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Title
An investigation of beam driven alfvén instabilities in the diii-d tokamak
Permalink
https://escholarship.org/uc/item/47j5f70z
Journal
Nuclear Fusion, 31(9)
ISSN
0029-5515
Authors
Heidbrink, WW
Strait, EJ
Doyle, E
et al.
Publication Date
1991
DOI
10.1088/0029-5515/31/9/002
Copyright Information
This work is made available under the terms of a Creative Commons Attribution
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University of California
AN INVESTIGATION OF BEAM DRIVEN
ALFVEN INSTABILITIES IN THE DIII-D TOKAMAK
W.W. HEIDBRINK*, E.J. STRAIT, E. DOYLE**,
G. SAGER***, R.T. SNIDER
General Atomics,
San Diego, California,
United States of America
ABSTRACT. Neutral beams were injected into low field (B = 0.7-1.0 T) deuterium plasmas in an attempt to
destabilize toroidicity induced Alfve'n eigenmodes (TAE modes). When the parallel beam velocity approached the
Alfve'n velocity and the volume averaged beam beta exceeded 2%, localized, propagating modes with n = 2-10
were observed. As much as 45% of the beam power was lost as a result of the modes. The threshold for TAE
instability is at least one order of magnitude higher than that predicted by Fu and VanDam (Phys. Fluids B 1
(1989) 1949).
1.
INTRODUCTION
To sustain ignition in a tokamak reactor, most of the
alpha particles produced in D-T fusion reactions must
thermalize in the plasma. If the energetic alpha popula-
tion drives collective instabilities that result in anomalous
losses of the alphas, the reactor will not ignite. There-
fore,
it is desirable, before construction of a reactor,
to assess the likelihood that alphas will drive collective
instabilities. In this paper, we describe experiments in
which neutral beam injection is employed to create an
energetic ion population that simulates the alphas. The
principal difference between a beam population and an
alpha population in a reactor is that the distribution of
beam ions is anisotropic in velocity space (the alpha
distribution is isotropic). In other regards, the beam
ion distribution effectively simulates alpha physics in
a 20 kV reactor such as the International Thermonuclear
Experimental Reactor (ITER) (Table
I).
Our experiments
are also relevant to neutral beam current drive with
~
1
MeV ions in future devices such as ITER [1].
If Alfve'n instabilities cause appreciable anomalous
losses or pitch angle scattering of the circulating beam
ions,
the current drive efficiency will be reduced and
a high plasma current will not be sustained. Finally,
destabilization of Alfve'n waves by energetic ions is of
fundamental interest, since super-Alfve'nic ion popula-
tions are common in space [2].
Permanent addresses:
* Physics Department, University of California, Irvine,
CA, USA.
** Electrical Engineering Department, University of California,
Los Angeles, CA, USA.
*** Nuclear Engineering Department, University of Illinois,
Urbana, IL, USA.
Destabilization of shear Alfve'n waves by circulating
fast ions has been explored theoretically by many
authors. In a homogeneous plasma, Alfve'n waves are
normal modes of the plasma that are weakly Landau
damped by electrons. The waves are analogous to
transverse waves on a string and propagate with a
phase velocity co/k| = v
A
= B/V47rn~m7, where the
'tension' of the string is provided by the magnetic
field B and the 'inertia' of the string is due to the ion
mass density ^iiv For instability, the waves must gain
enough energy from the fast ion distribution to overcome
electron damping. Fast ion distributions that are non-
monotonic in velocity space (dF/d\j > 0) can be
unstable through inverse Landau damping [3]. Although
these velocity space instabilities might be observed
transiently, steady state slowing down distributions
generally are monotonic in velocity space and thus
configuration space instabilities are of greater concern.
TABLE I. COMPARISON OF BEAM IONS IN
DIII-D AND ALPHAS IN ITER
Ratio Description
DIII-D ITER [1]
p
f
:pj:p
e
Gyroradii of fast ions, 6:1:0.16 10:1:0.16
thermal ions and electrons
v
e
:v
f
:Vi Velocities of electrons, 10:1:0.16 6:1:0.26
fast ions and thermal ions
/3
f
(0) Central fast ion pressure to S15% 2-4%
magnetic field pressure
v
(
/v
A
Fast ion velocity to sl.4 1.9
Alfve'n velocity
NUCLEAR FUSION, Vol.31, No.9 (1991)
1635
HEIDBRINK et al.
Because of the curvature drift in toroidal geometry,
circulating fast ions can resonate with Alfven waves
on different mode rational surfaces [4]. This provides
a mechanism to tap the free energy in the fast ion
pressure gradient. These so-called kinetic Alfve'n waves
(KAW) have radial eigenfunctions that are localized near
rational surfaces. A necessary condition for KAW
instability is that the beam parallel velocity exceed the
Alfve'n velocity v
B
/v
A
> 1. In contrast, global Alfve'n
eigenmodes (GAE) have radial eigenfunctions that span
most of the plasma [5]. Some eigenmodes have phase
velocities below the Alfve'n velocity and can therefore
resonate with beam ions of velocity as low as v
o
/v
A
= 0.5
[6].
Both the fast ion population and the plasma current
distribution affect GAE stability. Recent calculations
[7,
8] suggest that toroidal effects will stabilize these
modes in a reactor. Another class of Alfven waves with
globally extended eigenfunctions are the toroidicity
induced Alfve'n eigenmodes (TAE) [9]. These modes
arise owing to toroidal coupling between cylindrical
modes. Because the eigenfunction peaks between
rational surfaces, electron damping is predicted to be
smaller than for kinetic Alfve'n waves and the calculated
stability threshold is lower [10, 11]. A radially peaked
beam profile and v
B
/v
A
> 1 are necessary for TAE
instability [12]. Recent calculations predict that alphas
will drive low n (n is the toroidal mode number) TAE
modes unstable in a reactor [10, 12, 13] and that
extremely rapid diffusion of alphas will occur [14].
Intense neutral beam injection has been studied on
numerous tokamaks, but super-Alfve"nic populations
have been created relatively rarely. In the T-11 tokamak,
plasmas with v
s
/v
A
= 2 exhibited large voltage spikes
[15].
In Doublet III, fast ion losses were observed
when v
o
/v
A
— 1.3, but the results may have been due
to prompt orbit losses [16]. Low frequency instabilities
were observed in ISX-B [17] and JFT-2 [18] plasmas
with v
n
/v
A
= 1. Measurements of fluctuations in the
Alfve'n range of frequencies (50-1000 kHz) were not
performed in these previous experiments. Beam driven
instabilities with frequencies >50 kHz were observed
previously on PDX [19] and PBX [20], but the beam
ion populations were sub-Alfve'nic. Concurrently with
our study, Wong et al. [21] reported the observation
of TAE modes in TFTR.
This paper and the recent paper from PPPL [21]
report the first detailed studies of fast ion driven Alfve'n
instabilities in a tokamak. Since it can operate with small
values of the Alfve'n velocity and is equipped with intense
neutral beam injectors, the DIII-D facility is well suited
for studies of Alfve'n instabilities (Section 2). Instability
was only observed [22] when the parallel beam velocity
was close to the Alfve'n velocity and when the beam beta
(£2%) and the normalized beta (j3
n
= &aB/I £ 3.2)
were large (Section 3). The observed modes may be
toroidicity induced Alfven eigenmodes (Section 4). The
threshold for TAE instability is at least one order of
magnitude larger than predicted by simple analytic
formulas (Section 5).
2.
APPARATUS
An approximate expression for the growth rate of
TAE instability [10] is
co 4
_
_L)
F
_ £ ZA
2 /
e
v,
(1)
where j8
f
and
(3
e
are the local fast ion and electron beta,
respectively, co*
f
= -(m/r)(c/n
f
e
f
B)(dp
f
/dr) is the fast
ion diamagnetic frequency (m is the poloidal mode
number, e
f
, n
f
and p
f
are the fast ion charge, density
and pressure, respectively, and r is the minor radius),
F is proportional to the fraction of the fast ion distribu-
tion function that resonates with the mode, and the mode
frequency
u>
is approximately v
A
/2qR. Equation (1)
states that the beam drive (the first term on the RHS)
is opposed by electron damping (the second term
on the RHS). The beam drive is enhanced by large
beam beta (j6
f
), by a steep beam pressure gradient (w,
f
),
and by a distribution function with many resonant
particles (F). The wave particle resonance condition
is v
D
= v
A
/(2|m - nq|) [12]. Since the eigenfunction
for a gap mode peaks near q = (m + *)/n, this implies
that the beam ions must be nearly super-Alfve'nic
(
v
n
—
V
A)
f°
r
instability. The electron damping term
depends weakly on plasma temperature (ocVT
e
).
In terms of experimental operation, Eq. (1) suggests
the following prescription for Alfve'n instability:
—
Minimize the toroidal field to maximize j3
f
and
minimize v
A
;
—
Maximize the parallel beam velocity and beam
power;
—
Maximize the plasma mass-to-charge ratio to
minimize v
A
;
—
Use low to moderate plasma density; low density
increases /3
f
by reducing the slowing down time and
tends to minimize
/3
e
;
high density minimizes v
A
;
—
Obtain peaked profiles to maximize the beam density
gradient.
DIII-D [23] is well suited for Alfve'n instability
studies. Its low aspect ratio (a = 65 cm; major radius
1636
NUCLEAR FUSION. Vol.31, No.9 (1991)
BEAM DRIVEN ALFVEN INSTABILITIES IN DIII-D
CER
SOFT X-RAY
CHARGE
EXCHANGE
NEUTRAL
BEAM LINE
REFLECTOMETRY SCATTERING
FIG. 1. Plan view of the DIII-D tokamak. Eight neutral beam
sources housed in four beam boxes inject neutrals in the direction
of the plasma current. Active charge exchange measurements are
obtained by modulating one of the heating beams at 150°. The
neutral deposition is measured by the CER diagnostic that views
the nominally identical beam at 30°. Fluctuation diagnostics include
SXR cameras, a laser scattering diagnostic, microwave reflectometry,
a midplane Langmuir probe and numerous Mirnov coils (not shown).
Ro = 167 cm) and elongation
(K
—
2.0) permit low toroidal
field (£1.0 T), moderate density (n
e
- 5 x 10
13
cm'
3
),
moderate current (~
1
MA) operation without encoun-
tering density or q limits. Its neutral beams are intense
(£20 MW), energetic (£80 kV) and fairly tangential
(half of the sources inject at a tangency radius
R
tan
= 74 cm
and half of them inject at
R
tan
= 110 cm) (Fig. 1). The
neutral beams can be operated in either hydrogen or
deuterium. For 75 kV beam ions with R,
an
= 110 cm
that ionize on axis, the ratio of initial parallel velocity
v
yo = Rtan
v
o/Ro
t0
Alfve'n velocity v
A
is
0.53
1 -
2n
e
(2)
where n
13
is the electron density in units of 10
l3
cm"
3
,
B
T
is the magnetic field in T, n
H
/n
e
is the hydrogen
concentration and A
b
is the beam atomic mass. For
hydrogen injection (A
b
=1), super-Alfve'nic popula-
tions are readily obtained, while, for deuterium injection,
V
DO/
V
A ^ 1- However, the beam beta j3
f
is much smaller
for hydrogen injection than for deuterium injection,
since the beam power is smaller and the beam ion
slowing down time
T
S
is shorter (owing to the mass
dependence of
T
S
and the poorer confinement (lower T
e
)
generally obtained with H°
—
D
+
). In all the experiments
reported here, deuterium fill gas was used to maximize
niiTii. For the H°
—
D
+
experiments, helium glow discharge
cleaning, followed by deuterium discharge cleaning, was
employed after each discharge to minimize the concen-
tration of hydrogen in the plasma.
The principal fluctuation diagnostics (Fig. 1) were
soft X-ray (SXR) camera arrays [24] and extensive arrays
of electrostatically shielded Mirnov coils. For this study,
a poloidal array of 25 Mirnov loops (typically spaced
10-20° apart) and a toroidal array of eight loops near
the outboard midplane (with a variable spacing of 6-90°)
were employed. In principle, these arrays allow poloidal
mode numbers m £ 20 and toroidal mode numbers
n £ 30 to be detected. The electronics of the SXR
diagnostic passes signals up to 750 kHz. Data from
both diagnostics were archived at 500 kHz. A multi-
channel microwave reflectometer system [25] monitored
density fluctuations between 0 and 400 kHz for cut-off
layers below -2 x 10
l3
cm"
3
, which corresponded to
the plasma edge for these experiments. The far-infrared
(FIR) scattering system [26] was tuned to k = 2.5 cm'
1
and k = 5.0 cm"
1
to maximize the likelihood of detecting
the relatively long wavelength Alfve'n waves. For these
small values of k, the scattering volume encompassed
most of the plasma cross-section. Frequencies up to
1 MHz were monitored. Spectra from a floating
Langmuir probe situated ~ 1.4 cm behind the graphite
tiles in the horizontal midplane were obtained with a
spectrum analyser that swept between 100 kHz and
1 MHz every -120 ms. A DC break between the
probe and the spectrum analyser restricted the sensitivity
of this diagnostic to frequencies above
—
300 kHz.
The behaviour of the fast ions was diagnosed using
neutron scintillators during deuterium injection and
active charge exchange during hydrogen injection. The
neutron diagnostic [19, 27] has a maximum frequency
response of —20 kHz. For these experiments, the
charge exchange detector [28] was usually oriented to
intersect a heating beam near the centre of the plasma
(R = 169 cm) at a pitch angle (x = cos"
1
(v,/v) = 35°)
close to the angle of injection of the more tangential
beams. The heating beam was turned off for 10 ms
every 50 ms in order to measure the 'background'
signal from passive charge exchange and noise; the
difference between the charge exchange signal when
the beam is on and when it is off is the 'active' signal
from the volume where the charge exchange sightline
intersects the heating beam. Note that, since the beam
slowing down time was —45 ms in our H°— D
+
plasmas,
the beam ion population scarcely changed during
the 10 ms in which one of the beams was turned off.
For deuterium injection, interference associated with
2.5 MeV neutrons prevented valid charge exchange
measurements.
NUCLEAR FUSION, Vol.31, No.9 (1991)
1637
HEIDBRINK et al.
ION
EMISS
fRON
NEU1
tn
•n
a.
o
n/s)
M
o
vT
E
4
PASS B
u
200.0
100.0
0.0
-100.0
2.4
2.2
2.0
1.8
200.0
100.0
0.0
-100.0
1730 1734 173B
1742
TIME (ms)
1746 1750
FIG. 2. Signal from a Mirnov coil located near the outer midplane after digital filtering to remove
frequencies above 50 kHz (a) and below 100 kHz (c), together with the signal from a plastic scintillator (b).
Reductions in neutron emission correlate with high frequency bursts. At 1745 ms, B, = 0.8 T, I
p
= 0.7MA,
P
inj
= 13.1 MW and n
e
= 3.8 x 10
13
cm'
3
in a double-null divertor plasma.
Electron temperature and density were measured
with multichannel Thomson scattering [29] and by four
CO
2
interferometer chords. The effective ion charge
Z
eff
was inferred from Thomson scattering and multi-
channel visible bremsstrahlung data [30]. A multichannel
visible spectrometer system was tuned to measure the
helium charge exchange recombination line at 468.6 nm
for Tj measurements or H
a
light for beam deposition
measurements [31]; T
(
was also determined from the
neutron emission during H°
—
D
+
injection. In the
H°—•
D
+
experiments, the ratio of hydrogen density to
deuterium density was measured at the edge spectroscopi-
cally, using the ratio of H
a
light to D
a
light, and the
central deuterium concentration n
d
/n
e
was inferred
from the neutron emission at the end of a 2 ms
deuterium beam pulse [32].
3.
EXPERIMENT
3.1.
Instability data
In D°
—
D
+
plasmas with large beam and plasma
betas and relatively low Alfve'n velocity, instabilities
that may be related to TAE modes were observed. The
conditions for instability are summarized in Section 3.2;
here,
we describe the instabilities. Figure 2 shows
time traces from a magnetic probe near the outboard
midplane and from a neutron scintillator. The magnetic
probe trace has been digitally filtered to reveal a pair
of semi-continuous, low frequency modes (Fig. 2(a))
and bursts of high frequency oscillations (Fig. 2(c)).
Each high frequency burst correlates with a sudden
reduction in 2.5 MeV neutron emission (Fig. 2(b)).
These sudden reductions in neutron signal are an
indication that beam ions are lost from the plasma
centre at the bursts [19]. The magnitude (~6%) and
repetition rate (~ 220 Hz) of the neutron drops imply
a beam ion confinement time [19] of approximately
75 ms. Since the thermalization time v^ was approxi-
mately 60 ms in this discharge, this implies [33] that a
substantial fraction
(~45%)
of the beam power is lost
owing to these bursts.
These oscillations generally do not appear as a pure
mode in the Fourier spectrum (Fig. 3(a)). Figure 3(a)
shows the cross-power spectrum of the B
e
signals from
two magnetic probes that are spaced 45° toroidally
during the burst at 1746 ms shown in Fig. 2. The
toroidal mode numbers associated with the various
spectral peaks have been obtained from a separate
analysis using seven probes with toroidal spacings
down to 6° (Fig. 4). The semi-continuous low
1638
NUCLEAR FUSION, Vol.31, No.9 (1991)