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Title
Measurements of fast-ion acceleration at cyclotron harmonics using Balmer-alpha
spectroscopy
Permalink
https://escholarship.org/uc/item/9c48h40w
Journal
PLASMA PHYSICS AND CONTROLLED FUSION, 49(9)
ISSN
0741-3335
Authors
Heidbrink, WW
Luo, Y
Burrell, KH
et al.
Publication Date
2007
DOI
10.1088/0741-3335/49/9/008
Copyright Information
This work is made available under the terms of a Creative Commons Attribution License,
availalbe at https://creativecommons.org/licenses/by/4.0/
Peer reviewed
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IOP PUBLISHING PLASMA PHYSICS AND CONTROLLED FUSION
Plasma Phys. Control. Fusion 49 (2007) 1457–1475 doi:10.1088/0741-3335/49/9/008
Measurements of fast-ion acceleration at cyclotron
harmonics using Balmer-alpha spectroscopy
W W Heidbrink
1
, Y Luo
1
, K H Burrell
2
,RWHarvey
3
, R I Pinsker
2
and
E Ruskov
1
1
University of California, Irvine, California, USA
2
General Atomics, San Diego, California, USA
3
CompX, Del Mar, California, USA
Received 4 June 2007, in final form 26 June 2007
Published 1 August 2007
Online at
stacks.iop.org/PPCF/49/1457
Abstract
Combined neutral beam injection and fast wave heating at the fourth and fifth
cyclotron harmonics accelerate fast ions in the DIII-D tokamak. Measurements
with a nine-channel fast-ion D-alpha (FIDA) diagnostic indicate the formation
of a fast-ion tail above the injection energy. Tail formation correlates with
enhancement of the d–d neutron rate above the value that is expected in the
absence of fast-wave acceleration. FIDA spatial profiles and fast-ion pressure
profiles inferred from the equilibrium both indicate that the acceleration is near
the magnetic axis for a centrally located resonance layer. The enhancement
is largest 8–10 cm beyond the radius where the wave frequency equals the
cyclotron harmonic, probably due to a combination of Doppler-shift and orbital
effects. The fast-ion distribution function calculated by the CQL3D Fokker–
Planck code is fairly consistent with the data.
(Some figures in this article are in colour only in the electronic version)
1. Introduction
Cyclotron damping of fast waves in the ion cyclotron range of frequencies is a standard
heating scheme in magnetic fusion devices. Injected beam ions have been accelerated by ion
cyclotron heating (ICH) at cyclotron harmonics in many tokamaks [1–17]. Most measurements
of acceleration by ICH have employed neutral particle analysis [18, 19], although fusion
reaction measurements of neutrons and charged fusion products are also common [19, 20].
Differences between the perpendicular and equilibrium stored energy are used to measure the
anisotropic fast-ion energy [21]. Measurements of fast ions that escape on loss orbits can also
diagnose ion acceleration [22]. In recent years, gamma-ray tomography has emerged as a
powerful technique [23,24]. Collective Thomson scattering has also detected ions accelerated
by ICH [25].
0741-3335/07/091457+19$30.00 © 2007 IOP Publishing Ltd Printed in the UK 1457
1458 W W Heidbrink et al
Deuterium beam-ion acceleration at the 4th–8th harmonics was previously studied on the
DIII-D tokamak using established techniques [8, 10, 11, 14, 26, 27]. Recently, a new fast-ion
diagnostic technique was demonstrated at DIII-D during neutral beam injection [28]. Fast ions
that charge exchange with an injected neutral beam can emit Doppler-shifted Balmer-alpha
light. A dedicated instrument [29] that was designed to measure this fast-ion D-alpha (FIDA)
light achieved a spatial resolution of a few centimeters, an energy resolution of ∼ 10 keV, and
a temporal resolution of 1 ms [30]. For a vertical viewing geometry, the photon Doppler
shift is proportional to the vertical component of the fast-ion velocity, so measurements
with this instrument are sensitive to perpendicular acceleration. This paper contains the first
measurements of ion cyclotron acceleration using FIDA spectroscopy.
Section 2.1 describes the plasma conditions and fast-ion diagnostics, including a detailed
discussion of the portion of velocity space measured by FIDA spectroscopy. Section 2.2
contains examples of FIDA spectra and profiles. A database of fast-ion signals confirms
the validity of the FIDA measurements (section 2.3). Comparisons of the FIDA spectra and
profiles with predictions based on calculations by the CQL3D [31] Fokker–Planck code show
reasonable agreement (section 3). Section 4 states the major conclusion of the paper: FIDA
spectroscopy is a powerful technique for measurement of the energy spectrum and spatial
profile of ICH. Additional diagnostic details appear in the appendix.
2. Data
2.1. Plasma and fast-ion diagnostics
The experiments were performed in the DIII-D tokamak (major radius R
0
1.7 m, minor
radius a 0.6 m, graphite walls, deuterium plasmas) at the end of the 2005 campaign. The
conditions are nearly identical to the ones reported in [11]. Typically, one transmitter couples
0.7–1.0 MW at 60 MHz into L-mode plasmas. Counter-current drive phasing (90
◦
toroidal
phasing between straps) is employed, with the peak in the vacuum spectrum at n
5. In
some discharges, other transmitters couple up to 2 MW of power at 113–117 MHz but these
waves have little effect on the fast ions [32] and are not discussed here. At the usual toroidal field
of 1.9 T, the 60 MHz waves resonate with the deuterium cyclotron harmonic at several radial
locations, with the central resonance corresponding to the fourth harmonic (figure 1(a)). The
beams inject 75–81 keV deuterium beam ions in the direction of the plasma current at tangency
radii of 0.76 m (for the so-called ‘right’ sources) and 1.15 m (for the ‘left’ sources) (figure 1(b)).
Most plasmas are upper single null divertor discharges with an elongation of κ = 1.7. The ∇B
drift is usually downward to avoid H-mode transitions. Spectroscopic measurements of the
cold H-alpha and D-alpha lines imply that the hydrogen concentration is usually below 1%. The
dominant impurity is carbon and charge-exchange recombination [33] measurements indicate
typical central ion temperatures of T
i
= 5 keV, toroidal rotation velocities of 2 × 10
7
cm s
−1
,
and impurity concentrations of Z
eff
= 1.5.
A plastic scintillator that is cross-calibrated to an absolutely calibrated fission counter
measures the volume-averaged 2.5 MeV neutron rate [34]. Spatially resolved measurements
of the fast ions are obtained three ways. A compact electrostatic neutral particle analyser
(NPA) measures the active charge exchange signal at R = 1.95 m [35]; the analyser detects
perpendicular 50 keV neutrals from a vertical volume that is determined by the vertical extent
of the modulated neutral beam (figure 1). The second spatially resolved diagnostic relies on
motional Stark effect (MSE) [36] measurements of the internal magnetic field. The profile
of the total plasma pressure p
tot
is obtained from EFIT [37] reconstructions of the MHD
equilibrium that are consistent with the MSE data, with magnetics data, and with isotherms of
Measurements of fast-ion acceleration at cyclotron harmonics 1459
Figure 1. (a) Elevation of the DIII-D vacuum vessel, showing the separatrix and the q = 1, 2 and
3 surfaces (solid black curves), the locations where ω
RF
equals the third, fourth and fifth deuterium
cyclotron harmonic (dashed green curves), the NPA sightline (thick blue vertical line), and the
midplane locations of the FIDA Reticon (diamond) and CCD (solid triangle) chords. The hashed
region represents the approximate vertical extent of the heating beam that produces the FIDA and
NPA signals. The square indicates the approximate location of the FIDA collection optics. (b)
Plan view of the vessel, showing the toroidal location of the FIDA and NPA diagnostics and the
centerlines of the various left and right beams. The dotted line represents the magnetic axis.
the electron temperature as measured by an electron cyclotron emission (ECE) [38] diagnostic.
The thermal pressure p
th
from T
e
[38, 39], n
e
[39, 40], T
i
and carbon density measurements is
subtracted from the MHD pressure profile to obtain the fast-ion pressure profile p
f
[8,11]. The
uncertainty in p
f
is affected by both the uncertainty in the total pressure and the uncertainty
in thermal pressure. The uncertainty in p
th
is readily computed by propagating the estimated
random errors in the thermal density and temperature measurements. The uncertainty in p
tot
is more difficult to quantify because systematic errors in the EFIT equilibrium construction
exceed the errors associated with MSE, ECE, and magnetics measurement errors. For the
cases shown here, the absolute uncertainty in the fast-ion pressure is ∼ 20% (with δp
tot
and
δn
e
making the dominant contributions), while the relative uncertainty when comparing the
profiles with and without ICH is ∼ 10%.
The fourth and primary fast-ion diagnostic is FIDA. Beam modulation and fitting of
impurity lines is used to extract the fast-ion spectra from the interfering background light [30];
uncertainties in background subtraction are the dominant source of error and are represented
by error bars in the figures. In this paper, the spectra are often averaged over wavelength for
improved statistics. The wavelength bin is specified in terms of energy E
λ
along the (nearly
vertical) viewing chord. In reality, since the photon Doppler shift is only determined by one
component of the velocity, the diagnostic performs an effective average in velocity space over
this and higher energies [30,41]. Since the signals are proportional to the product of the injected
neutral density and the fast-ion density, the wavelength-integrated signals are usually divided
1460 W W Heidbrink et al
by the injected neutral density (as calculated by a pencil-beam code) to yield fast-ion ‘density’
measurements over the high-energy portion of velocity space. Two different instruments are
employed. One of these [29] measures spectra at two spatial locations with a high quantum
efficiency CCD camera. The second instrument has seven spatial channels but only measures
a portion of the spectrum (on the blue-shifted side) with slower, noisier Reticon photodiode
detectors. The spatial locations of the nine spatial channels are illustrated in figure 1.In
MHD-quiescent plasmas, the absolute magnitude of the spectra from the CCD channels is
in excellent agreement with simulations that employ the TRANSP [42] fast-ion distribution
function but the absolute profile for the Reticon detectors is inconsistent with theory [43]. In
contrast, relative changes in spatial profile are in excellent agreement with theory for both
systems [43]. Accordingly, in this paper, all spatial profiles are relative comparisons of the
profile without ICH to the profile with ICH. Unless otherwise indicated, the FIDA data in this
paper are from the dedicated system.
Balmer-alpha light can be emitted by hydrogen atoms as well as deuterium atoms.
For central fourth-harmonic heating on the deuterium beam ions, parasitic absorption by
hydrogen at the second harmonic also occurs. Although the residual hydrogen density in
these experiments is quite low (edge spectroscopy indicates that the hydrogen to deuterium
concentration is < 1%), a dilute population of hydrogen fast ions probably exists that
contributes to the FIDA signal. Empirically, there is no evidence of contamination of the
spectrum by hydrogen. Estimates based on calculations of the parasitic hydrogen absorption
[11] indicate that hydrogen fast ions may contribute 5% of the signal at E
λ
> 50 keV during
fourth harmonic heating. During fifth harmonic heating, any contribution is negligible.
The different fast-ion diagnostics weight the fast-ion distribution function differently in
velocity space (figure 2). Because of the rapid gyromotion, two velocity-space coordinates
suffice to describe the fast-ion distribution function. In this work, the fast-ion energy E and
the pitch p = v
/v are the selected coordinates. Figure 2(a) shows the fast-ion distribution
function calculated by TRANSP, F(E,p), at the location of the R = 180 cm FIDA channel
for a typical discharge in this study. (The definition of F employed by TRANSP includes the
Jacobian so that
F(E,p)dE dp yields the fast-ion density.) For injection by the more-
tangential left beams, the distribution peaks near p 0.6 in the plasma center. The NPA has
excellent energy resolution (∼ 3%) and is narrowly collimated (∼ 1
◦
), so the NPA essentially
measures a point in velocity space (figure 2(a)). It is convenient to describe the velocity-
space weighting of the various diagnostics by a weight function, W(E,p). The signal from
the diagnostic is then S =
W(E, p)F(E, p) dE dp. For the NPA, W is nearly a delta
function at E = 50 keV and p = 0. As a result, the signal (figure 2(b)) comes from the same
portion of velocity space as the peak in the weight function.
The weight function W for FIDA (figure 2(c)) depends on several factors. Through the
photon Doppler shift, a particular wavelength corresponds to a vertical energy E
λ
. Once a
value of E
λ
is specified, the minimum energy that can contribute this vertical energy consists
of a curve in velocity space [30]. For a vertical view, this curve is E = E
λ
/(1 − p
2
); this
accounts for the approximately parabolic shape of the W = 0 region in figure 2(c). Within this
region, the probability of emitting a photon with the specified wavelength is largest for ions
near the minimum-energy boundary (because they spend a greater fraction of their gyromotion
heading in the desired direction). This effect is symmetric in pitch and explains why the
weight function peaks at the minimum-energy curve. The final effect is associated with the
probability of a charge-exchange reaction. Reactions are more probable for fast ions that have
a component of velocity in the direction of the injected neutral beam; the weight function is
skewed toward positive values of pitch by this effect. Weight functions for other values of E
λ
are qualitatively similar (not shown). As figure 2(d) shows, for a typical distribution function,
![Figure 9. Signal enhancement during ICH for the neutron ( ), FIDA (♦), and NPA (x) diagnostics versus the normalized gyroradius of the injected beam ions for all of the fourth harmonic discharges with quiet MHD and > 0.5 MW of 60 MHz ICH in the database. The abscissa employs the approximation k⊥ ωRF/vA, with the Alfvén speed evaluated using the line averaged electron density and nominal toroidal field. The solid curve is taken from [11]. The FIDA data are from the R = 180 cm channel and are averaged over Eλ = 55–80 keV. The NPA points are the mean and standard deviation of several discharges with the analyser set to measure neutrals of 50 keV.](/figures/figure-9-signal-enhancement-during-ich-for-the-neutron-fida-197itp6c.webp)