Generation of Noninductive Current by Electron-Bernstein Waves on the COMPASS-D Tokamak

Abstract

Electron-Bernstein waves (EBW) were excited in the plasma by mode converted extraordinary (X) waves launched from the high field side of the COMPASS-D tokamak at different toroidal angles. It has been found experimentally that X-mode injection perpendicular to the magnetic field provides maximum heating efficiency. Noninductive currents of up to 100 kA were found to be driven by the EBW mode with countercurrent drive. These results are consistent with ray tracing and quasilinear Fokker-Planck simulations.

Full text

Generation of Noninductive Current by Electron-Bernstein Waves
on the COMPASS-D Tokamak
V. Shevchenko,
1
Y. Baranov,
1
M. O’Brien,
1
and A. Saveliev
2
1
EURATOM/UKAEA Fusion Association, Culham Science Centre, Abingdon, OX14 3DB, United Kingdom
2
Ioffe Institute, Politekhnicheskaya 26, 194021 St. Petersburg, Russia
(Received 24 July 2002; revised manuscript received 7 October 2002; published 10 December 2002)
Electron-Bernstein waves (EBW) were excited in the plasma by mode converted extraordinary (X)
waves launched from the high field side of the COMPASS-D tokamak at different toroidal angles. It has
been found experimentally that X-mode injection perpendicular to the magnetic field provides
maximum heating efficiency. Noninductive currents of up to 100 kA were found to be driven by the
EBW mode with countercurrent drive. These results are consistent with ray tracing and quasilinear
Fokker-Planck simulations.
DOI: 10.1103/PhysRevLett.89.265005 PACS numbers: 52.35.Hr, 52.50.Sw, 52.65.Ff
Electron-Bernstein waves (EBW) experience very lo-
calized damping on electrons at the electron cyclotron
resonance but, unlike the extraordinary (X) mode and the
ordinary (O) mode, the damping remains strong even at
high harmonics of the electron cyclotron (EC) frequency
!
ce
. EBW do not have any density cutoffs inside the
plasma and can, therefore, access plasmas of arbitrary
densities for frequencies above !
ce
. These features of
EBW present the possibility of efficient means for elec-
tron cyclotron resonance heating (ECRH) and current
drive in high beta plasmas, particularly in spherical
tokamaks, where the X-mode and O-mode propagation
into the plasma can be assured only at high !
ce
harmon-
ics leading to weak damping of these modes inside the
plasma. Plasma heating with the use of EBW excitation
via the O-X -B mode conversion mechanism has been
successfully demonstrated on the W7-AS stellarator [1].
EBW heating experiments with direct mode conversion
of the X mode, launched from the high field side (HFS), to
the EBW mode were carried out on theWT-3 tokamak [2].
In the present Letter, we present the first results of EBW
heating and current drive experiments conducted on the
COMPASS-D tokamak. COMPASS-D [3] presents a pos-
sibility for EBW excitation via direct mode conversion of
the X mode, launched from the HFS, to the EBW mode at
the upper hybrid resonance (UHR), allowing us to study
EBW plasma heating and current drive (see Fig. 1). Ac-
cording to cold plasma theory, the X mode is subject to
very weak damping at the !
ce
resonance for launch angles
nearly perpendicular to the magnetic field. Hence, the X
mode propagates to the UHR where it is always totally
converted to the EBW mode, with further absorption near
the !
ce
resonance. At launch angles far from perpendicu-
lar, the X-mode absorption becomes stronger, resulting in
predominant X-mode plasma heating. By varying the
toroidal launch angle, one can estimate the relative heat-
ing and current drive efficiencies of the X mode and the
EBW mode.
A highly reproducible plasma scenario has been chosen
for target plasma generation during these experiments
(see Fig. 2). The line averaged density, plasma current,
and central toroidal field were sustained at 1:8 
10
19
m
3
, 150 kA, and 2.05 T, respectively. A power of
600 kW at a frequency !=2 of 60 GHz with a constant
pulse duration of 100 ms was injected into the plasma at
the beginning of the flattop (100 ms) of plasma current
and density. The toroidal launch angle was changed shot
by shot in the range 32:6

from perpendicular, with a
step of 8:4

. ECRH power was injected with polar-
ization perpendicular to the magnetic field. Electron tem-
perature T
e
and density profiles n
e
were measured with
multipoint Thomson scattering (TS) every 50 ms. During
ECRH, the electron temperature appears to be noticeably
FIG. 1 (color online). Poloidal projection of EBW ray-tracing
results for the X mode launched from the HFS perpendicularly
to the magnetic field. Black areas correspond to strong damping
of EBWs.
VOLUME 89, NUMBER 26 P H Y S I C A L R E V I E W L E T T E R S 23 DECEMBER 2002
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higher for launch angles close to perpendicular to the
magnetic field, while the electron temperature profiles
do not show any significant transformation, such as peak-
ing or flattening, over the whole range of launch angles
[see Fig. 3(a)]. The central electron temperature, mea-
sured during ECRH, is plotted as a function of launch
angle in Fig. 3(b). The clear maximum at 0

launch angle
indicates higher heating efficiency with EBW excitation
than with the X-mode heating alone. The excess of the
maximum in electron temperature at perpendicular
launch is well above the error bars of the TS measure-
ments. The temperature was measured at 2 times during
the ECRH pulse. The electron temperature measured at
129 ms has the same dependence on the launch angle as
the temperature measured at 179 ms, so, evidently, en-
hanced plasma heating with perpendicular injection is
not a transient effect.
Changes in the surface loop voltage, V
loop
, required to
maintain constant plasma current during ECRH, do not
have any obvious dependence on the launch angle.
Typically the plasma was sustained at a central electron
temperature of 1.5 keV and a loop voltage of about 0.9 V
before ECRH injection. During ECRH the loop voltage
usually dropped down to the value of 0.5 V with slight
variations within 0.1 V over the range of launch angles.
Because of the temperature changes, one would expect
much greater reductions in the loop voltage, especially at
launch angles close to perpendicular when the electron
temperature reaches 3.5 keV. For instance, the loop volt-
age drops down to values less than 250 mV when ECRH
of the same power is employed at 2!
ce
in plasmas with
similar current and electron temperature before and dur-
ing ECRH injection. Such a big drop in loop voltage is
consistent with the plasma resistance (  T
3=2
e
) reduc-
tion during second harmonic ECRH .
Using the Poynting formulation for the plasma power
balance, we have
V
loop
 V
res

1
I
p
d
dt

LI
2
p
2

; (1)
where the first term V
res
is the voltage drop due to the
plasma resistance and the second term is responsible for
the voltage drop due to plasma current I
p
and plasma
inductance L variations. The plasma inductance is ob-
tained from the magnetic equilibrium reconstruction.
Typical behavior of the inductive term during ECRH is
shown in Fig. 2. One can see that loop voltage variations
-40 -30 -20 -10 0 10 20 30 40
1.5
2.0
2.5
3.0
3.5
-5 0 5 10 15 20 25
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
(b)
Central Electron Temperature, keV
Launch Angle, deg
T
e
-79ms
T
e
- 129 ms
T
e
- 179 ms
T
e
- 229 ms
(a)
0
o
launch
-32.6
o
launch
+32.6
o
launch
79 ms, Ohmic
Electron Temperature, keV
Z, cm
FIG. 3. (a) Electron temperature profiles measured with and
without ECRH. (b) Central electron temperature at different
times versus toroidal launch angle (measured from perpendicu-
lar). Vertical size of the symbols corresponds to the typical
error bars of TS measurements.
0.0 0.1 0.2 0.3
1.0
1.5
2.0
2.5
(S
SXR
/n
e
2
)(W
dia
/n
e
)
-1/2
Z
eff
,a.u.
Time, s
-0.4
-0.2
0.0
0.2
0.4
(2I
p
)
-1
d/dt(L
p
I
p
2
)
U
L
,V
0
50
100
150
Shot #30273
Plasma Current
I
p
,kA
0
5
10
15
Line Integrated Density
<N
e
l>, 10
18
m
-2
0
200
400
600
TS snaps
ECRH Power
P
ECRH
,kW
0.0
0.5
1.0
1.5
Loop Voltage
U
loop
,V
FIG. 2. Waveforms of main plasma parameters during EBW
experiments on COMPASS-D.
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due to the inductive part are significant only transiently
when ECRH is switched on and off, while in the middle
of the ECRH pulse the induced voltage is close to zero.
Thus, we can conclude that the loop voltage variations
during ECRH are mainly defined by the plasma conduc-
tivity changes and noninductive currents driven in the
plasma. The plasma conductance (
p
 Z
1
eff
T
3=2
e
) varia-
tions can be attributed only to the effective plasma ion
charge Z
eff
and T
e
. Z
eff
behavior during the shot can be
analyzed qualitatively with the use of soft x-ray (S
SXR
)
signals. T
e
and n
e
profile shapes are measured not to
change during the ECRH pulse, and we assume that the
Z
eff
profile also remains unchanged. Using relations for
measured S
SXR
and plasma diamagnetic energy W
dia
:
S
SXR
 Z
eff
n
2
e
T
1=2
e
and W
dia
 n
e
T
e
, one can write Z
eff

S
SXR
=n
2
e
W
dia
=n
e

1=2
. Estimations, conducted in this
way, indicate an almost constant value of Z
eff
during
the first half of the ECRH pulse and a gradual increase
during the second half with some remaining growth
afterwards, as illustrated in Fig. 2. Z
eff
reaches a new
stationary value typically 30 ms after the ECRH pulse.
The total growth is usually about 25%, which can be
attributed to the increase of the impurity flux from the
antenna during ECRH injection and afterwards. Thus,
assuming for simplicity that Z
eff
does not change during
the shot, the noninductive current driven in the plasma
can be estimated from the experimental V
loop
and T
e0
with the use of the simple relation,
I
CD
 I
p
 I
ECRH
BS
I
p
 I
OH
BS

V
ECRH
loop
V
OH
loop

T
ECRH
e0
T
OH
e0

3=2
; (2)
where the plasma current I
p
is fixed (150 kA), and the
bootstrap current I
OH
BS
during the Ohmic heating phase, as
estimated with the Fokker-Plank code [4], is about 12 kA,
while during ECRH it varies from 15 to 21 kA over the
range of launch angles. In order to take into account the
small Z
eff
growth during the second half of the ECRH
pulse and afterwards, the correction factor Z
OH
eff
=Z
ECRH
eff
has to be applied to the last term in formula (2). The
results are plotted in Fig. 4, from which it is clear that
quite a large current, up to 100 kA, must be driven in a
direction counter to the plasma current in order to main-
tain almost constant loop voltage over the range of elec-
tron temperatures during ECRH. The maximum of the
driven current corresponds to launch angles close to per-
pendicular to the magnetic field. At perpendicular launch,
only a small fraction of the injected power ( & 10%)is
absorbed in the plasma as the X mode, while the main
part of the power is converted into the EBW mode and
then absorbed near the !
ce
resonance. This indicates that
the EBW mode is responsible for the noninductive current
driven in this case. The scatter in the driven current
estimated from experimental data can mainly be attri-
buted to the scatter in electron temperature measure-
ments. TS measurements are taken instantly and the result
is very sensitive to the plasma activity. The other experi-
mental measurements used in the above analysis are
typically averaged over the plasma volume or smoothed
in time.
A new EBW ray-tracing code has been developed for
EBW current drive (CD) modeling in COMPASS-D. The
plasma equilibrium obtained from magnetic equilibrium
reconstruction and the electron density and temperature
profiles measured with TS were used as input parameters
for the EBW ray-tracing code. This code allows estima-
tion of power deposition profiles with relevant wave vec-
tor k profiles for both the X mode and the EBW mode in a
full tokamak equilibrium. These results have been used as
input data for a quasilinear relativistic Fokker-Planck
code [5], modified for EBW applications, in order to
simulate currents driven by the X mode and by the
EBW mode alone. The results of EBW CD modeling
including trapped electron effects are summarized in
Fig. 4. The X-mode driven current spans the range from
14 to 20 kA and becomes zero at angles close to per-
pendicular to the magnetic field. The current driven by
EBWdoes not change sign over the range of launch angles
and reaches a maximum of about 80 kA at perpendicu-
lar launch. The net ECRH driven current is predominantly
defined by the EBW fraction and is in good agreement
with experimental results. Estimates of the normalized
experimental EBW current drive efficiency give the value
of 
20CD
 R
0
n
e
I
CD
=P
ECRH
 0:035 (10
20
A=Wm
2
),
which is higher than the typical figure for O=X-mode
current drive but less efficient than for lower hybrid
current drive.
It was found from modeling that with the existing
antenna setup the EBW power deposition profile is located
well below the midplane for all negative and positive
-40 -30 -20 -10 0 10 20 30 40
-140
-120
-100
-80
-60
-40
-20
0
20
40
X-mode CD
EBW-mode CD
Net CD
Driven Current, kA
Launch Angle, deg
FIG. 4. Noninductive current driven in the plasma estimated
from experimental data and ray-tracing results for currents
driven by the X mode, the EBW mode alone, and the net
current due to ECRH. Circles and squares correspond to time
slices as in Fig. 3.
VOLUME 89, NUMBER 26 P H Y S I C A L R E V I E W L E T T E R S 23 DECEMBER 2002
265005-3 265005-3

toroidal launch angles (see Fig. 1). EBW driven current is
distributed in the range of 0:05a to 0:7a with the maxi-
mum at the radius of 0:3a as illustrated in Fig. 5. In-
terestingly, for the HFS launch geometry in COMPASS-D
the k
k
k  B=jBj (here B is a vector of local magnetic
field) related to the EBW fraction always becomes posi-
tive as the wave approaches the EC resonance independent
of the toroidal launch angle, and it changes sign to nega-
tive if the plasma current is reversed. In other words, for
the existing launch configuration, Bernstein waves always
drive current in the direction counter to the plasma cur-
rent (see Fig. 6). This is because of the influence of the
poloidal field as described below. The predicted magni-
tude of the current driven by EBW is proportional to the
power of the X mode reaching the UHR layer. The sign of
the driven current depends only on the EBW power de-
position profile with respect to the midplane or more
precisely to the magnetic axis. The power absorbed in
the plasma above the midplane generates current in the
codirection, while the power absorbed below the mid-
plane always generates current in the counterdirection. A
similar result has been numerically obtained for EBW
launched off midplane perpendicularly to the magnetic
field [6]. Our modeling shows that the direction of EBW
CD changes to opposite if the direction of the toroidal
field is reversed. Unfortunately, experiments with re-
versed toroidal magnetic field have not been possible. In
general, the sign of the driven current is determined by
the sign of k
k
=!
ce
 ! in the absorption region. In
tokamak plasmas usually B
’
 B

, where ’ and  are
the toroidal and poloidal components, respectively,
hence, k
k
 k
’
 k

B

=jBj. In the UHR layer EBW has
typically jk

B

=jBjj  jk
’
j, except for the vicinity of the
midplane, thus the sign of k
k
is mainly determined by
the sign of k

B

=jBj. As EBW propagates deeper into the
plasma, k

is developed, due to poloidal plasma inhomo-
geneity, resulting in a different sign of k
k
above and below
the midplane. Moreover, k

B

=jBj changes sign if the
plasma current is reversed and remains unchanged if
the toroidal field is reversed.
In summary, we have shown that the perpendicularly
launched X mode from the HFS of the tokamak provides
more efficient plasma heating at fundamental EC reso-
nance in comparison with the angular launch. Non-
inductive currents up to 100 kA were found to be driven
in the direction counter to the Ohmic current. Mainly
EBWs, which are efficiently mode converted from the X
mode in the UHR layer, are responsible for CD induced in
the plasma. The results are in good agreement with EBW
ray tracing and nonlinear Fokker-Plank modeling.
The authors thank Professor A. D. Piliya for his crucial
role in the EBW ray-tracing code development, and Dr. M.
Shoucri and Dr. I. Shkarovsky for providing the Fokker-
Planck code. This work was jointly funded by U.K.
Department of Trade Industry and EURATOM.
[1] H. P. Laqua et al., Phys. Rev. Lett. 78, 3467 (1997).
[2] T. Maekawa et al., Phys. Rev. Lett. 86, 3783 (2001).
[3] G. A. Whitehurst et al.,inProceedings of the 22nd EPS
Conference on Controlled Fusion and Plasma Physics,
Bournemouth, 1995 (The European Physical Society,
Abingdon, United Kingdom, 1995), Vol. 19C, p. I-345.
[4] M. O’Brien et al.,inProceedings of IAEA TCM on Ad-
vanced Simulations and Modelling of Thermonuclear
Plasma, Montreal, 1992 (IAEA, Vienna, 1993), p. 527.
[5] M. Shoucri and I. Shkarovsky, Comput. Phys. Commun.
82, 287 (1994).
[6] C. B. Forest et al., Phys. Plasmas 7, 1352 (2000).
0.0 0.2 0.4 0.6 0.8 1.0
0
1
2
3
J
EBW
,10
6
A/m
2
Normalized minor radius, r/a
0
o
launch
+16.7
o
launch
- 16.7
o
launch
+32.6
o
launch
- 32.6
o
launch
FIG. 5. The radial profiles of the current density generated by
EBW mode alone for different launch angles.
30 40 50 60 70 80
-40
-30
-20
-10
0
10
20
30 40 50 60 70 80
-40
-30
-20
-10
0
10
20
ECR layer
I
p
,B
t
Y, cm
X, cm
ECR layer
I
p
,B
t
Y, cm
X, cm
FIG. 6 (color online). Toroidal projections of EBW ray-
tracing results for toroidal launch angles of 16:7

(left) and
16:7

(right). Black areas correspond to strong damping
of EBWs, where k
k
> 0 and !>!
ce
. Note sgnI
CD

sgnk
k
=!
ce
 !.
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