22P132-P
QUEST Shape Reproduction Based on CCS Methodwith Two Kinds of Magnetic Sensors
２種類の磁気センサーを用いたCCS法に基づくQUEST断面形状再構成
K. Nakamura1, X.L. Liu2, E.B. Xue1, O. Mitarai3, K. Kurihara4, Y. Kawamata4, M. Sueoka4,
M. Hasegawa1, K. Tokunaga1, H. Zushi1, K. Hanada1, A. Fujisawa1, H. Idei1, Y. Nagashima1,S. Kawasaki1, H. Nakashima1, A. Higashijima1, K. Araki1, A. Fukuyama5
中村 一男1, 劉 暁龍2, 薛 二兵1, 御手洗 修3, 栗原 研一4, 川俣 陽一4, 末岡 通治4,長谷川 真1, 徳永 和俊1, 図子 秀樹1, 花田 和明1, 藤澤 彰英1, 出射 浩1, 永島 芳彦1,川崎 昌二1, 中島 寿年1, 東島 亜紀1, 荒木 邦明1, 福山 淳5
1

RIAM, Kyushu Univ., 6-1 Kasuga-koen, Kasuga City, Fukuoka, 816-8580 Japan,
2
IGSES, Kyushu Univ., 3Tokai Univ., 4JAEA, 5Kyoto Univ.
1
九大応力研 〒816-8580 福岡県春日市春日公園6-1, 2九大総理工, 3東海大, 4原子力機構, 5京大工Plasma shape control is studied in QUEST divertor configuration. In the shape reconstruction, eddy current
in vacuum vessel and plasma current in open magnetic surfaces need to be considered in Ohmic discharge
and in RF-driven plasma, respectively. Since magnetic probes have been installed in addition to flux loops,
CCS (Cauchy Condition Surface) can be set on the measuring surface and the eddy current effect can betaken into account. And the plasma current effect in the open magnetic surfaces outside of the closed
magnetic surfaces could be considered.

1. Introduction
CCS (Cauchy Condition Surface) method is anumerical approach to reproduce plasma shape,
which has good precision in conventional tokamaks[1]. The precision was confirmed also in ST and
decided to be applied to plasma shapereconstruction and the control in a sphericaltokamak QUEST (Q-shu University Experiment of
Steady-State Spherical Tokamak) (Bt = 0.25 T, R =0.68 m, a = 0.40 m) [2].
There are lots of plasma equilibrium
reconstruction techniques and they are used in large
tokamaks. In NSTX, they use an automatedversion of EFIT code [3]. In DIII-D, they improve
equilibrium reconstruction via Kalman-filter-based
vessel current estimation [4]. Here, the CCS method
can calculate the plasma boundary shape with noconstraint about the basis function set, though it
cannot calculate the internal distribution. Therefore,
the CCS method may reconstruct the plasma shapeprecisely using small number of magnetic sensors,
if the sensor signals are precise, since it is based onboundary
integralequations,which
ismathematically precise.
In present stage from the magnetic measurement,
it is known that the eddy current effect is large in
QUEST experiment, and so some proper model
should be selected to evaluate the eddy current,
which affect the plasma boundary reconstruction.
As the eddy current model, we divided the vacuum
vessel into 8 parts, in each part lots of filamentswith different current (distributed current density)
represent the eddy current [2]. The eddy current
density by not only CS (Center Solenoid) coil but
also plasma current is calculated using EDDYCAL(JAEA) [5]. The eddy currents are taken as
unknown variables and solved together with plasma
shape reconstruction by using least square method
or singular value decomposition [6].
2. Shape Reconstruction Based on CCS Method
The CCS method is an exact numerical method
which is based on the boundary integral equation.
The Cauchy condition surface is defined as ahypothetical plasma surface, where both theDirichlet (, poloidal flux function) and Neumann(Bt, poloidal magnetic field tangent to the CCS)
conditions are unknown. This surface is locatedinside the real plasma region. It is assumed thatCCS encloses all the plasmas and there are noplasmas outside the CCS [1]. After reconstruction,
only the flux surfaces outside of the plasmaboundary are right including the boundary, which issimilar to "image method" in calculation of static
field due to a point charge in the presence ofsemi-infinite ideal conductor.
3. Ohmic Plasma Shape Reconstruction with
Two Kinds of Magnetic Sensors
Figure 1 shows waveforms of CS, plasma andvertical field coil currents in ohmic discharge
assisted by ECRH (79 kW between 1.19 and 1.32

magnetic probes were installed last year, fourprobes were added last fiscal year, two more probes
and 4 partial Rogowski coils will be installed.
Increase in reconstruction precision is expected,
since CCS can be set also on the measuring surface.
2.0

PFC Current [kA]1.50

1.0-20

CS_Current
Plasma_Current
PF17_Current
PF26_Current
PF351_Current
PF352_Current

0.5
0.0

-40
-60

-0.5

-80
1.0

1.5

2.0
Time [sec]

2.5

3.0

Fig.1. Coil and plasma current waveform in QUEST
ohmic discharge.
PF3

1.5

Shot 11631
time 1.55sec
eddy 8parts

1.5

MP2PF2

1.0

Shot 11631
time 1.55sec
eddy 8parts

1.0

PF10.5

0.5

Z [m]

Z [m]

4. SummaryIn the ohmic plasma with a lot of high-energy
electrons, there may be anisotropic plasma pressure,which makes difficult a usual equilibrium analysis,
but the CCS method can reconstruct the plasma
shape precisely regardless of the anisotropy.
Though eddy current adjustment is necessary, eddy
current model must be simple for FB (FeedBack)control. We divided vacuum chamber into 8
sections according to numerical calculation of theeddy current distribution in the vacuum vessel by
EDDYCAL (JAEA).
Eddy current model based on several sections isconsidered to be essentially a projection (thenecessary condition is satisfied but the sufficient isnot). Eddy current mode expansion is a candidate
for higher precision. Inner current mode is higher
order and many modes are necessary, whichsuggests it is difficult for us to adopt in FB control.
The number of flux loops is better to be large fromthe reconstruction precision viewpoint. But someloops cross diagnostic ports and the error is large.
In case of CCS, sensor precision is more important
than the number, since CCS method is amathematically exact numerical one.
Since the tangential magnetic field on the flux
loop measurement surface must satisfy a boundary
integral equation, we can determine more
physically consistent eddy current density andshape reproduction by installing tangential
magnetic probes inside the vacuum chamber. Two20
Shot 11631

Ics, Ip [kA]sec). The CS current was swung in single polarity:
This time, after CS coil is excited in negative
polarity by power supply, by decreasing the current,
plasma current was started. At the same time, theplasma current is driven further by increasing PF26
coil current. Vertical field for horizontal
equilibrium was applied by PF17 coil before theplasma initiation and added further by PF26 coil. In
divertor coil PF35-12, -1 kA was kept before theplasma initiation and increased to -1.9 kA.
Figure 2 shows magnetic surfaces (t = 1.55 sec)reconstructed by CCS method. In thisreconstruction, 20 flux loops were used among 67
loops in (a), and two magnetic probes were used inaddition in (b). Uniform eddy currents wereassumed in 8 sections. The vertical asymmetry
suggests some asymmetry of magnetic fields oreddy currents. In these figures, null points are found,though closed magnetic surface contacts with innerprotecting limiter. The detachment could beaccomplished by further positive swing of CS coil,but improvement of the power supply is
indispensable for circulating current control.

0.0-0.5

0.0

-0.5

PF7
PF6

-1.0

-1.5

(a)

PF5
0.0

0.4

0.8
R [m]

1.2

1.6

MP1-1.0(b)

-1.5

0.0

0.4

0.8
R [m]

1.2

1.6

Fig.2. Magnetic surfaces reconstructed by CCS
method in ohmic discharge.

Acknowledgments
This work was performed with the support andunder the auspices of the NIFS bi-directional
collaborative research program (NIFS09KUTR043).
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