by the emissivity (ECESIM – DIII-D IDL-based code)

•Separation of sample volumes determinesradial wavenumber resolution, kr < 4 cm-1

•Radial sample size (∆r ~ 1 cm) for a single IF filter is slightly wider than the natural linewidth

•Linewidth (∆ r ~ 0.8 cm) is determined by the relativistic broadening and re-absorption in the plasma

am

plit

ud

eam

plit

ud

e

Calibrated fixed filter CECE signals give Te

Relatively calibrated signals give Te/Te

From the correlation coefficient function

Te~

/Te

2

Cxy (0)BvidBif

Calibrated tunable YIG CECE signals give Te from correlation function

Calibrated YIG CECE signals normalized to local Te give Te/Te from the

correlation function

Te~

/Te

2

Rxy (0)Te and Te/Te can also be calculated by integrating the cross-power spectrum, Pxy,

over frequency range, [f1 , fN] of interest

The CECE radiometer is calibrated to measure Te and Te , No calibration needed for Te/Te measurements

~ ~

Te~ 2

Rxy (0)

Te~

/Te

2

2f Pxy ( f i)i1

N

~

~ ~

~

~~

Thermal noise fluctuations decorrelate when ∆f ~ Bif

independent of radiation source, or sample volume in plasma

(c)

(a) 2-18 GHz noise source (input to first amplifier in

radiometer)

(b) W-band noise source (input at antenna)

(c) L-mode and H-mode plasmas

In optically grey plasma the density fluctuations can contribute to signal, leading to apparent temperature fluctuations

[Rempel RSI 1994]

Contribution from Density Fluctuations to Signal Due to Low Optical Depth are Negligible

Ray-tracing code GENRAY is used to estimate the effects of refraction on the CECE sample volume size and location

Ray-tracing (disk-to-disk)25.4 cm diameter (at mirror) to 3.8 cm diameter (in plasma)

Low-density plasmas n0~3.5x1019 m-3

Refractive effects:

Sample volume location Vertical up-shift < 0.5 cm

Sample volume diameter Spot size changes < 0.2 cm*

*Comparable to measurement uncertainty of spot-size in lab

(a) Case with density, ne = 4.3x10-19 m-3 only 80 % of cut-off density for 2fc 93 GHz. ne, cut-off (93 GHz) ~5.35 x10-19 m-3. (b) Case with density > 100 % of

cut-off density. Substantial refractive effects obvious for 15 degree mirror, no signal is seen for 7 degree mirror.

•Modulations of the index of refraction along the line of sight will not cause apparent Te if ECE is far from cut-off

Refractive effects are negligible for plasmasunder consideration: ne < 0.8 ne

cut-off

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Profile Comparison from ECH Experiment

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CERFIT Analysis Indicates Slight Reduction In Er for ECH Case - Expect Narrowing of Turbulent Spectra

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Temperature Fluctuations Increase Across Radius with ECH

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TGLF Results from ECH Experiment: TEM Linear Growth Rate Increases with ECH

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Gam

ma/(

Cs/

a)

Gam

ma/(

Cs/

a)

Beam Emission Spectroscopy (BES) measures spatially localized, long-wavelength density fluctuations

Documents

Presented at PPPL, Princeton, NJ May 20, 2008