Fast-ion D? (FIDA) Measurements of the Fast-ion Distribution Function

1
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-dimensiona
l 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.
2
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

3
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
4
FIDA is an application of Charge Exchange
Recombination Spectroscopy

1. The fast ion exchanges an electron with an
   injected neutral
2. Neutrals in the n3 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

5
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

6
Bright interfering sources are a challenge

• D? light from injected, halo, and edge neutrals
• Visible bremsstrahlung
• Impurity lines

Luo, RSI 78 (2007) 033505
7
Background Subtraction Normally Determines the
SignalNoise
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 Da light from edge
neutrals Dinj Da light from injected neutrals
(beam emission) Dhalo Da 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 Da
(Measure attenuated cold line) Dinj Injected Da
(Try to measure)
Use Beam-off measurements to eliminate black
terms
Heidbrink, RSI 79 (2008) 10E520
9
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.
10
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
12
Two main types of FIDA instruments spectrometer
or bandpass-filtered
Measure one side but attenuate D? line
Heidbrink, RSI 79 (2008) 10E520
13
Two main types of FIDA instruments spectrometer
or bandpass-filtered
Bandpass filter one side of the spectrum
or CCD
Podestà, RSI 79 (2008) 10E521.
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FIDA imaging Put bandpass filter in front of a
camera

• Oppositely directed fast ions from counter beam
  produces blue-shifted light (accepted by filter)

• Imaging neutral beam produces red-shifted light
  (filtered out)

Van Zeeland, PPCF 51(2009) 055001.
15
Photograph of an ASDEX-U instrument
grating (2000 l/mm)
Interference filter
Princeton Instruments EMCCD camera
180mm lenses f2.8
Geiger
grating (2000 l/mm)
16
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

• 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

Heidbrink, PPCF 49 (2007) 1457
18
Different Toroidal Angles Weight Velocity Space
Differently
R0
V2
V2
In this case, get much more signal from a view
with a toroidal component of 0.6.
19
vperp, vll are the best coordinates to use
10o
45o
100o
80o
V2
V2
Salewski, NF 51 (2011) 083014
20
Ideal views give information about both vperp
and vll
R0

• Imagine a population at a single point in
  vperp, vll space
• Shift gives information about vll
• Spread gives information about vperp

V2
V2
Ideal views are shifted by 15o from 0o or 90o
Salewski, NF 51 (2011) 083014
21
The weight function concept explains many
results
Luo, RSI 78 (2007) 033505

• 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

22
Use Forward Modeling to Simulate the Signal

• 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

R0
V2
V2
FIDASIM code is available for download
Heidbrink, Comm. Comp. Phys. (2010)
23
FIDASIM models FIDA, beam-emission, thermal, and
VB features
R0
V2
We plan to maintain a public version of Geigers
Fortran90 FIDASIM
V2
Heidbrink, Comm. Comp. Phys. (2010)
24
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.
25
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

• Average over time windows of interest
• Discard time points with contaminated background
• This example ion cyclotron acceleration of beam
  ions

Heidbrink, PPCF 49 (2007) 1457.
28
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.
29
Type 2 Relative change in time evolution

• 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

Van Zeeland, PPCF 50 (2008) 035009.
30
Severe Flattening of Fast-ion Profile Measured
during Alfven Eigenmodes

• Corroborated by neutron, current profile,
  toroidal rotation, and pressure profile
  measurements
• Spectral shape hardly distorted

Heidbrink, PRL 99 (2007) 245002 NF 48 (2008)
084001.
31
TAE Avalanches in NSTX Mode overlap enhanced
fast-ion transport

• Measure local drop in fast-ion density at MHD
  event using bandpass filter
• Fluctuations at mode frequency observed in sharp
  gradient region

Magnetics
Podestà, Phys. Pl. 16 (2009) 056104.
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View same radius from different angles to
distinguish response of different orbit types
R0
V2
Vertical
Beams
Tangential
V2
Muscatello, PPCF 54 (2012) 025006
Heidbrink RSI 79 (2008) 10E520.

• 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

33
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
34
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
35
More recent microturbulence data finds negligible
transport

• No MHD or fast-ion driven modes
• Well-diagnosed plasmas
• Spectra profile consistent with classical
  predictions for several cases

Pace, PoP (2013) in preparation
36
FIDA diagnostics are implemented worldwide
37
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

38
Outline

• 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?

39
Bright interfering sources present two challenges

1. Separate FIDA feature from other features
2. Large dynamic range of signal

edge D-alpha
Beam emission
60keV
90keV
CII
HeI
FIDA
Geiger, Plasma Phys. Cont. Fusion 53 (2011) 065010
Beam emission
40
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
41
Better approach measure beam emission

• FIDA ninj nf
• Infer ninj from beam emission
• ? arrange viewing geometry to measure both

Grierson RSI (2012) 10D529
42
Background Problem Scattered Da Contaminates
Signal Changes in Time

• Normal data analysis
• Remove impurity lines
• Subtract background (from beam-off time)
• Average over pixels to obtain FIDA(t)

The problem impurity and scattered D? light
change!
(Careless) Normal Analysis says fast ions bounce
back after sawtooth crash This is wrong!
Luo, RSI 78 (2007) 033505
43
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.
44
NSTX has both active and passive views
Vertical view
Top view
NB line B
44
45
Raw data show FIDA feature

• 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

45
46
Example of successful unsuccessful background
subtraction

• 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

46
47
Background offsets are caused by scattering of
the bright central line

• 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

Amplitude
includes some beam emission
47
48
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
49
Collisions with edge neutrals produce FIDA light
DIII-D example during off-axis fishbones

• 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!

Heidbrink, PPCF 53 (2011) 085007
50
Outline

• 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?

51
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
• Backlight fibers position integrating sphere
• Reconnect fibers measure of counts
• ? absolute intensity calibration

52
Plasma calibration procedure

• 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
52
53
Plasma calibration procedure sample data from
DIII-D oblique view

• Holospec spectrometer, Sarnoff camera, blue-side
  only
• Cold D? line strongly filtered
• Low beam voltage to avoid instabilities
• Calculated VB gt baseline
• Spectral shape in excellent agreement
• Satisfactory intensity agreement

53
54
NSTX example of erroneous intensity calibration

• 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 gt visible
  bremsstrahlung
• Low value of background suggests an intensity
  calibration error

54
55
Fitting multiple features pinpoints possible
sources of error

• 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?

55
56
Cross-checks identify possible sources of error

• 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

56
57
Summary on calibration checks

• 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

57
58
Backup slides
59
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.
60
Signal smaller Background larger
where nf Is the fast-ion density, (smaller) nn,I
are the neutral densities (injected halo)
(smaller) lt?? vgt is the reactivity to the n3
atomic level
(much larger)
61
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

62
Integrated modeling that fits all features

• FIDA ninj nf
• Infer ninj from beam emission
• ? arrange viewing geometry to measure both

Heidbrink, NF 52 (2012)