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Title
Sawtooth control using electron cyclotron current drive in ITER demonstration plasmas in
DIII-D
Permalink
https://escholarship.org/uc/item/8c90671v
Journal
Nuclear Fusion, 52(6)
ISSN
0029-5515
Authors
Chapman, IT
La Haye, RJ
Buttery, RJ
et al.
Publication Date
2012-06-01
DOI
10.1088/0029-5515/52/6/063006
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 and INTERNATIONAL ATOMIC ENERGY AGENCY NUCLEAR FUSION
Nucl. Fusion 52 (2012) 063006 (8pp) doi:10.1088/0029-5515/52/6/063006
Sawtooth control using electron cyclotron
current drive in ITER demonstration
plasmas in DIII-D
I.T. Chapman
1
, R.J. La Haye
2
, R.J. Buttery
2
, W.W. Heidbrink
3
,
G.L. Jackson
2
, C.M. Muscatello
3
, C.C. Petty
2
, R.I. Pinsker
2
,
B.J. Tobias
4
and F. Turco
5
1
Euratom/CCFE Fusion Association, Culham Science Centre, Abingdon, OX14 3DB, UK
2
General Atomics, PO Box 85608, San Diego, CA 92186-5608, USA
3
University of California, Irvine, CA 92697, USA
4
Princeton Plasma Physics Laboratory, Princeton, NJ 08543, USA
5
Department of Applied Physics and Applied Mathematics, Columbia University, New York,
USA
E-mail: ian.chapman@ccfe.ac.uk
Received 16 December 2011, accepted for publication 22 March 2012
Published 17 April 2012
Online at
stacks.iop.org/NF/52/063006
Abstract
Sawtooth control using electron cyclotron current drive (ECCD) has been demonstrated in ITER-like plasmas with
a large fast ion fraction, wide q = 1 radius and long uncontrolled sawtooth period in DIII-D. The sawtooth period
is minimized when the ECCD resonance is just inside the q = 1 surface. Sawtooth destabilization using driven
current inside q = 1 avoids the triggering of performance-degrading neoclassical tearing modes (NTMs), even at
much higher pressure than required in the ITER baseline scenario. Operation at β
N
= 3 without 3/2 or 2/1 NTMs
has been achieved in ITER demonstration plasmas when sawtooth control is applied using only modest ECCD
power. Numerical modelling qualitatively confirms that the achieved driven current changes the local magnetic
shear sufficiently to compensate for the stabilizing influence of the energetic particles in the plasma core.
1. Introduction
It is well known that tokamak macroscopic instabilities are
primarily driven by steepening gradients in the current density
or the pressure. Sawtooth oscillations are the manifestation
of the n = m = 1 internal kink mode, one such
magnetohydrodynamic (MHD) instability, characterized by
quasi-periodic collapses in the temperature and density in the
plasma core (here, m and n are the poloidal and toroidal
periodicity of the wave). However, minority populations of
super thermal ions can delay the onset of these instabilities,
thereby improving confinement properties of tokamaks and
allowingsteeper pressure and current gradients to develop. The
presence of fusion-born alpha particles in ITER is predicted to
significantly lengthen the time between consecutive sawtooth
crash events [1–4]. This means that when the sawtooth crash
occurs in the presence of stabilizing fast ions it is often
more violent and more likely to trigger neoclassical tearing
modes (NTMs), leading to a degradation in pressure and thus
in fusion performance. Indeed, long period sawteeth are
empirically shown to be more likely to trigger NTMs [5].
Consequently there is much interest in control schemes which
can maintain small, frequent sawtooth crashes which avoid
seeding deleterious NTMs.
When electron cyclotron resonance heating (ECRH) is
applied to the plasma, a change in the local current density
occurs due to the change in the temperature, and subsequent
change in the conductivity. When applied in the vicinity of
the resonant surface associated with the internal kink mode,
q = 1, this has the consequence of moving the radius of
the q = 1 surface, r
1
, and changing the magnetic shear
at q = 1, s
1
, thus affecting the likelihood of a sawtooth
crash. Here, the safety factor is q = dψ
φ
/dψ
θ
and the
magnetic shear is s = r/qdq/dr with ψ
θ
and ψ
φ
the poloidal
and toroidal magnetic fluxes respectively. Furthermore, by
adding a toroidal component to the wave vector of the
launched EC waves, an ancillary electron cyclotron driven
current results either parallel (co-electron cyclotron current
drive (ECCD)] or anti-parallel (counter-ECCD) to the ohmic
current, enhancing the potential to change s
1
. Figure 1
shows the case when ECCD is applied inside the q = 1
surface, where the local change in current density results in
an increase in the gradient of the q-profile at q = 1. Here
the blue current density profile is a typical H-mode profile
0029-5515/12/063006+08$33.00 1 © 2012 IAEA, Vienna Printed in the UK & the USA
Nucl. Fusion 52 (2012) 063006 I.T. Chapman et al
Current Density
q
Radiu
s
r
1
q=1
Figure 1. When ECCD is applied, a local perturbation to the current
density profile (red, where blue is the usual H-mode profile) results
in the q = 1 radius moving outwards and the magnetic shear
increasing.
with bootstrap peak near the edge, whereas the red curve
shows the ancillary electron cyclotron driven current inside
q = 1. The control of sawtooth oscillations in tokamaks
through noninductively driven currents has been demonstrated
on a number of machines [6–13], and consequently has
been included in the design of the sawtooth control system
for ITER [14, 15]. The history of sawtooth control using
current drive is reviewed in reference [16]. It is worth
noting that the control of sawteeth for NTM prevention using
ECCD has been demonstrated directly on ASDEX Upgrade:
Reference [17] shows that NTMs are avoided at high pressure
by complete suppression of the sawteeth using co-ECCD just
outside the q = 1 surface. Concomitant with the end of the
gyrotron pulse, a sawtooth crash occurred and an NTM was
triggered, resulting in a substantial degradation of the plasma
performance. However, it is widely accepted that sawteeth
cannot be avoided throughout an ITER discharge, and so a
similar demonstration of avoidance of NTMs with deliberately
accelerated frequent sawteeth is required. Furthermore,
experiments in JET demonstrated sawtooth destabilization and
consequent avoidance of NTMs, even at high β
N
in H-mode
[18, 19]. However, these experiments used ICRH as the control
actuator, rather than ECCD as reported here and planned for
ITER. Recently, the mechanism of sawtooth control when
using ICRH has been explained by tailoring the phase space of
the fast ion distribution [20, 21], so direct comparison between
the JET ICRH results and ECCD sawtooth control is complex.
The fundamental trigger of the sawtooth crash is thought
to be the onset of an m = n = 1 mode, although the dynamics
of this instability are constrained by many factors including not
only the macroscopic drive from ideal MHD, but collisionless
kinetic effects related to high energy particles [22–24] and
thermal particles [25, 26], as well as non-ideal effects localized
in the narrow layer around q = 1. A heuristic model
predicts that a sawtooth crash will occur in the presence of
energetic ions when various criteria are met [1, 27, 28], with the
defining one usually given in terms of a critical magnetic shear
determined either by the pressure gradient, s
1
>s
crit
(ω
∗i
),or
by the mode potential energy, written as
s
1
> max
s
crit
=
4δW
ξ
2
0
2
1
RB
2
c
ρ
ˆρ
,s
crit
(ω
∗
)
, (1)
where c
ρ
is a normalization coefficient of the order of unity,
ˆρ = ρ
i
/r
1
, ρ
i
is the ion Larmor radius, R is the major radius, B
is the toroidal field,
1
= r
1
/R, ξ
0
is the magnetic perturbation
at the magnetic axis and ω
∗i
is the ion diamagnetic frequency.
The change in the kink mode potential energy is defined such
that δW = δW
core
+ δW
h
and δW
core
= δW
f
+ δW
KO
where
δW
KO
is the change in the mode energy due to the collisionless
thermal ions [25], δW
h
is the change in energy due to the fast
ions and δW
f
is the ideal fluid mode drive [29].
The remaining concern about current drive control is
whether changes in s
1
can overcome the stabilization arising
from the presence of energetic particles. In ITER, the fusion-
born α particles are likely to give rise to a large stabilizing
potential energy contribution, δW
h
in the internal kink mode
dispersion relation, which coupled with the small ˆρ in the
denominator of equation (1) means the critical shear to drive the
internal kink mode unstable is increased. The result is that the
change in the magnetic shear may need to be prohibitively large
in order to compete with the kinetic stabilization, especially if
the fast ions arising from concurrent ion cyclotron resonance
heating (ICRH) and neutral beam injection (NBI) heating
exacerbate the situation [4]. Consequently, recent experiments
have focussed on destabilizing sawteeth using ECCD in the
presence of energetic particles. Sawtooth destabilization of
long period sawteeth induced by ICRH generated core fast
ions with energies 0.5 MeV was achieved in Tore Supra,
even with modest levels of ECCD power [30, 31]. Similarly,
ECCD destabilization has also been achieved in the presence
of ICRH accelerated NBI ions in ASDEX Upgrade [32]as
well as with normal NBI fast ions in ASDEX Upgrade [7] and
JT-60U [33]. Despite these promising results, destabilization
of so-called monster sawteeth—that is to say sawteeth with
periods longer than the energy confinement time, and hence
saturated central plasma temperature—in the presence of a
significant population of highly energetic particles at high β
h
(where β
h
is the fast ion pressure divided by the magnetic
pressure) has yet to be demonstrated in ITER-like conditions.
This paper aims to address this issue. In section 2 sawtooth
control in ITER demonstration plasmas is demonstrated in
DIII-D for long sawteeth in the presence of energetic NBI
ions. After demonstrating the optimal deposition for ECCD
in order to destabilize the sawteeth, the improvement in fusion
performance with sawtooth control is discussed in section 3.In
section 4 the effect of changing the magnetic shear is compared
with the stabilizing drive from the fast ions using numerical
simulation, before the implications of this work are discussed
in section 5.
2. Sawtooth control using ECCD in the presence of
energetic ions
ITER baseline demonstration plasmas have been developed
on DIII-D [34] to match many of the anticipated operating
parameters for ITER [35]: the plasma cross-section matches
2
Nucl. Fusion 52 (2012) 063006 I.T. Chapman et al
n (10
20
m
–3
)
P
NBI
(MW)
P
ECH
(MW)
n=1 rms
q
min
β
N
2
136345
(a)
(b)
(c)
(d)
(e)
(f)
1
0
2
0
1
Time (s)
2345
6
2
4
2
3.5
2.5
0.5
–
Figure 2. Time traces for a DIII-D shot 136345 which is a typical
ITER demonstration plasma with I
p
= 1.45 MA, B
T
= 1.92 T and
W
h
/W
f
≈ 0.2. (a) The density is relatively constant and allows the
pedestal collisionality to match that expected in ITER. (b) The NBI
power (modulation averaged over 100 ms here) is in β
N
feedback.
(c) The ECH power is directed off-axis to keep the density low.
(d) β
N
= 1.8 is kept constant and ITER baseline level. (e) The
plasma sawtooths throughout and (f ) q
min
is just below one,
resulting in a broad low-shear region expected in ITER ELMy
H-modes.
the ITER design scaled by a factor of 3.7; the plasma
confinement and normalized pressure match the target values
for ITER, namely H
98,y2
= 1.0 and β
N
= 1.8, where H
98,y2
is the energy confinement enhancement factor, β
N
= βaB
0
/I
p
where a is the minor radius, I
p
(MA) is the plasma current,
β = 2µ
0
p/B
2
0
and ··· represents an averaging over
the plasma volume and p is the plasma pressure; the field
(B
T
= 1.9 T) and current (I
p
= 1.45 MA) are set such that
I/aB = 1.415 which equates to I
p
= 15 MA in ITER; the
resultant safety factor at the 95% flux surface, q
95
= 3.1is
close to the ITER design value of 3.0; the density is set in
such a way that the pedestal collisionality is matched to that
expected in ITER; and finally, there is a broad low-shear region
of the safety factor resulting in ρ
1
= 0.35 approaching the
ρ
1
= 0.45 value expected in ITER (notwithstanding the large
error bar associated with this in the transport modelling). A
typical ITER demonstration plasma is illustrated in figure 2.
The plasma experiences monster sawteeth throughout, with
an average sawtooth period of τ
st
= 265 ms compared with
an energy confinement time of τ
E
= 220 ms. Scaling the
sawtooth period by the resistive diffusion time [36] and r
1
,
this period is roughly equivalent to 50 s in ITER, which is
approaching the expected critical sawtooth period likely to seed
NTMs [5].
Tearing mode activity is present throughout, with a benign
m/n = 4/3 tearing mode persisting throughout most of the
discharge, though not affecting confinement significantly, and
a m/n = 2/1 tearing mode triggered by a sawtooth crash near
the end of the flat-top (after the off-axis ECCD near q = 2
is turned off). Constant off-axis broad-deposition electron
cyclotron heating (ECH) is required to attain low density, likely
to work by driving an electron-temperature gradient mode in
the locality of the EC resonance, and to avoid a disruptive 2/1
mode. The off-axis ECCD near q = 2 is broad (in the sense
that it is broader than islands present in the plasma) and not
modulated, meaning that it is not optimized for stabilizing any
NTMs occurring in the plasma. In the plasmas reported here,
only co-current on-axis NBI is used. Whilst DIII-D is equipped
with both counter-current and off-axis neutral beams, both
have been shown numerically and empirically to destabilize
the internal kink mode and result in shorter sawtooth periods
[37–40]. Given that the aim of this paper is to demonstrate
the efficacy of ECCD destabilization in the presence of fast
ions, any ancillary sources of sawtooth destabilization are
omitted. This has the consequence that these DIII-D plasmas
have relatively high injected torque and thus rotate faster than
the toroidal frequency expected in ITER. It should be noted
that this differential rotation is likely to influence the potential
coupling between the 1/1 internal kink mode associated with
the sawteeth and higher m/n NTMs.
An important difference between these plasmas and the
ITER baseline scenario is the fraction of energetic particles.
The NBI induced fast ions constitute approximately 15% of
the stored energy, whereas the fusion-born alpha particles in
ITER, combined with NBI and ICRH fast ions, result in a fast
ion fraction (β
h
/β) in ITER approaching 45% (β
α
from
reference [41], β
NBI
from reference [42]).
The ECCD resonance was swept by performing very
slow ramps in the toroidal field, commensurate with slow
ramps in plasma current to keep the q-profile constant. These
ramps, which are typically only 6% variation over 2500 ms,
are necessarily slow since the sawtooth period was sometimes
longer than half a second and the ramps must proceed
sufficiently slowly that the optimal deposition location for
sawtooth destabilization can be inferred. Figure 3 shows
the EC driven current predicted by the TORAY-GA code
[43, 44]. Both the off-axis EC absorption location and the
amplitude of the driven current is relatively insensitive to
the sweep in the toroidal field because the rays are nearly
tangent to the flux surface due to the ray refraction at large
minor radius. Conversely, the 12% difference in toroidal field
between discharges 145688 and 145692 results in the on-axis
EC resonance location moving in the range ρ
EC
∈ [0.17, 0.35],
which spans a significant region both inside and outside the
q = 1 radius considering the relatively narrow ECCD width.
The fact that the off-axis EC deposition is relatively invariant
ensures that no adverse changes to current density profile affect
tearing stability at higher m/n rational surfaces and allow low
target density to be retained throughout to achieve a high fast
ion fraction.
The sawtooth behaviour in typical ITER demonstration
plasmas in DIII-D is shown in discharge 145861 in figure 4.
Here the 1.4 MW of ECH is directed off-axis to achieve a low
density and thus W
h
/W
total
= 0.12. The sawteeth are regular
with an average sawtooth period of 260 ms and the β
N
is kept
fixed by feedback on the auxiliary NBI power during the very
small I
p
,B
T
ramp. Also shown is a comparison shot with core
ECCD applied inside q = 1, with the sweep in field and current
moving the deposition from well inside q = 1 towards r
1
,but
not crossing q = 1. It is clear that the average sawtooth period
drops significantly and the shortest sawteeth are 125 ms, less
than half the uncontrolled period. This is a clear demonstration
3
Nucl. Fusion 52 (2012) 063006 I.T. Chapman et al
60
r
inv
q=2
q=2
145692 at t=4.065 s
145688 at t=4.065 s
r
inv
40
20
0
j
EC
(A cm
–2
MW
–1
)
120
80
40
0
0.20.0 0.4
ρ
0.6 0.8 1.0
Figure 3. The electron cyclotron driven current and heating profiles
for discharge 145692 when the core deposition is centred at
ρ = 0.35 and for shot 145688 when the core ECCD is at ρ = 0.17.
Despite the large sweep in core EC deposition, the off-axis
deposition remains almost unchanged.
2
145861
145859
β
N
1
4
P
ECH
(MW)n=1 rms
4
2
23
Time (s)
45
3
2
1
0
0.0
145859
145861
0.1
0.2
0.3
Sawtooth
Period (s)
Figure 4. The normalized beta, ECH power and n = 1 mode
activity for shots 145861 (no core ECCD) and 145859 (with core
ECCD). It is clear that the sawtooth frequency increases by
approximately 50% when there is ECCD just inside q = 1.
of robust sawtooth control in the presence of a significant
population of energetic particles. In this discharge 1.5 MW of
ECCD (compared with P
aux
= 5 MW) was required to reduce
the sawtooth period by 50%.
By performing a series of sweeps in field and current, the
deposition location of the ECCD can be moved from near the
magnetic axis to well outside the q = 1 surface, noting that
the inversion radius does move slightly as the ECCD resonance
moves. The field and current sweeps were performed in both
directions so that any hysteresis in the sawtooth period would
be evident. Figure 5 shows the sawtooth period as a function of
Sawtooth Period (ms)
Lower field and current
900
800
–0.3 –0.2 –0.1 0.0
ρ
dep
– ρ
1
0.1 0.2
700
600
500
400
300
200
100
0
Higher field and current
Mid field and current
Uncontrolled averaged low l
p
/B
T
Uncontrolled averaged high l
p
/B
T
Uncontrolled averaged mid l
p
/B
T
Figure 5. The sawtooth period as a function of the difference of the
q = 1 radius and the peak EC deposition radius, shown with a
best-fit third order polynomial to guide the eye. It is evident that the
sawtooth period is minimized when the ECCD is localized a small
distance inside the q = 1 surface, as expected. This is a clear
demonstration of such behaviour in H-mode plasmas with a large
fast ion fraction.
the difference between the EC resonance location calculated
by TORAY-GA and the inversion radius, here considered as
representative of the q = 1 surface. The inversion radii are
calculated by looking for inversion on the electron cyclotron
emission diagnostic, which has a radial resolution of 1 cm, the
soft x-ray diagnostic which has resolution of 2.5 cm and finally
by matching the mode frequency to the rotation profile from
charge exchange recombination spectroscopy. It is clear that
the minimum in sawtooth period occurs when the ECCD has
a resonance just inside the q = 1 surface, as one would expect
[8, 16], since this maximizes the local magnetic shear at q = 1.
That this strong correlation—which has previously been shown
in L-mode and low power plasmas [7, 8, 12, 45–47]—persists
in the presence of energetic ions is encouraging and shows
that ECCD is an applicable actuator in ITER plasmas. The
optimal destabilization occurs for a broad range of deposition,
ρ
dep
− ρ
1
∈ [−0.2, −0.03].
3. Improved performance using ECCD sawtooth
control in ITER demonstration plasmas
As discussed in section 2, the ITER demonstration plasmas
in DIII-D are susceptible to performance-degrading tearing
modes (either 3/2 or 2/1), even at the relatively modest
normalized pressure of β
N
= 1.8. That is not to say that tearing
modes are ubiquitous in these plasmas, but they are common
depending upon subtle nuances of the current profile [48],
even more so at low applied torque. The most deleterious
instability is the m/n = 2/1 NTM which is usually triggered
by an edge-localized mode (ELM) or a sawtooth crash that
triggers an ELM or by a sawtooth alone. Whilst stabilization
of the 2/1 NTM has been shown to lead to much improved
performance in DIII-D [49], it is preferable to avoid triggering
the NTMs by utilizing sawtooth control. NTM control requires
ECCD power near q = 2 which means that it does not usefully
heat the core of the plasma, whereas the ECCD for sawtooth
control described in section 2 is inside q = 1. Furthermore,
4
