Measurements of Mode Converted Ion Cyclotron Wave
with Phase Contrast Imaging in Alcator C-Mod and
Comparisons with Synthetic PCI Simulations in TORIC
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Citation
Tsujii, N. et al. “Measurements of Mode Converted Ion Cyclotron
Wave with Phase Contrast Imaging in Alcator C-Mod and
Comparisons with Synthetic PCI Simulations in TORIC.” AIP
Conf. Proc., Vol. 1187, Proceedings of the 18th Topical
Conference on Radio Frequency Power in Plasmas, 2009. 6568. ©2009 American Institute of Physics.
As Published
http://dx.doi.org/10.1063/1.3273838
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American Institute of Physics
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Final published version
Accessed
Thu May 26 09:57:19 EDT 2016
Citable Link
http://hdl.handle.net/1721.1/66299
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and may be subject to US copyright law. Please refer to the
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Detailed Terms
Measurements of Mode Converted Ion Cyclotron
Wave with Phase Contrast Imaging in Alcator
C-Mod and Comparisons with Synthetic PCI
Simulations in TORIC
N. Tsujii, M. Porkolab, E. M. Edlund, L. Lin, Y. Lin, J. C. Wright and
S. J. Wukitch
MIT Plasma Science and Fusion Center, Cambridge, MA 02139, USA
Abstract. Mode converted ion cyclotron wave (ICW) has been observed with phase contrast imaging (PCI) in D-'He plasmas in Alcator C-Mod [1,2]. The measurements were carried out with the
optical heterodyne technique using acousto-optic modulators which modulate the C02 laser beam
intensity near the ion cyclotron frequency [3]. With recently improved calibration of the PCI system
using a calibrated sound wave source, the measurements have been compared with the full-wave
code TORIC, as interpreted by a synthetic diagnostic. Because of the line-integrated nature of the
PCI signal, the predictions are sensitive to the exact wave field pattern. The simulations are found
to be in qualitative agreement with the measurements.
Keywords: ICRF, mode conversion, phase contrast imaging, Alcator C-Mod, TORIC
PACS: 52.35.Hr, 52.50.Qt, 52.55.Fa, 52.65.Ff, 52.70.Kz
INTRODUCTION
Waves in the ion cyclotron range of frequencies (ICRF) are used extensively for auxiliary
heating in fusion experiments. In a multi-species plasma, fast magnetosonic wave (FW)
lauched from the antenna can convert to ion bemstein wave (IBW) and ion cyclotron
wave (ICW) around the ion-ion hybrid resonance layer (mode conversion layer). Ion
cyclotron wave was seen to drive strong flow in a plasma [2], which could be used to
suppress turbulence and improve confinement. Experimental verification of rf simulation
codes for these mode conversion scenarios is important. The elecfron density fluctuation
of the rf wave is measured directly with the phase contrast imaging (PCI) diagnostic in
C-Mod. The measurements are compared with the full-wave simulation of TORIC [4].
PHASE CONTRAST IMAGING
The phase contrast imaging (PCI) diagnostic images the phase shift infroduced to the
incident laser beam by long wavelength fluctuations that exist in the medium. Electron
density fluctuations in a plasma infroduce a small phase shift to the incident laser beam,
i ? o ^ i ? = i?oe'^W,
(/)(x) = / dz{k{x)-ko)
(1)
:i; -rgAo / dz«e(x).
(2)
CPW&l, Radio Frequency Power in Plasmas
edited by V. Bobkov and J.-M. Noterdaeme
© 2009 Amencanlnstitute of Physics 978-0-7354-0753-4/09/$25.00
65
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shot = 1080522007
shot = 1080522007
0.051
Lb
E 0.04I
1.4
'
,
MC, 9% ^He
i
A
0.66
0.68
FIGURE 1.
1 .ir
^ O.O3I
0.70
c 0.02 -
1.0
§ 0.01 -
o.a
^
n K
0.00 .
t
1.2
^
i
-10 -5 0
k„[c
5
10
1.0 2.0 3.0
rf power[MW]
The density fluctuations observed by PCI at the rf frequency and the rf power trace
where rg = e^/4K£omeC^ and AQ is the incident laser wavelength (AQ = 10.6 jim in CMod PCI system). By introducing ;r/2 phase delay to the k = 0 component of the beam,
phase variation is converted to amplitude variation.
IfCI°^re?^
/ dzHeix).
(3)
The mode converted ion cyclotron wave was observed by PCI in a D-^He mode
conversion experiment. The plasma parameters were Bt ^ 5.1 T, Ip ~ 0.80 MA, rie —
1.5 X lO^*' m^^, Te= 1-2 keV. The ^He concentration was around 9% for efficient power
deposition to ^He ions through mode converted ICW. The antenna was operated at 50.0
MHz, which placed the D-^He mode conversion layer in the core of the plasma at this
^He concentration. Strong flow was generated in this plasma in response to rf power
injection at a multi-MW level [2]. The laser amplitude was modulated using an acoustooptic modulator for heterodyne detection of the density fluctuation at the rf frequency
[5].
The radial structure and the wavenumber spectrum of the fluctuation with the rf power
trace are shown in Fig. 1. The PCI signal shows waves propagating in the positive
kR direction (towards the low field side) around the mode conversion layer when the
rf is turned on. Although the signal increases with increasing rf power up to 1.0 s, it
decreases at later times despite of the fact that the rf power is still increasing. This could
be partially explained by the sensitivity of the signal to the exact wave field pattern, but
is not understood well. The comparison with the simulation is done at 1.0 s where the
PCI signal is the strongest.
SIMULATION OF ICRF WAVES
The wave electric field and the electron density fluctuations were simulated by the fullwave ICRF simulation code TORIC [4]. It is a finite Larmour radius code in an axisymmetric geometry. The results are shown in Fig. 2. IBW and ICW are the short wave
length features around the MC layer that propagate perpendicular to it. Close to the
midplane, IBW propagates to the high field side of the layer and away from the midplane
66
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I
0.50
0.60
0.70
R[m]
i
O.l
0.50
0.60
0.70
R[m]
O.l
FIGURE 2. TORIC simulation at ? = 1.0 s. Left: E-, Right: He. Bt = 5.1 T, Ip = 0.80 MA, He =
1.5 X 102« m-3, Te = 2.l keV, m^Jne = 0.09, / = 50.0 MHz
ICW propagates to the low field side. FW can be seen as the long wavelength structure
that exists over the entire plasma cross section. The electron density fluctuations can be
calculated from the electric field as,
ne =
V-Je
, Je = C>e-E.
(4)
eco
COMPARISON OF SIMULATION AND EXPERIMENT
The PCI signal is calculated from the simulated density fluctuation by integrating the
density fluctuation along the PCI chord and applying phase plate response which cuts off
the low-A: fluctuation. The simulated and the measured PCI signals are shown in Fig. 3.
The signals are simulated for slightly different PCI beam incident angles. Because of the
line-integration, the simulated signals are rather sensitive to the angle of the integration
chord.
The C-Mod PCI system is most sensitive to ICW. Ion cyclotron wave is excited at the
MC layer and damps away as it propagates towards the ^He cyclotron resonance layer at
the low field side. The spatial extent and the wavenumber spectrum of the simulated and
the measured PCI signal agree well, and are consistent with the local dispersion relation
of ICW. On the other hand, the fluctuation intensity differs at least by a factor of 10.
Since the wave amplitude depends on how much power is coupled into the plasma and
the partition of the power into ICW and IBW, the fluctuation amplitude is much harder
to predict. Edge loss mechanisms are not accounted for in the code, and this could result
in larger field amplitudes in the simulation. On the experimental side, the PCI signal
might be smaller than reality, since inaccurate alignment would result in reduction of
the measured signal. Considering the sensitivity of the PCI signal to the slight change
in the PCI laser beam orientation, uncertainty in the magnetic configuration is another
possibility for the discrepancy. Finally, the mode conversion eificiency predicted by the
code might be in question.
67
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shot =
1080522007, t[s] =
1.002
shot =
o
1080522007, t[s] =
1.002
0.10-
1 nn r ^^A^A6^A&jLijt
-15
-10
R[m]
-5
.^AAAA
0
k„[cm"']
5
10
15
FIGURE 3. Comparison of the measured and the simulated PCI signal. Left: Radial structure, Right:
Wavenumber spectrum. Diamonds: measurements (x30), curves: simulations for different PCI laser
incident angle 0
SUMMARY
Mode converted ICW was measured in C-Mod plasmas by a calibrated PCI diagnostic. The PCI signal was simulated using the ICRF full-wave code TORIC. Both the
simulation and the experiment are consistent with the local dispersion relation of ICW.
However, the measured fluctuation intensity was low by at least a factor of 10 from code
predictions. Further investigation on the experimental setup and codes needs to be done
to resolve the quantitative disagreement. We are presently also working on comparisons
with AORSA [6] and the results will be presented in the future.
ACKNOWLEDGMENTS
The authors thank the Alcator C-Mod operation and ICRF group. This research used the
MIT Plasma Science and Fusion Center Theory Group parallel computational cluster
This work is supported by U.S. Department of Energy under DE-FG02-94-ER54235
and DE-FC02-99-ER54512.
REFERENCES
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5.
E. Nelson-Melby, et al., Phys. Rev. Lett. 90, 155004 (2003).
Y. Lin, et al., Phys. Rev. Lett 101, 235002 (2008).
M. Porkolab, et al., IEEE Trans. Plasma Sci. 34, 229 (2006).
M. Brambilla, Plasma Phys. Control, Fusion 41, 1 (1999).
A. Mazurenko, Phase Contrast Imaging on the Alcator C-Mod Tokamak, Ph.D. thesis, Massachusetts
Institute of Technology, Cambridge, MA 02139 (2001).
6. E. F. Jaeger, et al., Phys. Plasmas 8, 1573 (2001).
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