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Title
Hydrogenic fast-ion diagnostic using Balmer-alpha light
Permalink
https://escholarship.org/uc/item/0nn915t5
Journal
Plasma Physics and Controlled Fusion, 46(12 A)
ISSN
0741-3335
Authors
Heidbrink, WW
Burrell, KH
Luo, Y
et al.
Publication Date
2004-12-01
DOI
10.1088/0741-3335/46/12/005
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/
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INSTITUTE OF PHYSICS PUBLISHING PLASMA PHYSICS AND CONTROLLED FUSION
Plasma Phys. Control. Fusion 46 (2004) 1855–1875 PII: S0741-3335(04)82842-2
Hydrogenic fast-ion diagnostic using Balmer-alpha
light
W W Heidbrink
1
, K H Burrell
2
, Y Luo
1
,NAPablant
3
and E Ruskov
1
1
University of California, Irvine, CA, USA
2
General Atomics, San Diego, CA, USA
3
University of California, San Diego, CA, USA
Received 30 June 2004, in final form 15 October 2004
Published 16 November 2004
Online at
stacks.iop.org/PPCF/46/1855
doi:10.1088/0741-3335/46/12/005
Abstract
Hydrogenic fast-ion populations are common in toroidal magnetic fusion
devices, especially in devices with neutral beam injection. As the fast ions orbit
around the device and pass through a neutral beam, some fast ions neutralize and
emit Balmer-alpha light. The intensity of this emission is weak compared with
the signals from the injected neutrals, the warm (halo) neutrals and the cold edge
neutrals, but, for a favourable viewing geometry, the emission is Doppler shifted
away from these bright interfering signals. Signals from fast ions are detected in
the DIII-D tokamak. When the electron density exceeds ∼7×10
19
m
−3
, visible
bremsstrahlung obscures the fast-ion signal. The intrinsic spatial resolution of
the diagnostic is ∼5 cm for 40 keV amu
−1
fast ions. The technique is well
suited for diagnosis of fast-ion populations in devices with fast-ion energies
(∼30 keV amu
−1
), minor radii (∼0.6 m) and plasma densities (10
20
m
−3
) that
are similar to those of DIII-D.
(Some figures in this article are in colour only in the electronic version)
1. Introduction
One of the most common forms of plasma heating in magnetic fusion devices is injection of
hydrogenic neutral beams. The injected neutrals ionize in the plasma, then execute orbits in
the confining magnetic field. As these ions gradually thermalize, they form a population of
energetic ions in the plasma that is described by a distribution function f
f
(v, r). Hydrogenic
fast-ion populations are also produced by ion cyclotron heating and by fusion reactions.
A number of existing techniques [1] provide information about the fast-ion distribution
function. Some fast ions undergo nuclear reactions: analysis of escaping neutrons, charged
fusion products and gamma rays is one standard approach. Other fast ions neutralize in a
charge-exchange reaction: analysis of the escaping neutrals is another standard technique.
Inferences based on measurements of the pressure profile and of the stored energy are also
0741-3335/04/121855+21$30.00 © 2004 IOP Publishing Ltd Printed in the UK 1855
1856 W W Heidbrink et al
widely employed. Collective scattering of microwaves off the fast-ion feature can also provide
useful information [2].
Diagnosis of the fast-ion population is important because the fast ions are often a
major source of energy, momentum and particles for the plasma. Moreover, the fast-ion
pressure and driven current can have a significant impact on macroscopic stability properties.
Although dilute populations of fast ions often behave classically, intense populations can drive
instabilities that redistribute or expel the fast ions from the plasma [3]. This is often the case in
experiments in the DIII-D tokamak, where anomalous fast-ion diffusion rates of approximately
0.3 m
2
s
−1
are commonly inferred during neutral beam injection [4]. In DIII-D, it is difficult
or expensive to detect diffusion at this level using the standard techniques [5].
Excited states of atomic hydrogen radiate the Lyman and Balmer series of spectral lines.
The most familiar of these are the Lyman-alpha line, which is a transition from the n = 2
to n = 1 energy level, and the Balmer-alpha line, which is the 3 → 2 transition. Because
Lyman alpha is in the ultraviolet, it is relatively difficult to measure, but the Balmer-alpha
transition emits a visible photon, which is easily measured using standard lenses, spectrometers
and cameras. Indeed, Balmer-alpha light from the plasma edge is measured on virtually all
magnetic fusion devices as a monitor of plasma recycling and transport and to determine the
relative abundances of different hydrogenic species [6]. The spatial profile of Balmer-alpha
light from injected neutrals is used to measure the deposition of the neutral beams in the
plasma [7, 8]; the spectrum is used to detect magnetic [9] and electric fields [10, 11] through
Stark splitting, and fluctuations in the emission are related to fluctuations in the electron
density [12]. Balmer-alpha light from the thermal ions that charge exchange with an injected
beam provides information on the local ion temperature [13,14] and deuterium density [8,15].
In both astronomy and plasma physics Balmer-alpha radiation is also known as H
α
light or, in
the case of deuterium atoms, D
α
.
Conceptually, the use of D
α
light to diagnose a fast deuterium population is similar
to the diagnosis of fast helium populations using charge exchange recombination (CER)
spectroscopy [16]. Fast helium populations during
3
He neutral beam injection were measured
on JET [17, 18]. Alpha particles produced in deuterium–tritium reactions were measured on
the Tokamak Fusion Test Reactor (TFTR) [19, 20].
For spectroscopic measurements of either fast helium ions or fast hydrogenic ions, avoiding
the bright emission from other sources is a major challenge. There are several populations
of hydrogenic neutrals in a typical tokamak plasma [21] (figure 1). At the plasma edge and
pedestal region, there are enormous populations of relatively cold neutrals from the walls and
divertor that are excited in the plasma periphery. These edge neutrals radiate brightly near the
unshifted wavelength of the Balmer-alpha transition (at 656.1 nm for D
α
). The penetration
distance of edge neutrals into the bulk plasma is approximately the geometric mean of the
mean free path for ionization and the mean free path for charge exchange, which is only a few
centimetres in a typical tokamak.
Neutrals injected from neutral beam lines are the second major population. The velocities
of these neutrals are determined by the accelerating grids of the neutral beam source. There are
three discrete energies: the neutrals with the full acceleration voltage, neutrals with one-half
of the acceleration voltage and neutrals with one-third of the acceleration voltage. The small
divergence of the neutral beam source implies that both the direction of the velocity vector
and the spatial extent of the injected neutrals are well defined. Because of their great velocity
(2.8 ×10
6
ms
−1
for an 80 keV deuteron), the Doppler shift of the D
α
emission can be as large
as 6 nm. In addition to the Doppler shift, there is also Stark splitting of the line associated with
both the motional
v × B Stark effect and with plasma electric fields. This splitting accounts
for the ∼1 nm spread of the three peaks in the full-energy D
α
line in figure 1.
Hydrogenic fast-ion diagnostic using Balmer-alpha light 1857
651 652 653 654 655 656 657
0
2
4
6
8
WAVELENGTH (nm)
SIGNAL (a.u.)
}
}
Injected
1/2 & 1/3
Halo
Background
Edge
Edge
Halo
Injected
Injected
Full
(b)
(a)
30° Neutral Beam
330°
Midplane
15
°
Midplane
Unshifted Wavelength
Figure 1. (a) Plan view of the DIII-D tokamak showing the modulated neutral beam source and
the two sightlines for the data in this paper. Injected neutrals are in the beam ‘footprint’, warm halo
neutrals are in a cloud around the injected beam, and cold edge neutrals are near the walls of the
chamber. (b) Spectrum for the fibre that views the 30˚ modulated beam from the 330˚ midplane
port when the beam is on (——) and off (- - - -). The contributions to the spectrum of the injected,
halo and edge neutrals are indicated.
The injected neutrals ionize through either electron-impact ionization with plasma
electrons or through charge exchange with plasma ions. In a charge exchange event with
a hydrogenic ion, the energetic injected neutral generates a neutral with the velocity of the
thermal plasma. These warm neutrals can radiate promptly and they generally undergo several
subsequent charge-exchange reactions before being ionized by electron impact. A warm, ‘halo’
neutral population forms around the injected beam. The velocity distribution of this population
is approximately the local velocity distribution of the plasma ions. For an ion temperature of
T
i
= 5 keV, the resulting Doppler shift of the D
α
line is approximately 1.5 nm.
Upon ionization, injected neutrals form a population of fast ions. These fast ions circulate
around the torus on orbits that are determined by their velocity and the confining magnetic
field. On a longer timescale, Coulomb collisions with the plasma cause gradual deceleration
and spreading of the velocity distribution. An axisymmetric, supra-thermal distribution, f
f
,
of fast ions is created that depends on four variables: the fast-ion energy, E, the projection of
the velocity vector onto the magnetic field, v
/v (also called the ‘pitch’), and the radial and
poloidal positions, r. When these fast ions orbit through an injected neutral beam, a small
fraction of them undergo a charge-exchange reaction and become a hydrogen atom. The goal
1858 W W Heidbrink et al
of this technique is to extract information about f
f
from the Balmer-alpha light emitted by
these atoms.
The spectrum in figure 1 highlights the difficulties with a naive implementation of this
concept. These data are from a fibre that views a neutral beam source tangentially in the
midplane. Injected neutrals are travelling towards the fibre and so the radiation is blue-shifted.
The bright contributions from edge and halo neutrals on the blue-shifted side of the central peak
are also evident. For these plasma conditions, the fast-ion population is travelling primarily
in the direction of the injected beam with a broad distribution of energies and velocities,
and so a broad blue-shifted fast-ion ‘line’ that spans the entire abscissa is expected. This
line is relatively weak, however. The fast-ion signal is proportional to the fast-ion density,
n
f
, while the halo signal is proportional to the thermal plasma density, n
i
. As a crude
estimate of the spectral intensity, dI/dλ, the ratio of the fast-ion signal to the halo signal
is roughly (n
f
/n
i
)
√
T
i
/E ∼ 10
−3
. This implies that the expected signal is smaller than typical
backgrounds from bremsstrahlung and impurity radiation. Accurate background subtraction
based on modulation of the injected neutral source is essential for the success of this concept.
Even with accurate background subtraction, detection of a fast-ion signal is problematic for
the geometry shown in figure 1.
Fortunately, there are more favourable geometries. Figure 2 illustrates the situation for
a fibre located above the heating beam. Because the injected neutrals travel exclusively
horizontally, this geometry eliminates their Doppler shift. In contrast, the fast ions gyrate
vertically in the magnetic field due to the perpendicular component of their velocity. They travel
down during half of their cyclotron orbit and up during the other half, and so a population of
fast ions produces a spectrum with red- and blue-shifted wings. This effect is most pronounced
for the idealized, monoenergetic distribution shown in figure 2, but the basic effect is present for
more realistic distributions. With accurate background subtraction, the signal from fast ions
is detectable.
This paper reports the first experimental measurements of D
α
light from a fast-
ion population. Initial measurements have the expected spectral, temporal and density
dependences (section 2). The prospects for future application of this technique are considered
next (section 3). Conclusions and plans are summarized in section 4. A simulation code used
to model the data and to assess the achievable spatial resolution is described in the appendix.
2. Initial data
As an initial test of the concept, the spectrometer of the DIII-D CER spectroscopy diagnostic
[22] was shifted from its usual wavelength to the D
α
transition. The first test with a tangential
view of the beam, shown in figure 1(b), highlighted the difficulties. After realizing the
importance of exploiting the perpendicular gyromotion to avoid the bright interfering lines,
an observation with the fibres at the 15˚ midplane port was attempted. With this radial view
(figure 1(a)), the injected neutrals are moving away from the detector, and so their D
α
emission
is red-shifted. This view is nearly perpendicular to the magnetic field, and so the fast-ion
gyromotion produces a large Doppler shift in both directions, as in figure 2. The CER diagnostic
cannot span the entire spectral range of interest, and so the instrument was tuned to view the
uncontaminated blue portion of the spectrum and to just miss the bright central line produced
by the edge and halo neutrals.
A typical discharge for the experiments with the radial-view data is shown in figure 3.
Several neutral beams inject into the discharge, but only one source injects neutrals in the
sightline of the detector. This source injects steadily at the beginning of beam injection from
1.9 to 2.7 s, is off while other sources inject from 2.7 to 3.8 s, steadily injects again for the next
![Figure 11. (a) Contours of the fast-ion distribution function for neutral beam injection of 75 keV deuterium atoms at an injection angle of v‖0/v = 0.6 in a plasmawith Te = 4 keV andZeff = 2.5 as calculated by the steady state Fokker–Planck algorithm in [40]. The long-dash line indicates where the charge-exchange reactivity, σv(|vf −vn|), is maximized for a tangentially injected neutralizing beam of 80 keV deuterium atoms; the short-dash lines indicate where σv is 25% of its maximum value. (b) Approximate calculation of the spectral intensity, dI/dλ, for a vertical view of this fast-ion distribution in a purely toroidal field. The spectra for v‖0/v = 0.9 and 0.2 are also shown.](/figures/figure-11-a-contours-of-the-fast-ion-distribution-function-33chbjae.webp)
