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Title
Fast-ion Dα measurements of the fast-ion distribution (invited).
Permalink
https://escholarship.org/uc/item/57n6445n
Journal
The Review of scientific instruments, 81(10)
ISSN
0034-6748
Author
Heidbrink, WW
Publication Date
2010-10-01
DOI
10.1063/1.3478739
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Fast-ion D
␣
measurements of the fast-ion distribution „invited…
a…
W. W. Heidbrink
b兲
University of California, Irvine, California 92697, USA
共Presented 18 May 2010; received 13 May 2010; accepted 23 June 2010;
published online 25 October 2010兲
The fast-ion D
␣
共FIDA兲 diagnostic is an application of charge-exchange recombination
spectroscopy. Fast ions that neutralize in an injected neutral beam emit Balmer-
␣
light with a large
Doppler shift. The spectral shift is exploited to distinguish the FIDA emission from other bright
sources of D
␣
light. Background subtraction is the main technical challenge. A spectroscopic
diagnostic typically achieves temporal, energy, and transverse spatial resolution of ⬃1 ms,
⬃10 keV, and ⬃2 cm, respectively. Installations that use narrow-band filters achieve high spatial
and temporal resolution at the expense of spectral information. For high temporal resolution, the
bandpass-filtered light goes directly to a photomultiplier, allowing detection of ⬃50 kHz
oscillations in FIDA signal. For two-dimensional spatial profiles, the bandpass-filtered light goes to
a charge-coupled device camera; detailed images of fast-ion redistribution at instabilities are
obtained. Qualitative and quantitative models relate the measured FIDA signals to the fast-ion
distribution function. The first quantitative comparisons between theory and experiment found
excellent agreement in beam-heated magnetohydrodynamics 共MHD兲-quiescent plasmas. FIDA
diagnostics are now in operation at magnetic-fusion facilities worldwide. They are used to study
fast-ion acceleration by ion cyclotron heating, to detect fast-ion transport by MHD modes and
microturbulence, and to study fast-ion driven instabilities. © 2010 American Institute of
Physics. 关doi:10.1063/1.3478739兴
I. INTRODUCTION
Hydrogenic superthermal energetic ions are present in
most magnetic fusion experiments. These fast ions are in-
jected by neutral beams or accelerated by wave heating.
Many aspects of plasma behavior cannot be understood with-
out knowledge of the fast-ion distribution function.
In recent years, a new technique has emerged as a pow-
erful diagnostic of the fast-ion distribution function. This
technique, known as fast-ion D
␣
共FIDA兲, exploits visible
light emitted by energetic deuterium ions as they pass
through a neutral beam. Similar measurements of energetic
helium ions were made in the 1990s.
1,2
The first FIDA mea-
surements were made on the DIII-D tokamak and published
in 2004.
3
In 2007, FIDA diagnostics were installed on the
National Spherical Torus Experiment 共NSTX兲.
4
By now,
FIDA diagnostics are installed or are under development at
six magnetic fusion facilities. The purpose of this paper is to
summarize FIDA research in its initial stage of development.
Section II discusses the measurement itself: the underly-
ing atomic processes, the challenge of distinguishing the
FIDA light from other bright sources in the spectral range of
interest, and the instrumentation employed to date. Section
III considers the relationship between the measured light and
the desired quantity, the fast-ion distribution function. The
final section 共Sec. IV兲 summarizes past, present, and future
applications of the diagnostic.
II. THE FIDA MEASUREMENT
A FIDA measurement is an application of charge-
exchange recombination spectroscopy.
5
The basic process is
illustrated in Fig. 1共a兲. A deuterium ion orbits through a neu-
tral beam and a charge exchange event occurs, neutralizing
the fast ion. Since it is uncharged, the neutralized fast ion
travels in a straight line. Often the fast neutral is in an ex-
cited atomic state. As it travels, it may change its energy
level either through collisions with the plasma or through
radiative decay. If it undergoes a Balmer-
␣
transition, which
is a transition from the n=3 to the n =2 level, it emits a
visible D
␣
photon.
Figures 1共b兲–1共d兲 describe the process in more detail.
The probability of the initial neutralization event depends
strongly on the relative velocity between the fast ion and the
injected neutral. In reality, four neutral populations are im-
portant. The injected neutral beam has a full-energy, half-
energy, and third-energy component. In addition, charge-
exchange events with the bulk thermal deuterium population
create a cloud of “halo” neutrals in the vicinity of the in-
jected beam. The density of this halo neutral population is
comparable to the injected neutral densities. These four neu-
tral populations each have their own distributions of excited
states. Although the occupation of the ground state far ex-
ceeds the occupation levels for excited states, the probability
that the fast ion will arrive in the n= 3 state after a charge-
a兲
Invited paper, published as part of the Proceedings of the 18th Topical
Conference on High-Temperature Plasma Diagnostics, Wildwood, New
Jersey, May 2010.
b兲
Electronic mail: bill.heidbrink@uci.edu.
REVIEW OF SCIENTIFIC INSTRUMENTS 81, 10D727 共2010兲
0034-6748/2010/81共10兲/10D727/8/$30.00 © 2010 American Institute of Physics81, 10D727-1
exchange reaction with a ground-state neutral is very low;
see the reactivity
v
for a n =1→ 3 reaction in Fig. 1共b兲.In
contrast, the occupation levels for excited states in the in-
jected beam are below 1% but the reactivities for n =2→ 3
and n =3→ 3 reactions are orders of magnitude larger than
for ground-state donors. The result is that reactions from the
n= 1, 2, and 3 levels all make comparable contributions to
the number of neutralized fast ions in the n = 3 state. Conse-
quently, the initial population of neutralized fast ions is far
from equilibrium. Figure 1共c兲 shows a typical example of the
subsequent relaxation of the neutral population toward equi-
librium values. These curves are calculated by solving the
collisional-radiative equations that describe transitions be-
tween atomic energy levels. The fast neutral only travels a
few centimeters before the n =3 population has decayed.
Some 共 ⬍44%兲 of the n = 3 neutrals emit a Balmer-
␣
photon.
The spectrum of these photons depends on both the Doppler
shift and on Stark splitting; Fig. 1共d兲 shows three examples
of the relative importance of these two factors. The unshifted
D
␣
line is at 656.1 nm. The Doppler shift provides informa-
tion on one component of the initial fast-ion velocity and
shifts the line 2–6 nm. The Stark splitting is caused primarily
by the motional Stark effect and so depends on the velocity
v
ជ
of the neutral relative to the magnetic field B
ជ
. The ⱗ1nm
共for B⬵2T兲 Stark splitting effectively acts as a line-
broadening mechanism that degrades the spectral resolution
of the measurement.
Figure 2 shows a quantitative example of these atomic
physics considerations for a typical DIII-D case. Distribu-
tions of initial occupation levels are plotted in Fig. 2共a兲. Be-
cause of the strong cross-section effect 关Fig. 2共b兲兴, the initial
occupation levels of the n =2–4 states exceed 1%. These
levels are an order of magnitude higher than the equilibrium
levels in this region of the plasma, which are of order 0.1%.
As a result, rapid adjustment of the energy levels occurs, as
illustrated for one case in Fig. 1共c兲. Figure 2共b兲 shows the
average distance traveled before a photon is emitted for the
ensemble of initial states shown in Fig. 2共a兲. Within 2 cm of
the neutralization event, nearly 100% of the D
␣
photons
have been emitted. This is consistent with a rough estimate:
A typical fast-ion velocity is 2 ⫻ 10
8
cm/ s and the combined
3→ 1 and 3 → 2 radiative decay rate is 10
8
/ s , with collisions
increasing the decay rate still further. The rapid decay from
highly excited levels has the important implication that the
intrinsic spatial resolution of the FIDA technique is ⬍2 cm.
共Reference 3 and subsequent publications erroneously state
that the intrinsic resolution is ⬃5 cm.兲 In conventional
charge-exchange recombination spectroscopy with impurity
ions, a “plume” effect can degrade the spatial resolution of
the measurement
7
but, for FIDA, because the excited atom is
neutral, the subsequent trajectory is unaffected by the mag-
netic field. Although the transverse spatial resolution can be
Fast
Ion
Photon
Charge
Exchange
Radiates
Fast neutral
v
f,ll
Injected
Neutral
Plasma Collision
+
WAVELENGTH
(
nm
)
RELATIVE INTENSITY
70 keV
2.0 T
1
0.1
0.01
0.001
0
10 20 30
FRACTIONAL OCCUPATION
TIME STEP
n=1
n=2
n=3
n=4
(a)
(c)
3cm
unshifted line
(d)
n=1 -> 3 (x 10)
n=3 -> 3
n=2 -> 3
n=1 -> 1
(b)
10
-6
σ v (cm3/s)
10
-7
10
-8
20 40 60 80 100
DEUTERIUM RELATIVE ENERGY (keV)
FIG. 1. 共Color online兲共a兲 The FIDA process. A fast ion
traverses a neutral beam and is neutralized in a charge
exchange reaction. The atomic energy levels change
while the neutral propagates. Some neutrals radiate a
D
␣
photon that is Doppler shifted by the velocity com-
ponent in the direction of emission. 共b兲 Charge ex-
change reactivities for transitions from various energy
levels to the n =3 level. The abscissa is the relative
energy between the ion and neutral computed from the
relative velocity. Note that transitions from the ground
state are ten times less probable than shown. 共c兲 Time
evolution of level occupations obtained from solution
of the collisional-radiative transition equations for
80 keV neutrals in a DIII-D discharge. The neutral only
travels a few centimeters before the n = 3 occupation
level decays to a negligible level. 共d兲 Sample of spectra
from 70 keV neutrals for various velocity vectors rela-
tive to the photon and magnetic-field directions. The
shift from 656.1 nm 共dashed line兲 is due to the Doppler
shift; the line splitting is caused by the motional Stark
effect.
1 2 3 4
0.1
1.0
10
100
Atomic Energy Level
Fractional Occupation
(
%
)
Equilibrium
0.0 0.5 1.0 1.5 2.0 2.5
0.0
0.2
0.4
0.6
0.8
1.0
Distance
(
cm
)
Light Fraction
(b)
(a)
FIG. 2. 共Color online兲共a兲 Distribution of initial energy levels 共 x兲 for an
ensemble of reactions in DIII-D discharge No. 132607 共Ref. 6兲. The dia-
mond symbols represent the equilibrium distribution of states at the same
location in the plasma. 共b兲 Distance traveled by the atom before radiating a
D
␣
photon for the distribution shown in 共a兲. 共The calculation includes the
charge-exchange reaction probabilities for the various initial conditions.兲
Nearly all of the light is emitted within a distance of 2 cm.
10D727-2 W. W. Heidbrink Rev. Sci. Instrum. 81, 10D727 共2010兲
small, the resolution along the line of sight is determined by
the extent of the neutral beam and its halo. For example, for
a vertical view on DIII-D, the vertical full width at half
maximum is ⬃30 cm.
The principal challenge in a FIDA measurement is dis-
tinguishing the FIDA signal from other bright sources of
light in the same spectral region. The intensity of the beam
emission spectrum 共BES兲 radiated by the injected neutrals is
typically two orders of magnitude larger than the FIDA sig-
nal 共Fig. 3兲.D
␣
light from halo neutrals is comparable to the
injected neutral light. To make a successful measurement, the
viewing geometry must be selected to Doppler shift the
FIDA feature away from the BES feature and away from the
unshifted D
␣
line. The original FIDA measurements utilized
a vertical view
3
but, in recent years, tangential geometries
have been successfully employed 共for example, Refs. 6 and
8兲. Other contaminants in the spectrum include impurity
lines, visible bremsstrahlung, and the very bright emission
from atomic deuterium at the edge of the device. Impurity
lines are usually removed by fitting. Visible bremsstrahlung
is removed by background subtraction 共below兲 or by moni-
toring a spectral region beyond the largest expected Doppler
shift. 共Visible bremsstrahlung is a nearly flat spectral feature
in this wavelength band.兲 The cold D
␣
line is centered on the
rest wavelength of 656.1 nm.
Approaches to removing these “backgrounds” from the
spectrum are discussed in some detail in Ref. 9. Some instal-
lations use beam modulation to measure the background,
some use a toroidally displaced reference view that misses
the injected beam, and some attempt to fit the entire spec-
trum. Beam modulation assumes temporal stationarity of the
plasma, while a displaced reference view assumes toroidal
symmetry. Neither assumption is perfectly valid. Reference
views are available at NSTX 共Ref. 4兲 and, more recently, at
DIII-D.
10
A comparison between the two approaches for a
condition with relatively low FIDA signal is shown in Fig. 4.
The derived spectra are similar but not identical. In the best
of circumstances, the systematic uncertainty associated with
background subtraction is of O 共10%兲.
The cold D
␣
line is narrow but very bright. As in a laser
scattering measurement, care is required to minimize scat-
tered light in the spectral regions of interest. Temporal varia-
tions in background that correlate with fluctuations in the
cold D
␣
intensity have been reported.
11
One expedient is to
measure the intensity of the cold D
␣
feature together with
the desired spectrum. Because the cold feature is several or-
ders of magnitude brighter than the FIDA signal, it is usually
necessary to filter the cold D
␣
line to avoid detector
saturation.
4,9
In a DIII-D experiment, Doppler-shifted light from a dis-
tant neutral beam reflected off a metallic surface and con-
taminated the measurements 共Fig. 17 of Ref. 6兲. In general,
the line-of-sight for a FIDA measurement should terminate
in a blackened surface.
On ASDEX-U, the spectra have fewer contaminating im-
purity lines when the tokamak gas valve is distant toroidally
from the FIDA line-of-sight
12
but this effect is not observed
on DIII-D.
In general, three sources of error can contribute to the
uncertainty of a measurement: photon statistics, readout and
dark current noise, and uncertainty in the background sub-
traction. In most cases, uncertainty in the background sub-
traction dominates the overall uncertainty.
11
The challenges
are exacerbated by instabilities. A primary purpose of a
FIDA diagnostic is to study the impact of instabilities on
fast-ion confinement but, unfortunately, instabilities expel
particles and heat into the plasma edge, which alters the
backgrounds. Figure 11 of Ref. 11 shows an example where
simplistic application of a background-subtraction algorithm
implies unphysical evolution of the fast-ion density but rea-
sonable corrections for the time-evolving background yield a
sensible result.
Figure 5 illustrates various ways to measure the FIDA
light. To establish feasibility, nearly every facility begins by
tuning an existing charge-exchange recombination instru-
ment to one side of the cold D
␣
line.
3,8,13–15
The first dedi-
cated FIDA instrument
11
measured the spectrum on both
Radiance (ph/cm
2
/s/nm)
Beam
Emission
Thermal
(Halo)
Wavelen
g
th (nm)
Cold D
α
10
12
10
13
10
14
10
15
650 652 654 656 658 660 662
FIDA
Visible
Bremsstrahlung
FIG. 3. 共Color online兲 Various sources of light in the D
␣
spectral band for
a typical case. The spectral intensity of D
␣
light from edge neutrals is
largest. Radiation from injected neutrals and from halo neutrals is an order
of magnitude larger than the FIDA and visible bremsstrahlung spectral
features.
651 652 653
0
1.0
2.0
Wavelength (nm)
Radiance (10
12
ph/s/cm
2
/nm)
Active, Beam On
Active, Beam Off
Passive, Beam On
Passive, Beam On
Beam On - Beam Off
Active - Passive
132668
FIG. 4. 共Color online兲 Comparison of different methods of background
subtraction for a NSTX discharge with average beam power of only
0.5 MW. The blueshifted side of the spectrum is shown. The two spectra
labeled “active, beam on” and “active, beam off” are from a fiber that views
the injected neutral beam; the difference of these signals is the FIDA spec-
trum obtained from beam modulation and is labeled “beam on-beam off.”
The dashed line labeled “passive, beam on” is from a toroidally separated
view acquired when the injected beam is on. 共A slight difference in passive
signal is observed during beam modulation.兲 The dashed FIDA spectrum
labeled “active-passive” is obtained using this signal to subtract the back-
ground. Passive impurity lines at 650.0 and 651.5 nm are evident in the raw
spectra but disappear upon background subtraction.
10D727-3 W. W. Heidbrink Rev. Sci. Instrum. 81, 10D727 共2010兲
sides of the rest wavelength. To avoid saturation of the de-
tector by the cold D
␣
line, after the light was dispersed by
the spectrometer, a solid bar blocked light at 656.1 nm. Sub-
sequently, the bar was replaced by a strip of neutral-density
filter 共optical density OD2 or OD3兲 in order to monitor the
intensity of the cold line. The NSTX diagnostic uses this
approach and employs a high throughput transmission grat-
ing spectrometer.
4
If only one side of the line is used, it is
convenient to place a bandpass filter at the entrance of the
spectrometer and arrange the transmission so the cold line is
severely attenuated but still measurable.
9
An alternative ap-
proach is to sacrifice spectral resolution for improved tem-
poral or spatial resolution 关Fig. 5共b兲兴. In this approach, the
spectrometer is replaced by a filter with a passband of
2–4 nm. For maximal temporal resolution, a photomultiplier
replaces the charge-coupled device 共CCD兲 camera, as in the
NSTX 共Ref. 4兲 and DIII-D 共Ref. 10兲 “f-FIDA” diagnostics.
For improved spatial resolution, light from an imaging fiber-
optic bundle passes through a bandpass filter and a two-
dimensional image is acquired by a CCD camera.
6
III. RELATIONSHIP TO THE FAST-ION
DISTRIBUTION FUNCTION
The goal of a FIDA measurement is to provide informa-
tion about the fast-ion distribution function F. In general, the
distribution function has a complicated dependence on both
velocity-space and configuration-space coordinates. In an
axisymmetric tokamak, the distribution function can be ex-
pressed as a function of three “constants of motion” but these
convenient theoretical coordinates do not correspond to use-
ful laboratory coordinates. A common set of coordinates used
by experimentalists is the 共E , p , R, z兲 coordinates used in the
TRANSP NUBEAM code,
16
where E is the fast-ion energy,
p=
v
储
/
v
is the pitch of the fast-ion velocity vector relative to
the magnetic field, R is the major radius, and z is vertical
position. The challenge addressed in this section is to relate
the FIDA spectral intensity versus wavelength to the fast-ion
distribution function F共E , p , R, z兲.
Through the Doppler shift, the FIDA spectrum depends
on one component of the fast-ion velocity. In that sense, a
FIDA measurement is similar to fast-ion measurements with
collective Thomson scattering 共CTS兲, which also depends on
one component of the velocity vector. Specialists in CTS
have published several papers addressing the relationship be-
tween a one-dimensional spectrum and the full distribution
function. Egedal and Bindslev
17
rigorously tackle the ques-
tion: Can you invert a set of CTS measurements to infer the
distribution function? They conclude that a unique inversion
is impossible but, with multiple CTS viewing angles, plau-
sible reconstructions exist. As the atomic physics of the
FIDA process is more complex than the collective scattering
process, their conclusion that a unique inversion is impos-
sible certainly applies to FIDA.
A convenient way to understand the relationship be-
tween any fast-ion diagnostic and F is to construct a weight
function W共E , p, R , z兲. The measured signal S is the convo-
lution of the weight function with the distribution function
S =
冕冕冕冕
共W ⴱ F兲dE dp dR dz . 共1兲
Approximate expressions for several common diagnostics
are given in Appendix A of Ref. 18. Figure 6共c兲 shows an
example of the velocity-space dependence of the weight
function W for a representative vertically viewing FIDA di-
agnostic. Two factors determine this dependence. The first of
these is the geometrical relationship between one velocity
component and the variables E and p. Formulas that describe
Wavelen
g
th (nm)
650 652 654 656 658 660 662
Bandpass
Filter
Bar
ND
Filter
PMT
/
CCD
Fiber
Fiber
Lens
Filter
F
ilter
Spectrometer
Lens
Lens
CCD
Camera
(c)
(
a
)(
b
)
FIG. 5. 共Color online兲 Schematic illustrations of 共a兲 the spectroscopic ap-
proach to a FIDA measurement, 共b兲 the bandpass-filtered approach, and 共c兲
the resulting effect on the spectrum. In a spectroscopic measurement, light
that is dispersed by a spectrometer is measured with a CCD camera. If the
full spectrum is measured, a neutral density filter 关solid central curve in 共c兲兴
or blocking bar 关dashed curve in 共c兲兴 placed in the focal plane between the
spectrometer and camera attenuates the intensity of the cold D
␣
line. If only
one side of the spectrum is measured, a filter at the entrance to the spec-
trometer attenuates the cold D
␣
line. In a f-FIDA or two-dimensional im-
aging application, a bandpass filter selects the desired spectral band 关left
curve in 共c兲兴 before detection by a photomultiplier or CCD camera.
30 40 50 60 70 80
Energy (keV)
(a) Geometry
(b) CX probability
(c) Weight
P
i
tchP
i
tchP
i
tch
-1
0
1
-1
0
1
-1
0
1
FIG. 6. 共Color online兲 FIDA weight function W vs energy and pitch for a
nearly vertical view in DIII-D. The contours are on a linear scale for a
blueshifted wavelength corresponding to E
=40 keV. 共a兲 Contribution to
the weight function associated with measuring a single component of the
velocity. 共b兲 Contribution to the weight function associated with variations
in neutralization probability. 共c兲 Total weight function W.
10D727-4 W. W. Heidbrink Rev. Sci. Instrum. 81, 10D727 共2010兲