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Title
Anomalous flattening of the fast-ion profile during Alfvén-Eigenmode activity.
Permalink
https://escholarship.org/uc/item/7rx558qx
Journal
Physical review letters, 99(24)
ISSN
0031-9007
Authors
Heidbrink, WW
Gorelenkov, NN
Luo, Y
et al.
Publication Date
2007-12-01
DOI
10.1103/physrevlett.99.245002
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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Anomalous Flattening of the Fast-Ion Profile during Alfve
´
n-Eigenmode Activity
W. W. Heidbrink,
1
N. N. Gorelenkov,
2
Y. Luo,
1
M. A. Van Zeeland,
3
R. B. White,
2
M. E. Austin,
4
K. H. Burrell,
3
G. J. Kramer,
2
M. A. Makowski,
5
G. R. McKee,
6
R. Nazikian,
2
and the DIII-D team
1
University of California, Irvine, California 92697, USA
2
Princeton Plasma Physics Laboratory, Princeton, New Jersey 08543, USA
3
General Atomics, P.O. Box 85608, San Diego, California 92186-5608, USA
4
University of Texas, Austin, Texas 78712-0263, USA
5
Lawrence Livermore National Laboratory, Livermore, California 94550, USA
6
University of Wisconsin, Madison, Wisconsin 53706, USA
(Received 29 June 2007; published 12 December 2007)
Neutral-beam injection into plasmas with negative central shear produces a rich spectrum of toroidicity-
induced and reversed-shear Alfve
´
n eigenmodes in the DIII-D tokamak. The first application of fast-ion D
(FIDA) spectroscopy to Alfve
´
n-eigenmode physics shows that the central fast-ion profile is anomalously
flat in the inner half of the discharge. Neutron and equilibrium measurements corroborate the FIDA data.
The current density driven by fast ions is also strongly modified. Calculations based on the measured
mode amplitudes do not explain the observed fast-ion transport.
DOI: 10.1103/PhysRevLett.99.245002 PACS numbers: 52.55.Pi, 52.35.Bj, 52.55.Fa
particles produced in deuterium-tritium fusion reac-
tions may drive Alfve
´
n eigenmodes [1,2] unstable in ITER
and other burning plasma experiments. If they do, the most
important practical issue is the resultant fast-ion transport.
Will benign local flattening of the -particle pressure
profile occur? Or will the particles escape from the
plasma and damage the first wall? The expulsion of fast
ions by toroidicity-induced Alfve
´
n eigenmodes (TAE) has
damaged internal vessel components in two tokamaks
[3,4]. The damage was explained qualitatively in terms of
wave-particle resonances and orbital effects, but no quan-
titative comparisons between the measured fluctuation
levels and the expected transport were given in these
publications. In the only quantitative studies of this im-
portant issue [5,6], wave amplitudes an order of magnitude
larger than the measured values were needed to predict the
large losses observed experimentally.
The fast-ion and instability diagnostics were coarse in
these early studies, suggesting that misinterpretation of the
available signals might account for the discrepancy. In the
work reported here, however, both the instabilities and the
fast-ion response are very well characterized. Never-
theless, the calculated fast-ion transport is still much
smaller than the observed value.
The DIII-D tokamak has an extensive suite of fluctuation
diagnostics with the bandwidth and sensitivity needed to
detect Alfve
´
n instabilities. A 40-channel electron cyclotron
emission (ECE) diagnostic measures electron temperature
(T
e
) fluctuations, density (n
e
) fluctuations are measured by
reflectometry, beam-emission spectroscopy, and CO
2
in-
terferometry and magnetic fluctuations are measured by
Mirnov coils. A detailed comparison of these measure-
ments with the mode structures predicted by linear ideal
MHD theory was recently reported [7]. Both the electron
temperature and the electron density eigenfunctions are in
excellent agreement with the
NOVA code [8] for the n 3
TAE and the reversed-shear Alfve
´
n eigenmode (RSAE). (n
is the toroidal mode number.) This Letter documents the
fast-ion response to these well-characterized wave fields.
In the baseline discharge (no. 122117) [7], 4.6 MW of
80-keV deuterium neutral beams are injected in the direc-
tion of the plasma current into a low-density (
n
e
2
10
13
cm
3
), magnetically diverted, deuterium plasma with
central T
e
1–2 keV. The beams are injected early in the
current ramp to produce a reversed-shear plasma with an
off-axis minimum in the safety factor q at
q min
. (The
normalized minor radius coordinate is proportional to the
square root of the toroidal flux .) The central beam
pressure is large ( 50% of the total), and the ratio of
the injected beam speed to the Alfve
´
n speed is 0:45.At
the magnetic axis, the peak of the fast-ion distribution
function occurs at a pitch of v
k
=v 0:68.
The fast-ion response to the instabilities is determined
by four independent techniques. The primary diagnostic is
a new charge-exchange recombination spectroscopy tech-
nique that utilizes the Doppler-shifted Balmer- light
emitted by fast ions [9,10]. Beam modulation and fitting
of impurity lines is used to extract the fast-ion spectra from
the interfering background light [10]; uncertainties in
background subtraction are the dominant source of error
and are represented by error bars in the figures. In this
Letter, the spectra from this fast-ion D
(FIDA) diagnostic
are averaged over wavelengths that correspond to energies
along the vertical line of sight of E
30–60 keV. The
wavelength-integrated signals are divided by the injected
neutral density to yield fast-ion density measurements in
most of the high-energy portion of velocity space [11] with
a spatial resolution of a few centimeters. The second
diagnostic is the volume-averaged deuterium-deuterium
neutron rate S
n
. Under these conditions, S
n
is dominated
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by beam-plasma reactions between the fast and thermal
populations, so the signal is proportional to the number of
high-energy fast ions in the plasma. To detect effects
caused by the instabilities, the signal is normalized to the
classically expected rate due to collisional processes (as
calculated by
TRANSP [12]). The third diagnostic relies on
motional Stark effect (MSE) measurements of the internal
magnetic field. The profile of the total plasma pressure is
obtained from
EFIT [13] reconstructions of the MHD equi-
librium that are consistent with the MSE and magnetics
data and with isotherms of the electron temperature. The
thermal pressure from T
e
, n
e
, T
i
, and carbon density mea-
surements (the dominant impurity) is subtracted from the
MHD pressure profile to obtain the fast-ion pressure p
f
.
The absolute uncertainty in the inferred fast-ion pressure at
0:25 is 16% and the relative uncertainty is 8%.In
the fourth technique, the evolution of the q profile provides
information on the neutral-beam current drive (NBCD)
profile, which is sensitive to the spatial profile of circulat-
ing fast ions. In addition to the evolution of q
min
inferred
from the equilibrium reconstructions, rational values of
q
min
are also inferred from the temporal pattern of
frequency-sweeping RSAEs with different toroidal mode
numbers [2].
Strong Alfve
´
n activity occurs early in the discharge
[Fig. 1(a)]. RSAEs that are localized near
q min
and
more global TAEs are both observed [7]. When the fre-
quency of a RSAE sweeps across a TAE frequency, the
eigenfunctions mix. Throughout the period of strong ac-
tivity, both the neutron rate and the FIDA density are
suppressed relative to their classically expected values
[Fig. 1(b)]. The magnitude of this suppression correlates
with the amplitude of the mode activity. Figure 2 shows
data from five similar discharges with different values of
beam power. Because of the complexity of the Alfve
´
n
activity, it is difficult to quantify the composite amplitude.
Figure 2 uses the amplitude of the ten strongest modes as
measured by ECE; the correlation is similar using a
bandpass-filtered Mirnov signal. These results strongly
suggest that the observed reductions in the fast-ion signal
are caused by the Alfve
´
n activity.
The Alfve
´
n activity flattens the fast-ion spatial profile.
Both the FIDA density profile and the fast-ion pressure
profile from MSE are much flatter during the strongest
activity than they are later in the discharge (Fig. 3).
Although the pressure profile peaks as the activity weak-
ens, it is still less peaked than classically expected at 1.2 s.
This is in contrast to the profiles observed in MHD-
quiescent plasmas, which are in excellent agreement with
the
TRANSP predictions [14].
The FIDA spectrum is sensitive to the perpendicular
energy distribution [14]; distorted spectra are sometimes
observed during Alfve
´
n activity and are common during
ion cyclotron heating [11]. In discharge no. 122117, how-
ever, the spectra agree (within the uncertainties) with the
spectral shape normally observed in quiet plasmas. This
suggests that the transport process changes the average
perpendicular energy of the fast ions no more than
5 keV.
In the presence of this fast-ion transport, the plasma
current diffuses more gradually than classically predicted
[Fig. 4(a)]. Two independent measurements of the evolu-
tion of q
min
are in excellent agreement. They differ mark-
edly from the classical predictions calculated by special
TRANSP simulations that begin with the measured equilib-
rium, then evolve the current profile assuming neoclassical
0.3 0.5 0.7 0.9
0.0
0.4
0.8
EXP / CLASSICAL
FIDA
NEUTRONS
60
100
140
FREQUENCY (kHz)
(a)
TIME (s)
#122117
180 cm
195 cm
#122117
(a)
(b)
FIG. 1 (color online). (a) Cross power of radial and vertical
CO
2
interferometer channels showing the many RSAEs
(upward-sweeping lines) and TAEs ( horizontal lines) in the
plasma. (b) Neutron rate and FIDA densities at R 180 and
195 cm vs time. The signals are normalized by the classical
TRANSP neutron and beam-ion density predictions, respectively.
The absolute calibrations of the neutron and FIDA data are
adjusted so that the ratio is unity in the preceding 2.3 MW
discharge at 2.0 s (when the Alfve
´
n activity is undetectable).
0 0.5 1.0 1.5 2.0
Mode Amplitude (a.u.)
0.0
0.4
0.8
1.2
(Fast Ions) / (Classical)
2.3 MW
4.6
7.1
9.3
11.4
#122116-20
FIDA
Neutrons
FIG. 2 (color online). Normalized neutron rate and R
180 cm FIDA density versus approximate mode amplitude at
various times in five successive discharges with increasing
amounts of beam power. The dashed lines are linear fits to the
data.
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flux diffusion. These simulations adjust the boundary value
of the parallel electric field to match the measured plasma
current. For either of two extreme assumptions—either
classical NBCD or no NBCD whatsoever—the predicted
diffusion is far more rapid than experimentally observed.
Evidently, both the classical NBCD profile and the neo-
classical conductivity profile are more peaked than the
actual current profile. A simulation that uses the NBCD
expected from a centrally flattened fast-ion density profile
is in better agreement with experiment. Gradual evolution
of q
min
was previously reported [15] in more poorly diag-
nosed discharges. In contrast, in the discharge with lower
beam power and much weaker Alfve
´
n activity, the current
evolution is close to the classical expectation [Fig. 4(b)].
The strongest modes in the spectrum [Fig. 1(a)] have
peak internal magnetic perturbations of B
r
=B & 10
3
.
Published theoretical simulations of fast-ion transport
often require larger amplitudes than this to obtain signifi-
cant transport; see, e.g., Refs. [5,6,16]. To determine if the
measured Alfve
´
n activity can explain the observed fast-ion
transport, the 11 strongest toroidal modes are matched to
NOVA linear eigenfunctions and the amplitudes are scaled
to agree with the ECE measurements. Reliable mode iden-
tification is possible for the largest 7–8 modes but is
problematic for the weakest ones or for modes with similar
frequencies. For each toroidal mode, the strongest poloidal
harmonics m are selected and a total of 151 (n, m) helical
perturbations with their experimental amplitudes and fre-
quencies are entered into the Hamiltonian guiding center
code
ORBIT [17]. Shear Alfve
´
n waves with weak kinetic
effects are assumed (E
k
B
k
0), so the transport
caused by parallel electric and magnetic wave fields is
neglected. Evolution of the frequency and mode structure
is ignored since these barely change on orbital time scales.
The initial fast-ion birth distribution function F
0
is taken
from
TRANSP. The particle orbits are computed in the
presence of pitch-angle scattering and the perturbed fields,
then the distribution function F is sampled for comparison
with F
0
.
This procedure cannot account for the observed fast-ion
transport. Figure 5 shows the change in the distribution
function in the region of velocity space that makes the
dominant contribution to the measured fast-ion signals for
ORBIT runs where the mode amplitudes are artificially
1
2
3
4
5
400 600 800 1000 1200
TIME (ms)
q
m
in
TRANSP
EFIT (MSE)
RSAE
Cascade
TIME (ms)
q
m
in
400 600 800 1000 1200 1400 1600
0
2
4
6
#122116
#122117
STRONG ALFVEN
WEAK ALFVEN
(a)
(b)
FIG. 4 (color online). Measured evolution of q
min
from MSE-
based equilibrium reconstructions (line) and RSAE rational
integer crossings (diamond) in discharges with (a) strong
Alfve
´
n activity (4.6 MW) and (b) weak Alfve
´
n activity
(2.3 MW). The
TRANSP simulations assume either classical
NBCD (solid line) or the NBCD from a centrally flattened
fast-ion density profile (dashed line).
0.0 0.2 0.4 0.6 0.8
-0.4
-0.3
-0.2
-0.1
0.0
0.1
NORMALIZED MINOR RADIUS
∆ F / F
0
Ad Hoc Diffusion (Experiment)
8
ms
3
1.5
ms
Coll
isions
Collisions + Modes
FIG. 5 (color online). Change in the distribution function of
fast ions with E 60 keV and v
k
=v 0:4–0:7 vs ; F is
normalized to the maximum value of the initial distribution
function. The dashed lines are with collisions alone; the solid
lines include collisions and 151 helical modes at 5 times the
experimental amplitudes for the TAEs and RSAEs that are
observed at 356 ms. The distribution function is sampled after
0.95–1.9 ms (green), 1.9–3.8 ms (turquoise), and 5.5–11 ms
(purple). The (red) curve compares a
TRANSP simulation with
D
B
5m
2
=s inside 0:55 and zero outside with a standard
(D
B
0) simulation.
0.1 0.2 0.3 0.4 0.5 0.6 0.7
0
0.5
1.0
1.5
NORMALIZED MINOR RADIUS
FAST-ION PRESSURE (10
4
Pa)
TRANSP
EFIT
FIDA
0.36 s
1.20 s
#122117
FIG. 3 (color online). Fast-ion pressure profiles and FIDA
density profiles versus at two different times that correspond
to normalized neutron rates of 0.66 and 0.94. The dashed lines
are the classical pressure profile predicted by
TRANSP. The FIDA
density profile is normalized to the MSE-
EFIT p
f
profile at 1.2 s.
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enhanced by a factor of 5. Even with this enormous en-
hancement, which is much larger than the experimental
uncertainty of &10%, the transport is smaller than ob-
served. To estimate the experimental transport, an ad hoc
diffusion coefficient D
B
is employed in a sequence of
special
TRANSP runs that hold all other plasma parame-
ters fixed. Spatially variable diffusion that is very large
(* 5m
2
=s) inside ’ 0:55 and tiny outside is needed for
consistency with the measured FIDA and p
f
profiles. The
ORBIT simulations predict transport in the correct locations
but, even with 5 times the measured amplitude, the change
in the distribution function is far too small. The predicted
transport is comparable to neoclassical diffusion.
The
ORBIT simulation uses the strongest modes ob-
served experimentally at a single representative time.
However, many weaker intermittent modes appear at lower
frequencies; perhaps these play an important role in the
observed transport. (Neoclassical tearing modes are
absent.)
In summary, four independent diagnostics all indicate
strong transport of fast ions in reversed-shear discharges
with multiple TAE and RSAE modes that have B
r
=B &
O10
3
. In quiet plasmas, these same diagnostics agree
with classical [14] and ion cyclotron [11] theory.
Moreover, similar profiles are measured with different
techniques during Alfve
´
n activity on JT-60U [18]. The
mode amplitudes are also measured by four independent
diagnostics [7]. The hypothesis that diagnostic inadequa-
cies account for the discrepancy between theory and ex-
periment is therefore excluded. Fast-ion transport is
remarkably effective in plasmas with Alfve
´
n activity.
Identification of the mechanism responsible for this trans-
port is an urgent task in burning plasma physics.
This work was funded by U.S. DOE Subcontract
No. SC-G903402 to U.S. DOE Contracts No. DE-FC02-
04ER54698, No. DE-AC02-76CHO3073, No. DE-FG03-
97ER54415, No. W-7405-ENG-48, and No. DE-FG02-
89ER53296.
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