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
Van Zeeland, PPCF 51(2009) 055001.
Benedijt Geiger
Additional collaborators
Deyong Liu, Emil Ruskov, Yubao Zhu, Clive
Michael, David Pace, Mirko Salewski and1
many others
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
2
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
3
FIDA is an application of Charge
Exchange Recombination Spectroscopy
1. 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
4
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
5
Bright interfering sources are a challenge
•D light from injected,
halo, and edge neutrals
•Visible bremsstrahlung
•Impurity lines
Luo, RSI 78 (2007) 033505
6
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
7
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)
Use “Beam-off” measurements to eliminate black terms
Heidbrink, RSI 79 (2008) 10E520
8
Must extract the FIDA signal from the
background
1. Used beam modulation
for background
subtraction
NSTX
2. Can use a toroidally
displaced view that
misses the beam
3. Fit the entire spectrum
(all sources)
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.
9
Two main types of FIDA instruments:
spectrometer or bandpass-filtered
Tune to one side
of the D line
10
Two main types of FIDA instruments:
spectrometer or bandpass-filtered
Measure full
spectrum but block
(attenuate) D line
Luo, RSI 78 (2007) 033505
11
Two main types of FIDA instruments:
spectrometer or bandpass-filtered
Measure one side
but attenuate
D line
Heidbrink, RSI 79 (2008) 10E520
12
Two main types of FIDA instruments:
spectrometer or bandpass-filtered
Bandpass filter
one side of the
spectrum
or CCD
Podestà, RSI 79 (2008) 10E521.
13
FIDA imaging: Put bandpass filter in front of a
camera
•Oppositely directed
fast ions from counter
beam produces blueshifted light (accepted
by filter)
Van Zeeland, PPCF 51(2009) 055001.
•“Imaging” neutral
beam produces redshifted light (filtered
out)
14
Photograph of an ASDEX-U instrument
grating (2000 l/mm)
Geiger
Interference filter
Princeton Instruments
EMCCD camera
180mm lenses f2.8
15
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?
16
The “weight function” describes the portion of
phase space measured by a diagnostic
Signal   (W  F ) dE dPitch
•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 17
Different Toroidal Angles Weight
Velocity Space Differently
V2
R0
V2
In this case, get much more signal from a view
18
with a toroidal component of 0.6.
|vperp|, vll are the best coordinates to use
10o
V2
45o
80o
100
o
V2
Salewski, NF 51 (2011) 083014
19
Ideal views give information about both
|vperp| and vll
V2
R0
•Imagine a
population at a
single point in
|vperp|, vll space
•Shift gives
information about
V2
vll
•Spread gives
information about
vperp
Salewski, NF 51 (2011) 083014
Ideal views are shifted
by ~15o from 0o or 90o
20
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
21
Use Forward Modeling to Simulate the Signal
•Forward modeling using a theory-based distribution
V2 ….
function from TRANSP,
R0
•Machine-specific subroutines for beam & detector
geometry
•Data input: files with plasma parameters mapped onto flux
coordinates
•Compute neutral densities of injected beam & halo
V2
•Weighted Monte Carlo computes neutralization
probability, collisional-radiative transitions, and spectra
FIDASIM code is available for download
Heidbrink, Comm. Comp. Phys. (2010)
22
FIDASIM models FIDA, beam-emission, thermal,
and VB features
R0
V2
We plan to maintain a public
version of Geiger’s Fortran90
FIDASIM
V2
Heidbrink, Comm. Comp. Phys. (2010)
23
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.
24
FIDA image agrees with theory
•One normalization in this
comparison
Van Zeeland, PPCF 51(2009) 055001.
25
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?
26
Type 1: Relative change in spectra
•Average over
time windows of
interest
Heidbrink, PPCF 49 (2007) 1457.
•Discard time
points with
contaminated
background
•This example: ion
cyclotron
acceleration of
beam ions
27
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.
28
Type 2: Relative change in time evolution
•Integrate over range
of wavelengths
•Divide integrated
signal by neutral
density 
“FIDA density”
Van Zeeland, PPCF 50 (2008) 035009.
•This example: Alfvén
eigenmode activity is
altered by Electron
Cyclotron Heating
(ECH); weaker modes
 better confinement
29
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.
30
TAE “Avalanches” in NSTX: Mode overlap &
enhanced fast-ion transport
Magnetics
•Measure local drop in fast-ion
density at MHD event using
bandpass filter
sh#128455
120
100
•Fluctuations at mode frequency
observed in sharp gradient region
f [kHz]
80
60
40
20
0
200
2
220
240
260
280
NB power
neutrons
0
200
220
240
260
t [ms]
280
300
Podestà, Phys. Pl. 16 (2009) 056104.
31
View same radius from different angles to
distinguish response of different orbit types
Vertical
R0
V2
Beams
Tangential
Muscatello, PPCF 54 (2012) 025006 V2
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
32
Type 3: Absolute Comparison with Theory
•Integrate over time
window of interest
•Use calibration to get
absolute radiance
•For profile, also
integrate over
wavelengths
Heidbrink PRL 103 (2009) 175001;
PPCF 51 (2009) 125001
•Compute theoretical
spectra and profile
•This example: driftwave turbulence in high
temperature plasma
causes large fast-ion 33
transport
Microturbulence causes fast-ion transport when
E/T (energy/temperature) is small
•Small MHD or fastion driven modes
•Co-tangential offaxis 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
34
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
35
FIDA diagnostics are implemented worldwide
LHD
TEXTOR
Delabie RSI 79 (2008) 10E522.
MAST
Osakabe, RSI 79 (2008) 10E519.
ASDEX-U
Beam
emission
FIDA
emission
Geiger (2010) private communication.
Michael (2010) private communication.
36
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
37
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?
38
Bright interfering sources present two
challenges
1) Separate FIDA
feature from
other features
edge D-alpha
Beam emission
2) Large dynamic
range of signal
60keV
90keV
CII
HeI
FIDA
Geiger, Plasma Phys. Cont.
Fusion 53 (2011) 065010
39
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
40
Better approach: measure beam emission
•FIDA ~ ninj nf
•Infer ninj from
beam emission
 arrange viewing
geometry to
measure both
Grierson RSI (2012) 10D529
41
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)
The problem: impurity and
(Careless)DNormal
Analysis
scattered
light
change!

says fast ions “bounce
back” after sawtooth crash
This is wrong!
Luo, RSI 78 (2007) 033505
42
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
D3D main ion4
Czerny-Turner
1Podestà,
2Luo,
Sarnoff
Sarnoff
blue-side w/ filter
mild saturation
RSI 79 (2008) 10E521.
RSI 78 (2007) 033505.
3Muscatello,
4Grierson,
RSI 81 (2010) 10D316.
Phys. Pl. 19 (2012) 056107.
43
NSTX has both active and passive views
Top view
Vertical view
NB line: B
44
44
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
45
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
46
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
47
Cold D line causes problems
•Avoid views with large
recycling
•Ideal detector solution:
narrow notch filter that
attenuates cold line
NSTX solution sees
scattered light
•Holospec transmission
grating spectrometer has
high throughput but more
scattered light
•Want to measure full
spectrum
•No filter (Grierson) causes
48
detector saturation
Collisions with edge neutrals produce FIDA light
•Existing FIDA diagnostics
use active emission from
an injected neutral beam
DIII-D example during off-axis fishbones
•Passive emission is
observed when fast ions
pass through the highneutral density region at
the plasma edge*
•For strong instabilities,
the passive FIDA light is
stronger than beam
emission!
*Heidbrink, PPCF 53 (2011) 085007
49
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?
50
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
51
Plasma calibration procedure
• Make low-power MHD-quiescent
beam ions are classical
plasmas
so
• Compute the fast-ion distribution function with the
TRANSP NUBEAM1 module.
• Predict the FIDA spectra
synthetic diagnostic code.
with
the
FIDASIM2
• Measure spectra; subtract background; apply
intensity calibration.
1Pankin,
Comp. Phys. Commun. 159 (2004) 157
2Heidbrink,
Comm. Comp. Phys. 10 (2011) 716
52
52
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 > baseline
•Spectral shape in excellent agreement
•Satisfactory intensity agreement
53
53
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 > visible bremsstrahlung
•Low value of background
suggests an intensity
calibration error
54
54
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
55
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
56
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
57
Backup slides
58
A FIDA Measurement in ITER would give useful
information
• Because the chargeexchange cross section
peaks at low energies, the
technique
 measures ions
with v ~ vinj
• The predicted signal is
sensitive to anomalous
losses
Heidbrink, PPCF 46 (2004) 1855.
59
Signal smaller; Background larger
FIDA ~ i n f nn ,i   v i
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
V .B. ~ n / Te
(much larger)
60
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
61
Integrated modeling that fits all features
•FIDA ~ ninj nf
•Infer ninj from
beam emission
 arrange viewing
geometry to
measure both
Heidbrink, NF 52 (2012)
62