Presented at

1
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,
USA c)University of California-San Diego, La
Jolla, California, USA d)University of Texas,
Austin, Texas, USA e)General Atomics, P.O. Box
85608, San Diego, California, USA f)Lawrence
Livermore National Laboratory, Livermore,
California, USA

Presented at PPPL, Princeton, NJ May 20, 2008
1
2
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 ( lt 1),
  Trapped electron mode (TEM) ( lt
  2 ) Electron temperature gradient (ETG)
  mode ( gt 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

2
3
Summary of Results

• 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

3
4
Correlation Electron Cyclotron Emission (CECE)
Diagnostic Measures Local, Low-k Electron
Temperature Fluctuations
SSB receiver with two channel filter bank
?f1
?f2

250 MHz

• Emission in non-overlapping frequency bands
• Separated by less than turbulence correlation
  length
• Cross-correlate signals to measure RMS amplitude
  and spectrum

?f2
?f1
110 MHz
4
5
The Thermal Noise is Uncorrelated When
Intermediate Frequency Filter Bandwidths Do Not
Overlap

• 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 Bsiglt Bvid
• MHD modes (Bsigltlt Bvid ) often observed in a
  single radiometer channel

6
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

CECE
Te/Te

n/n
BES
1.2 cm
0.9 cm
6
7
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

7
8
Temperature Fluctuations Are Measured in L-mode,
H-mode and Ohmic Plasmas in a Single Discharge

• 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

r/a 0.74
8
9
Spectra Evolve in Time, with Large Reduction in
Te/Te After L-H Transition

• 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 with
• QH-mode experiments, a
• factor 5 reduction has been
• observed at same radius (Schmitz, PRL 100,
  035002,(2008))

VExB 4.1 km/sec
VExB 7.1 km/sec
VExB 6.5 km/sec
VExB 2.4 km/sec
9
10
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

10
11
The Profile of Temperature Fluctuations in L-mode
Is Compared to the Profile of Density
Fluctuations
Use series of repeat discharges to measure
profiles of Te/Te and n/n Stationary,
sawtooth-free L-mode. ne 2.5 x 10 19 m-3 Te
450 eV Ti 500 eV


1300-1700 ms used in analysis
11
12
Plasma Profiles, Plasma Frequencies, and Optical
Depth in L-mode Plasma of Interest

• 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 lt
r/a lt 0.9
12
13
Temperature and Density Fluctuations Have Similar
Spectra and 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 0.3lt r/a lt 0.9

13
14
Outline

• Temporal evolution of temperature fluctuations

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

• Comparison with nonlinear simulations

• Comparison of temperature and density
  fluctuations in ECH experiment

14
15

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

• 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

15
16
Synthetic Diagnostics That Model the BES and CECE
Sample Volumes are Used to Spatially Filter the
Raw GYRO Data
CECE PSF
CECE Sample volumes
BES PSF
CECE sample volume Antenna pattern and natural
linewidth
BES sample volumes
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)
16
17
Shapes of BES and CECE Sample Volumes Result In
Different Filtering of the High Frequencies

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

r/a 0.5
(McKee, PRL 2000)

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

- Radial extent causes symmetric attenuation of
all wavenumbers
r/a 0.5

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

- Poloidal extent causes more attenuation of
higher wavenumbers
(Bravenec, RSI 1995)
17
18
At r/a 0.75 GYRO Underestimates the
Experimental Fluctuation Levels
Density Fluctuations

• Density Fluctuations

GYRO (40-400 kHz) ne/ne 0.33-0.007 Experiment
(40-400 kHz) n/n 1.1-0.2

(ne/ne)2/kHz

• Temperature Fluctuations

GYRO (40-400 kHz) Te/Te 0.5-0.02 Experiment
(40-400 kHz) Te/Te 1.5-0.2

(Te/Te)2/kHz
Temperature Fluctuations
18
18
19
At r/a 0.5 GYRO Shows Reasonable Agreement
With Experimental Fluctuation Levels

• Density Fluctuations

GYRO (40-400 kHz) ne/ne 0.560.008
Experiment (40-400 kHz) n/n 0.55-0.12

(ne/ne)2/kHz

• Temperature Fluctuations

(Te/Te)2/kHz
GYRO (40-400 kHz) Te/Te 0.66-0.2 Experiment
(40-400 kHz) Te/Te 0.4-0.2



19
20


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

• At r/a 0.5,
• At r/a 0.75,
• Common result

2
(RMS level)
20
21
GYRO Predicts Temperature Fluctuation
Contribution to Energy Flux at r/a 0.5

• 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

21
22
Outline

• Temporal evolution of temperature fluctuations

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

• Comparison with nonlinear simulations

• Comparison of temperature and density
  fluctuations in ECH experiment

22
23
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

• Density is held constant
• Heat fluxes and heat diffusivities increase
• TGLF indicates increase in TEM growth rate

Times used in analysis 1500-1700 ms
23
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Increases in Heat Flux and TEM Growth Rate
Correlate With Increase in Te/Te, but ñ/n Does
Not Change


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

BES n/n stays the same NB only
1.2-0.2 NB ECH 1.2-0.2

• Change in spectral shape due to dominant
  Doppler shift
• Reduction in Er with ECH causes spectra to
  shift to lower frequencies

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

24
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Summary of Results

• 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

25
26
Future Work

• 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 )

Simultaneous measurements of multiple fluctuating
fields improve understanding of turbulence and
transport, provide the opportunity for
challenging comparisons with nonlinear
gyrokinetic simulations
26
27
BACK-UP SLIDES
27
28
Generic PSF Convolution Integral and CECE PSF
model as Asymmetric Gaussian
29
BES PSF
30
ITG is dominant Instability at Long Wavelengths,
r/a 0.5
GYRO Transport Fluxes
Linear Growth Rate
ci
ce
31
ITG is dominant instability at Low-k, TEM
dominant at Higher-k, at r/a 0.75
Linear Growth Rate
GYRO Transport Fluxes
ci
ITG
TEM
nei
ce
gExB
kqrs
kqrs
32
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
Experiment
Experiment
GYRO
GYRO
33
Use TGLF to Calculate Flux-Matched Profiles
Disagreements with experimental fluctuation
levels motivate future workwith simulations and
experiments
34
Growth Rate of Most Unstable Mode Increases With
Radius, Consistent With Measured Fluctuations

• TGLF (Trapped gyro-Landau-fluid) code used
  for linear stability analysis
• ITG mode (fREAL lt 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

34
35

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

• 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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Correlation Radiometry Needed for Measurements of
Turbulent Temperature Fluctuations from ECE

• 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

Bif 110 MHz , Bvid 2.5 MHz sensitivity
Te/Te gt 15
Sensitivity improves Te/Te gt 0.2

• 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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CECE Gaussian Optics Provide Small Spot-Size
Needed for Turbulence Measurements
Laboratory tests 94 GHz incident beam focused
using parabolic mirror The beam agrees well with
a Gaussian spatial profile.
1/e2 power diameter
CECE is sensitive to long wavelength
fluctuations of electron temperature
Small spot-size makes turbulence measurements
possible
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Radial Extent of CECE Sample Volume is Determined
by the Natural Linewidth, with Small Corrections
From Filter Width

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

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

amplitude

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

• Separation of sample volumes determines
• radial wavenumber resolution, kr lt 4 cm-1

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

Calibrated fixed filter CECE signals give Te

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 and Te/Te can also be calculated by
integrating the cross-power spectrum, Pxy, over
frequency range, f1 , fN of interest

Relatively calibrated signals give Te/Te From the
correlation coefficient function
40
Thermal noise fluctuations decorrelate when ?f
Bif independent of radiation source, or sample
volume in plasma
(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
(c)
41
Contribution from Density Fluctuations to Signal
Due to Low Optical Depth are Negligible
In optically grey plasma the density fluctuations
can contribute to signal, leading to apparent
temperature fluctuations
42
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 n03.5x1019 m-3 Refractive
effects Sample volume location Vertical
up-shift lt 0.5 cm Sample volume diameter Spot
size changes lt 0.2 cm Comparable to
measurement uncertainty of spot-size in lab
43
Refractive effects are negligible for
plasmas under consideration ne lt 0.8 necut-off

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

• (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 gt 100 of cut-off
density. Substantial refractive effects
obvious for 15 degree mirror, no signal is
seen for 7 degree mirror.
44
Profile Comparison from ECH Experiment
44
45
CERFIT Analysis Indicates Slight Reduction In Er
for ECH Case - Expect Narrowing of Turbulent
Spectra
45
46
Temperature Fluctuations Increase Across Radius
with ECH
46
47
TGLF Results from ECH Experiment TEM Linear
Growth Rate Increases with ECH
Gamma/(Cs/a)
Gamma/(Cs/a)
47
48
Beam Emission Spectroscopy (BES) measures
spatially localized, long-wavelength density
fluctuations