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Title
Velocity-space studies of fast-ion transport at a sawtooth crash in neutral-beam heated
plasmas
Permalink
https://escholarship.org/uc/item/7tp21519
Journal
Plasma Physics and Controlled Fusion, 54(2)
ISSN
0741-3335
Authors
Muscatello, CM
Heidbrink, WW
Kolesnichenko, YI
et al.
Publication Date
2012-02-01
DOI
10.1088/0741-3335/54/2/025006
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 54 (2012) 025006 (13pp) doi:10.1088/0741-3335/54/2/025006
Velocity-space studies of fast-ion
transport at a sawtooth crash in
neutral-beam heated plasmas
C M Muscatello
1
, W W Heidbrink
1
, Ya I Kolesnichenko
2
, V V Lutsenko
2
,
M A Van Zeeland
3
and Yu V Yakovenko
2
1
Department of Physics and Astronomy, University of California-Irvine, Irvine, CA, USA
2
Institute for Nuclear Research, Kiev, Ukraine
3
General Atomics, PO Box 85608 San Diego, CA 92186-5608, USA
Received 26 August 2011, in final form 28 November 2011
Published 5 January 2012
Online at
stacks.iop.org/PPCF/54/025006
Abstract
In tokamaks the crash phase of the sawtooth instability causes fast-ion transport. The DIII-D
tokamak is equipped with a suite of core fast-ion diagnostics that can probe different parts of
phase space. Over a variety of operating conditions, energetic passing ions are observed to
undergo larger redistribution than their trapped counterparts. Passing ions of all energies are
redistributed, but only low-energy (40 keV) trapped ions suffer redistribution. The transport
process is modeled using a numerical approach to the drift-kinetic equation. The simulation
reproduces the characteristic that circulating energetic ions experience the greatest levels of
internal transport. An analytic treatment of particle drifts suggests that the difference in
observed transport depends on the magnitude of toroidal drift.
(Some figures may appear in colour only in the online journal)
1. Introduction
Among the many internal instabilities inherent to tokamak
plasmas, sawteeth are periodic events occurring on large
spatial scales without necessarily causing discharge disruption.
Sawteeth were observed to cause internal redistribution
of various species of fast ions: beam deuterium [1, 2],
fusion-born proton and helium-3 [3], and both passing and
trapped deuterium–tritium alphas [4, 5]. The velocity-space
dependence of fast-ion transport by the sawtooth instability
was studied previously on TFTR and TEXTOR. On TFTR,
the pellet charge-exchange (PCX) and alpha-charge exchange
recombination spectroscopy (α-CHERS) diagnostics obtained
data on the redistribution of trapped and passing fast ions
at a sawtooth crash [6]. A large depletion in the core
passing-ion density was detected during a crash event with
α-CHERS. The lack of core PCX data makes it difficult to
assess the effect of sawteeth on the trapped energetic-ion
population, but a broadening in the profile is observed. A more
recent investigation on TEXTOR utilized a collective Thomson
scattering (CTS) diagnostic during sawteeth to resolve the 1D
fast-ion distribution function for various angles with respect
to the magnetic field [7]. It was found that trapped energetic
ions are less susceptible to sawtooth-induced transport than the
passing population.
Differences between the effect of sawteeth on passing
and trapped ions extend to the theoretical realm as well.
Modeling of the redistribution of passing energetic ions
invoking attachment to the evolving flux surfaces during the
crash reproduces experimental results [4]. On the other
hand, application of the flux-attached model to the trapped-
ion population yields poor agreement with experiment [6]. To
account for this difference, the theoretical works invoke two
distinct transport mechanisms: transport by flux-attachment
[4] (dominant for passing particles) and transport by
E × B
drift [6] (dominant for trapped particles). However, it can be
shown that
E × B drift and flux-attachment are cause and
effect [8]; a particle that is well-situated near a flux surface
moves with the surface by the
E × B drift. Therefore,
any particle attached to an evolving flux surface is prone
to sawtooth-induced transport, but the frozen-in condition is
broken by particles that experience strong toroidal drifts. To
our knowledge, no previous publications have shown that
toroidal drift effects lead to the measured transport differences.
0741-3335/12/025006+13$33.00 1 © 2012 IOP Publishing Ltd Printed in the UK & the USA
Plasma Phys. Control. Fusion 54 (2012) 025006 C M Muscatello et al
R (m)
1.0 1.5 2.0 2.5
–1.5
–1.0
–0.5
0.0
0.5
1.0
1.5
z (m)
B
t
I
p
•
×
Figure 1. Poloidal cross-section of DIII-D for shot 141182. The
thin contours are surfaces of constant magnetic flux; the dashed
contour is the q = 1 surface; the inner thick contour (bean shape) is
the last closed flux surface; the outer thick contour indicates the wall
of the vessel.
In this paper, we present experimental data of velocity-
spaced-resolved fast-ion signals during sawteeth on DIII-D.
Consistent with previous results, we observe stronger
redistribution of passing fast ions compared with their trapped
counterparts. A drift-kinetic simulation is performed, and the
results qualitatively agree with the observation that passing fast
ions experience the greatest degree of redistribution. To remind
the reader of the extensive theoretical work done in this subject,
an abbreviated sketch of the important aspects of the theory will
be presented. The theory associates the transport difference
between passing and trapped fast ions to their magnitude of
toroidal drift. A critical energy exists where toroidal drift plays
a crucial role in the degree of transport. The critical energy
can be represented in velocity space, dictating a redistribution
boundary. We show that changes in the energy spectrum of
fast ions are consistent with an analytic calculation of the
redistribution boundary. The paper is organized as follows. In
section 2 we present our experimental setup and data. Section 3
summarizes the results from our simulations and includes an
analytic sketch of particle drifts. Our concluding remarks can
be found in section 4.
2. Experimental setup and results
With its extensive suite of diagnostics, neutral-beam injection
system, plasma control system, and array of magnetic field
shaping coils, the DIII-D tokamak [9] is a highly versatile
and well-diagnosed machine. The focus of the first part
of this section is an analysis of fast-ion data for similar
DIII-D shots 141182 and 141195. Figure 1 is an elevation
of the plasma cross-section for shot 141182 as calculated by
the equilibrium reconstruction code EFIT [10]; the magnetic
axis is R
axis
= 1.72 m. The motional Stark effect (MSE)
polarimeter [11] measures the pitch of the local magnetic
field. MSE is utilized to constrain the safety factor (q) profile
and equilibrium reconstruction. The dashed flux surface
indicates the location of the q = 1 surface (normalized toroidal
flux ρ ≈ 0.3) just before a crash. The plasma current I
p
and toroidal field B
t
are 1.3 MA and 1.9 T, respectively. In
these discharges, I
p
is directed counter-clockwise, and B
t
is clockwise viewed from the top of the tokamak (so that
the ion ∇
B drift is downward). A time history of shot
141182 is shown in figure 2. The top trace is the electron
temperature T
e
measured by the central electron cyclotron
emission (ECE) channel at the midplane [12]. The middle
trace is the neutron emission measured by a plastic scintillator
located about 30
◦
above the midplane [13]. The bottom
trace is the fluctuations of the magnetic field measured by a
Mirnov coil at the midplane. The average sawtooth period
and amplitude (defined as |T
e precrash
− T
e postcrash
|/T
e precrash
,
and determined by the central ECE channel) are 85 ± 5ms
and 0.35 ± 0.02, respectively. Precrash and postcrash
plasma profiles are plotted in figure 3. Ion temperature,
toroidal rotation velocity and main impurity (carbon) density
are inferred from the charge-exchange recombination (CER)
diagnostic [14]. The precrash/postcrash profiles are generated
by averaging 10 ms before/after five consecutive sawtooth
crashes. Random errors are calculated using the ensemble
standard deviation. The fast-ion population is generated
through deuteron neutral-beam injection at an average full
injection energy of 75 keV. Four neutral-beam sources are
modulated on and off for diagnostic background subtraction
and for the purpose of reducing the overall power to keep the
discharge in L-mode. The average full injection energy is
calculated by weighting the injection voltage of each source
according to its duty cycle. Sawtooth repeatability is necessary
for fast-ion profile reconstruction prior to and following a
crash. Long time domains (≈1 s) of uniform sawteeth are
produced in order to obtain average precrash and postcrash
profiles with sufficient statistics. During the sawtoothing
portion of all discharges discussed here, no other MHD activity
such as Alfv
´
en eigenmodes, fishbones or tearing modes is
detected.
DIII-D has an extensive fast-ion diagnostic suite that
probes different regions of phase space. Fast-ion deuterium-
alpha (FIDA) is the main diagnostic technique used in this
paper to measure the confined fast-ion profiles [15]. At
the time of writing, three sets of FIDA collection optics are
currently in use at DIII-D. They are named according to the
geometry of their sightlines in the tokamak. Projections of the
sightlines for the three installations are shown in figure 4 in two
different planes: figure 4(a) shows the poloidal plane (at fixed
toroidal angle) and figure 4(b) the plan view at the midplane
(z = 0). The active collection volume of the any sightline
is the intersection of the sightline with the neutral beam. In
figure 4(a) the vertical extent of a neutral beam is indicated by
the horizontal gray lines. In figure 4(b) the beam trajectory in
the midplane is indicated by the gray swatches. Each viewing
2
Plasma Phys. Control. Fusion 54 (2012) 025006 C M Muscatello et al
Time (ms)
2700 2800 2900 3000
–40
0
40
dB/dt (T/s)
1.1
1.2
1.3
1.4
2.5
3.0
3.5
Neutron
Rate (au)
T
e
(0) (keV)
(b)
(a)
(c)
Figure 2. Time slice from shot 141182. (a) Central electron temperature (T
e
) measured by the ECE diagnostic; (b) neutron emission
measured by a scintillator; (c) magnetic fluctuations measured by a Mirnov coil.
2.05
2.45
2.93
3.50
0
2
4
T
e
(keV)
Normalized ρ
ρ
0.0 0.3 0.6 0.9
Normalized ρ
0.0 0.3 0.6 0.9
Normalized ρ
0.0 0.3 0.6 0.9
(d)
(a)
(e)
(b)
(f)
(c)
1
3
1.00
1.20
1.43
1.71
0.70
0.84
q
0
2
4
n
e
(10
13
cm
–3
)
1
3
1.0
1.2
1.4
0.4
0.6
0.8
0.0
0.2
Rotation (10
5
rad/s)
0.08
0.10
0.04
0.06
0.00
0.02
n
c
(10
13
cm
–3
)
4
5
2
3
0
1
T
i
(keV)
postcrash
precrash
Figure 3. Precrash (dark blue) and postcrash (orange) profiles for (a) safety factor, (b) electron density, (c) ion temperature, (d) electron
temperature, ( e) toroidal rotation, (f ) main impurity (carbon) density. Random errors from ensemble averaging are indicated by the
thickness of the profile plots.
chord of a spectroscopic FIDA system measures the photonic
D
α
spectrum produced by a population of deuterium ions that
undergo charge-exchange with injected neutral deuterons. The
unshifted wavelength λ
0
ofaD
α
photon is 656.1 nm. However,
a photon emitted from a moving source is Doppler shifted
depending on the velocity of the source. More specifically, the
Doppler shift λ depends on the dot product of the velocity
of the moving source and the direction vector of the emitted
photon. Therefore, λ depends on the energy of the moving
source along the emitted photon direction; let us call this
energy E
λ
. FIDA measures the D
α
spectrum and each value
of wavelength thus corresponds to an E
λ
value. For FIDA,
E
λ
translates to the fast-ion energy component parallel to the
diagnostic sightline. Therefore, ions with various values of
pitch (χ ≡ V
/V where V
is the ion velocity component
parallel to the magnetic field) and total energy E can contribute
to a measured fast-ion energy E
λ
of the spectrum. This leads
to an instrumental weighting in fast-ion phase space depending
on several factors described in [16].
To produce FIDA spatial profiles, spectra from each radial
chord are integrated over a particular wavelength band. These
values are then divided by the local neutral density to produce
profiles which are approximately proportional to the fast-
ion density. The neutral density calculation approximates
the ionization cross-section given plasma density, plasma
temperature, plasma toroidal rotation and impurity density
3
Plasma Phys. Control. Fusion 54 (2012) 025006 C M Muscatello et al
(b)(a)
Figure 4. Projections of the FIDA sightlines for three different
optical installations. (a) Poloidal plane at a fixed toroidal angle.
Horizontal gray lines indicate the approximate vertical extent of the
neutral beam. (b) Plan view from the top of the tokamak. Gray
swatches indicate beam trajectories in the midplane.
profiles. The profiles are spline fits to experimental
measurements. In addition to the profiles, the neutral density
calculation also requires values for the injected neutral-beam
power and the full, 1/2 and 1/3 energy species fractions.
Errors in the profiles, reported injected power, and species
mix propagate to errors in the calculated neutral density. The
dependence of the neutral density uncertainty on the errors
of the input parameters can be determined by independently
adjusting the parameter values. Out of all the plasma
profiles, the neutral deposition is most sensitive on the plasma
density profile. A reduction in the plasma density profile
by 10% negligibly affects the neutral density at the edge but
increases it in the core by 10%. Inaccurate plasma density
profile modeling can lead to unsystematic uncertainties in the
calculated neutral density. A reduction in the injected power
by 10% reduces the neutral density by 10% uniformly across
the beam trajectory. Fortunately, uncertainty in the reported
injected power value is a systematic error which does not affect
relative comparisons. A reduction in the full-energy species
fraction by 10% negligibly reduces the neutral density by 5%
uniformly across the beam trajectory. Therefore, uncertainties
in the plasma density profile are likely the largest source of
error. In the cases studied here, errors in the electron density
profile are determined by a Monte Carlo method and yield
values of less than 10% across the profile.
Figure 5 shows the weight functions that represent
the contribution to the FIDA signal when the spectrum
is integrated between energies E
λ
= 30 and 60 keV
for the spectroscopic FIDA systems currently on DIII-D.
Figures 5(a) and (b) depict the instrumental weight functions
in velocity-space for two spectroscopic FIDA systems, the
vertical [15] and near-tangential [17] instruments, respectively.
DIII-D is also equipped with an imaging system that
detects a two-dimensional poloidal cross-section of the fast-
deuterium profile when used in conjunction with a narrowband
interference filter [18]. The bandwidth is ≈4 nm centered
on λ = 652 nm which corresponds to E
λ
= 10–80 keV.
The FIDA imaging weight function is shown in figure 5(c).
Although FIDA integrates much of the velocity space, the
viewing geometries of the three systems skew the coverage
differently. Comparing the three, the instrument function of
the vertical system is nearly symmetric about particle pitch of
zero and strongly weighted about zero. The nearly tangential
system is heavily weighted toward large positive values of
pitch, while 2D FIDA weights large negative values of pitch
most heavily. The sign of the pitch indicates the direction of the
particle parallel motion with respect to the I
p
direction, where
negative values indicate opposite direction to I
p
. The overlaid
dashed lines indicate fast ion trapped/passing boundaries that
are calculated using a guiding-center orbit integration tool (see
the appendix of [19]). These plots demonstrate the practicality
of using the three systems to investigate the different dynamics
of fast ions with varying orbit types.
In order to obtain high quality fast-ion signals, the
discharges are chosen to be low-density L-mode deuterium
plasmas. The signal-to-noise ratio of the FIDA signal
is poor for line-averaged densities above ∼7 × 10
19
m
−3
,
and edge-localized modes (ELMs) introduce scattered light
into the diagnostic, contaminating the spectra. In addition,
simultaneous data acquisition during the same shot was desired
for the two spectroscopic systems. Therefore, careful beam
programming must be employed; otherwise, the vertical
system’s diagnostic beam can contaminate the tangential
system’s signal (and vice versa), inhibiting proper background
subtraction. The beam programming on shot 141182 was set
up so the beams were interleaved with intervals where both
diagnostic beams are off for background subtraction. Average
precrash and postcrash spectra are generated by averaging over
many sawtooth cycles. For the vertical and near-tangential
systems, spectra from various radial locations within the first
and last 10% of each sawtooth cycle are chosen. Obtaining
the desired FIDA spectra requires a background subtraction
procedure described in [15], as shown schematically in figure 6.
An ensemble of active (beam-on) spectra and background
(beam-off) spectra are collected for precrash and postcrash
phases. The average precrash and postcrash spectra are
calculated by subtracting the average background spectrum
from the average active spectrum. This subtraction technique
assumes that the background spectrum is insensitive to the
crash event. However, it has been observed that a sawtooth
crash can cause changes in the background D
α
signal [15].
On shot 141182, a passive D
α
filterscope indicates that the
background signal jumps less than 10% following a crash.
Spectra from the tangential and vertical systems for a radial
chord intersecting the midplane at R = 186 cm are shown
in figure 7. Random errors from ensemble averaging are the
largest source of uncertainty in these spectra. The average
error in the vertical spectra is ∼20% of the signal and ∼10%
in the tangential spectra. Evidently, ions in the entire measured
spectral range of the tangential system are redistributed, while
there appears to be an energy dependence in the redistribution
measured by the vertical system. The dashed vertical line
(λ = 652 nm, E
λ
= 36 keV) indicates the maximum Doppler
shift where deviations between the precrash and postcrash
spectra are observed by the vertical system.
To generate spatial profiles from the spectroscopic
systems, integration of the spectrum from each radial chord
4
