Fast-ion D (FIDA) Measurements of the Fast-ion Distribution Function
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Fast-ion D (FIDA) Measurements of the Fast-ion Distribution Function
Bill Heidbrink
DIII-D Instruments
Keith Burrell, Yadong Luo, Chris Muscatello, Brian Grierson
NSTX Instruments
Ron Bell, Mario Podestà
Two-dimensional imaging
Mike Van Zeeland, Jonathan Yu
ASDEX Upgrade Instruments
Benedijt Geiger
Additional collaborators
Deyong Liu, Emil Ruskov, Yubao Zhu, Clive Michael, David Pace, Mirko Salewski and many others
Van Zeeland, PPCF 51(2009) 055001.
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Why Measure the Fast-ion Distribution Function?
1. The distribution function F(E,pitch,R,z) is a complicated function in phase space
2. Fast ions are major sources of heat and momentum. needed to understand transport & stability
3. They drive instabilities that can expel fast ions and cause damage
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Outline
1. What is FIDA? How do we distinguish the FIDA light from all the other sources?
2. How does the FIDA signal relate to the fast-ion distribution function? Is our interpretation correct?
3. What are the applications?
4. What are the practical challenges? (New section)
5. How can we check the results? (New section)Slides in first three sections are from my 2010 HTPD invited talk: Rev. Sci. Instrum. 81 (2010) 10D727
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FIDA is an application of Charge Exchange Recombination
Spectroscopy1. The fast ion
exchanges an electron with an injected neutral
2. Neutrals in the n=3 state relax to an equilibrium population; some radiate
3. The Doppler shift of the emitted photon depends on a component of the fast-ion velocity
3 cm
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FIDA is Charge Exchange Recombination Spectroscopy--with a
twist•The radiating atom is a neutral no plume effect
•The fast ion distribution function is very complicated need more than moments of the distribution
•The Doppler shift is large low spectral resolution OK for FIDA feature but good resolution desirable anyway
•Many sources of bright interference like a laser scattering measurement
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Bright interfering sources are a challenge
•D light from injected, halo, and edge neutrals
•Visible bremsstrahlung
•Impurity lines
Luo, RSI 78 (2007) 033505
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Background Subtraction Normally Determines the Signal:Noise
T = F + Fedge+ V + Icx + Incx + Dcold + Dinj + Dhalo
(red only appears w/ beam)
T = Total signal
F = Active Fast-ion signal (the desired quantity)
Fedge= FIDA light from edge neutrals
V = Visible bremsstrahlung
Icx = Impurity charge-exchange lines
Incx = Impurity non-charge-exchange lines
Dcold = Scattered D light from edge neutrals
Dinj = D light from injected neutrals (beam emission)
Dhalo = D light from halo neutrals
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Must measure all other sources for an accurate FIDA measurement
T = F + V + Icx + Incx + Dcold + Dinj + Dhalo
T = Total signal
F = Fast-ion signal
V = Visible bremsstrahlung
Icx = Impurity CX (Fit to remove)
Incx = Impurity non-CX
Dcold = Cold D (Measure attenuated cold line)
Dinj = Injected D (Try to measure)
Heidbrink, RSI 79 (2008) 10E520
Use “Beam-off” measurements to eliminate black terms
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Must extract the FIDA signal from the background
1. Used beam modulation for background subtraction
2. Can use a toroidally displaced view that misses the beam
3. Fit the entire spectrum (all sources)
NSTX
Background subtraction via beam modulation works in a temporally stationary plasma; an equivalent view that misses the beam works if the plasma is spatially uniform.
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Two main types of FIDA instruments: spectrometer or bandpass-filtered
Tune to one side of the D line
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Two main types of FIDA instruments: spectrometer or bandpass-filtered
Measure full spectrum but block (attenuate) D line
Luo, RSI 78 (2007) 033505
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Two main types of FIDA instruments: spectrometer or bandpass-filtered
Measure one side but attenuate D line
Heidbrink, RSI 79 (2008) 10E520
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Two main types of FIDA instruments: spectrometer or bandpass-filtered
Bandpass filter one side of the spectrum
Podestà, RSI 79 (2008) 10E521.
or CCD
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14Van Zeeland, PPCF 51(2009) 055001.
•“Imaging” neutral beam produces red-shifted light (filtered out)
FIDA imaging: Put bandpass filter in front of a camera
•Oppositely directed fast ions from counter beam produces blue-shifted light (accepted by filter)
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Photograph of an ASDEX-U instrument
grating (2000 l/mm) Princeton Instruments EMCCD camera
180mm lenses f2.8
Interference filter
Geiger
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Outline
1. FIDA is charge-exchange recombination light that is Doppler-shifted away from other bright D sources.
2. How does the FIDA signal relate to the fast-ion distribution function? Is our interpretation correct?
3. What are the applications?
4. What are the practical challenges?
5. How can we check the results?
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The “weight function” describes the portion of phase space measured by a
diagnostic
Heidbrink, PPCF 49 (2007) 1457
•Define a “weight function” in phase space
•Like an “instrument function” for spectroscopy
•Doppler shift only determines one velocity component energy & pitch not uniquely determined
dPitchdEFWSignal )(
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Different Toroidal Angles Weight Velocity Space Differently
V2
R0V2
In this case, get much more signal from a view with a toroidal component of 0.6.
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|vperp|, vll are the best coordinates to use
V2
V2
Salewski, NF 51 (2011) 083014
10o 45o 80o 100o
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Ideal views give information about both |vperp| and vll
V2
R0V2 •Imagine a
population at a single point in |vperp|, vll space
•Shift gives information about vll
•Spread gives information about vperp
Ideal views are shifted by ~15o from 0o or 90o
Salewski, NF 51 (2011) 083014
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The “weight function” concept explains many results
•Changing Te changes NPA signal more than FIDA signal
•NPA measures a “point” in velocity space; FIDA averages
•More pitch-angle scattering at larger Te
Luo, RSI 78 (2007) 033505
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Use Forward Modeling to Simulate the Signal
V2
R0V2
•Forward modeling using a theory-based distribution function from TRANSP, ….
•Machine-specific subroutines for beam & detector geometry
•Data input: files with plasma parameters mapped onto flux coordinates
•Compute neutral densities of injected beam & halo
•Weighted Monte Carlo computes neutralization probability, collisional-radiative transitions, and spectra
Heidbrink, Comm. Comp. Phys. (2010)
FIDASIM code is available for download
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FIDASIM models FIDA, beam-emission, thermal, and VB features
V2
R0V2
Heidbrink, Comm. Comp. Phys. (2010)
We plan to maintain a public version of Geiger’s Fortran90 FIDASIM
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Excellent Results were Obtained with the First Dedicated Instrument
•Studied quiet plasmas first where theoretical fast-ion distribution function is known
•Spectral shape & magnitude agree with theory
•Relative changes in spatial profile agree with theory
•Dependence on injection energy, injection angle, viewing angle, beam power, Te, & ne all make sense
•Consistent with neutrons & NPA
Luo, Phys. Pl. 14 (2007) 112503.
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FIDA image agrees with theory
•One normalization in this comparison
Van Zeeland, PPCF 51(2009) 055001.
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Outline
1. FIDA is charge-exchange recombination light that is Doppler-shifted away from other bright D sources.
2. FIDA measures one velocity component of the fast-ion distribution function. Measurements in MHD-quiescent plasmas are consistent with theoretical predictions.
3. What are the applications?
4. What are the practical challenges?
5. How can we check the results?
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Type 1: Relative change in spectra
Heidbrink, PPCF 49 (2007) 1457.
•Average over time windows of interest
•Discard time points with contaminated background
•This example: ion cyclotron acceleration of beam ions
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High-harmonic heating in a spherical tokamak produces a broader profile than
in DIII-D•Many resonance layers in NSTX
•Very large gyroradius
Heidbrink, PPCF 49 (2007) 1457.
Liu, PPCF 52 (2010) 025006.
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Type 2: Relative change in time evolution
Van Zeeland, PPCF 50 (2008) 035009.
•Integrate over range of wavelengths
•Divide integrated signal by neutral density “FIDA density”
•This example: Alfvén eigenmode activity is altered by Electron Cyclotron Heating (ECH); weaker modes better confinement
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Severe Flattening of Fast-ion Profile Measured during Alfven Eigenmodes
Heidbrink, PRL 99 (2007) 245002; NF 48 (2008) 084001.
•Corroborated by neutron, current profile, toroidal rotation, and pressure profile measurements
•Spectral shape hardly distorted
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TAE “Avalanches” in NSTX: Mode overlap & enhanced fast-ion transport
sh#128455
f [k
Hz]
200 220 240 260 2800
20
40
60
80
100
120
200 220 240 260 280 3000
2
t [ms]
NB power neutrons
•Measure local drop in fast-ion density at MHD event using bandpass filter
•Fluctuations at mode frequency observed in sharp gradient region
Podestà, Phys. Pl. 16 (2009) 056104.
Magnetics
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View same radius from different angles to distinguish response of
different orbit types
V2
R0V2
•Vertical view most sensitive to “trapped” ions
•Tangential view most sensitive to “passing” ions
•“Sawtooth” crash rearranges field in plasma center
•Passing ions most affected, as predicted by theory
Heidbrink RSI 79 (2008) 10E520.
Muscatello, PPCF 54 (2012) 025006
Vertical
Tangential
Beams
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Type 3: Absolute Comparison with Theory
•Integrate over time window of interest
•Use calibration to get absolute radiance
•For profile, also integrate over wavelengths
•Compute theoretical spectra and profile
•This example: drift-wave turbulence in high temperature plasma causes large fast-ion transport
Heidbrink PRL 103 (2009) 175001; PPCF 51 (2009) 125001
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Microturbulence causes fast-ion transport when E/T (energy/temperature) is small
•Small MHD or fast-ion driven modes
•Co-tangential off-axis injection
•Low power case in good agreement at small minor radius but discrepant at low Doppler shift (low energy)
•High power case discrepant everywhere
Heidbrink PRL 103 (2009) 175001; PPCF 51 (2009) 125001
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More recent microturbulence data finds negligible transport
Pace, PoP (2013) in preparation
•No MHD or fast-ion driven modes
•Well-diagnosed plasmas
•Spectra & profile consistent with classical predictions for several cases
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FIDA diagnostics are implemented worldwide
TEXTOR
Delabie RSI 79 (2008) 10E522.
Michael (2010) private communication.
MAST
Osakabe, RSI 79 (2008) 10E519.
LHD
Beam emissionFIDA emission
Geiger (2010) private communication.
ASDEX-U
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FIDA is a powerful diagnostic of the fast-ion distribution function
•Spectral information one velocity coordinate
•Spatial resolution of a few centimeters
•By integrating light over the wing, get sub-millisecond temporal resolution
•With spectral integration, get two-dimensional images
•Radiance absolute comparisons with theory
Highlights of applications to date
•Confirm TRANSP predictions in MHD-quiescent plasmas
•Measure RF acceleration of fast ions
•Diagnose transport by Alfven eigenmodes
•Measure fast-ion transport by microturbulence
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Outline
1. FIDA is charge-exchange recombination light that is Doppler-shifted away from other bright D sources.
2. FIDA measures one velocity component of the fast-ion distribution function. Measurements in MHD-quiescent plasmas are consistent with theoretical predictions.
3. FIDA measures transport by instabilities and acceleration by ICRH
4. What are the main practical challenges?
5. How can we check our results?
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Bright interfering sources present two challenges
1) Separate FIDA feature from other features
2) Large dynamic range of signal60keV
FIDA
CII HeI
Beam emission
edge D-alpha
90keV
Geiger, Plasma Phys. Cont. Fusion 53 (2011) 065010
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Initial (obsolete) approach: Avoid beam emission
•Filter or avoid the cold D line
•Spectral intensity of injected neutral light is ~100 times brighter
•A vertical view works
Heidbrink, PPCF 46 (2004) 1855
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Better approach: measure beam emission
Grierson RSI (2012) 10D529
•FIDA ~ ninj nf
•Infer ninj from beam emission
arrange viewing geometry to measure both
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Background Problem: Scattered D Contaminates Signal & Changes in Time
Normal data analysis
•Remove impurity lines
•Subtract background (from beam-off time)
•Average over pixels to obtain FIDA(t)
Luo, RSI 78 (2007) 033505
(Careless) Normal Analysis says fast ions “bounce back” after sawtooth crash
This is wrong!
The problem: impurity and scattered D light change!
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Four approaches to the very bright cold line
Name Spectrometer Camera Cold D
NSTX vertical1 Holospec Photonmax ND filter
D3D vertical2 Czerny-Turner Sarnoff blue-side only
D3D oblique3 Holospec Sarnoff blue-side w/ filter
D3D main ion4 Czerny-Turner Sarnoff mild saturation
1Podestà, RSI 79 (2008) 10E521.
2Luo, RSI 78 (2007) 033505.
3Muscatello, RSI 81 (2010) 10D316.
4Grierson, Phys. Pl. 19 (2012) 056107.
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Top viewTop view Vertical view
Vertical view
NB line: B
NSTX has both active and passive views
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•Compare “beam-on” and “beam-off” spectra from adjacent time bins
•FIDA feature evident from magnetic axis to outer edge on active channels
•Spectra include impurity lines
Raw data show FIDA feature
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•Net spectra should go to zero at large Doppler shifts
•Should get same spectra from beam modulation (“beam on – beam off”) & reference view (“active view – passive view)
•Beam modulation spectra for reference view should be flat and ~ zero.
•Blue-shifted spectra meet criteria for this case
•Red-shifted spectra do not
Example of successful & unsuccessful background subtraction
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•Measure modulated spectra (“beam on – beam off”) in three bands: Large blue shift (above injection energy), cold D line*, Large red shift
•Compile database for 11 times in 9 shots
•Strong correlations for all channels for both red and blue sides of spectra
*includes some beam emission
Amplitude
Background offsets are caused by scattering of the bright central line
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Cold D line causes problems
•Avoid views with large recycling
•Ideal detector solution: narrow notch filter that attenuates cold line
•Holospec transmission grating spectrometer has high throughput but more scattered light
•Want to measure full spectrum
•No filter (Grierson) causes detector saturation
NSTX solution sees scattered light
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Collisions with edge neutrals produce FIDA light
•Existing FIDA diagnostics use active emission from an injected neutral beam
•Passive emission is observed when fast ions pass through the high-neutral density region at the plasma edge*
•For strong instabilities, the passive FIDA light is stronger than beam emission!
DIII-D example during off-axis fishbones
*Heidbrink, PPCF 53 (2011) 085007
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Outline
1. FIDA is charge-exchange recombination light that is Doppler-shifted away from other bright D sources.
2. FIDA measures one velocity component of the fast-ion distribution function. Measurements in MHD-quiescent plasmas are consistent with theoretical predictions.
3. FIDA measures transport by instabilities and acceleration by ICRH
4. The cold D line and varying backgrounds are major challenges
5. How can we check our results?
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Motivation for multiple calibration techniques
•Optical components change during tokamak operations
•Check validity of background subtraction
•Check validity of diagnostic modeling
The standard in-vessel calibration procedure:
1. Backlight fibers & position integrating sphere
2. Reconnect fibers; measure # of counts
absolute intensity calibration
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• Make low-power MHD-quiescent plasmas so beam ions are classical
• Compute the fast-ion distribution function with the TRANSP NUBEAM1 module.
• Predict the FIDA spectra with the FIDASIM2 synthetic diagnostic code.
• Measure spectra; subtract background; apply intensity calibration.
1Pankin, Comp. Phys. Commun. 159 (2004) 157 2Heidbrink, Comm. Comp. Phys. 10 (2011) 716
Plasma calibration procedure
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•Holospec spectrometer, Sarnoff camera, blue-side only
•Cold D line strongly filtered
•Low beam voltage to avoid instabilities
•Calculated VB > baseline
•Spectral shape in excellent agreement
•Satisfactory intensity agreement
Plasma calibration procedure: sample data from DIII-D oblique view
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•White plate and in-vessel source used to calibrate data
•Visible bremsstrahlung calculated from plasma parameters inside last-closed flux surface
•Background spectra should be > visible bremsstrahlung
•Low value of background suggests an intensity calibration error
NSTX example of erroneous intensity calibration
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•DIII-D “main-ion CER” system
•Good agreement for beam emission correct modeling of injected neutrals
•Good agreement of baseline with VB intensity calibration valid
•Discrepancy of both thermal line & FIDA underestimate of halo neutral density?
Fitting multiple features pinpoints possible sources of error
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Measurement errors
• Intensity calibration low-power beam shot, VB
• Background subtraction modulation/reference view, D correlation
Beam parameters
• Beam power, species mix, spatial profile BES
Plasma parameters
• Density, temperature, equilibrium VB
Modeling errors
• “Bugs”
• Deficiencies in model Thermal/FIDA comparison
Cross-checks identify possible sources of error
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• Low-power beam-heated plasmas provide a valuable check on FIDA measurements
• Multiple checks of background subtraction are desirable
• Measure other features such as visible bremsstrahlung, beam emission, and the thermal D line to check the measurements & modeling
Summary on calibration checks
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Backup slides
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A FIDA Measurement in ITER would give useful information
• Because the charge-exchange cross section peaks at low energies, the technique measures ions with
• The predicted signal is sensitive to anomalous losses
Heidbrink, PPCF 46 (2004) 1855.
injvv
~
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Signal smaller; Background larger
,~ i f n i iFIDA n n v
where nf Is the fast-ion density, (smaller)
nn,I are the neutral densities (injected & halo) (smaller)
< v> is the reactivity to the n=3 atomic level
2. . ~ /e eV B n T (much larger)
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FIDA Measurements in ITER are very challenging
• FIDA technique favors low density plasmas• Light from visible bremsstrahlung much brighter
than predicted FIDA light (but measurements at few % level were successful in TFTR)
• How do you determine the background?• Can imagine fitting the theoretical spectral
shape for improved sensitivity but our recent data show “anomalous processes” alter the spectral shape!
• Perhaps can still calculate a reduced chi-square & say whether the data are consistent with neoclassical transport
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Integrated modeling that fits all features
•FIDA ~ ninj nf
•Infer ninj from beam emission
arrange viewing geometry to measure both
Heidbrink, NF 52 (2012)