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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

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)