23P081-P
Development of simulator for plasma position and shape control in JT-60SA
JT-60SA位置形状制御シミュレータの開発
Yoshiaki Miyata, Takahiro Suzuki, Takaaki Fujita and Shunsuke Ide
宮田 良明, 鈴木 隆博，藤田 隆明，井手 俊介
Fusion Research and Development Directorate, Japan Atomic Energy Agency
801-1 Mukoyama, Naka, Ibaraki-ken 311-0193, Japan
日本原子力研究開発機構 核融合研究開発部門 〒311-0193 茨城県那珂市向山801-1
The plasma position and shape control is important issue in JT-60SA, ITER and future fusion reactor which
has a small number of coils. In order to study the plasma position and shape control, we are developing asimulator which consists of an equilibrium solver and an ‘isoflux’ controller. The controller controls
poloidal field (PF) coil currents so as to keep the poloidal flux is equal at all of specified locations. The
equilibrium solver identifies an equilibrium under the specified PF coil current and implements the effectof eddy current. The position and shape control has been simulated in response to prescribed change inthe poloidal beta and the internal inductance due to heating.

1. Introduction
The plasma position and shape control isimportant issue in JT-60SA, ITER and future fusion
reactor which has a small number of coils. The
precise control of the plasma position is key issue inorder to avoid damages on the first wall. It isnecessary that the control logic implements theeffect of shielding magnetic field because of large
eddy current on the vacuum vessel in JT-60SA. The
position and shape control simulator which
implements the effect of eddy current is developedwith the intention of studying technique of plasma
position and shape control. In section 2, we
describe the outline of control simulator. In section
3, the position and shape control has been simulated
in response to prescribed change in the poloidal
beta and internal inductance.
2. Outline of Control Simulator
The simulator consists of the equilibrium
calculation part and the controller part. The plasma
equilibrium for a given set of coil current isobtained in the equilibrium calculation part. The setof coil current is modified to adjust the plasma
position and shape at the next time step in thecontroller part. By iterating these procedures,
feedback control of plasma position and shape bycontrol of the coil current is simulated. The control
logic of coil current will be optimized by thesimulator. Figure 1 shows calculation flow. In ausual equilibrium code, the plasma position andshape is given and the coil current is adjusted toobtain the equilibrium with a given position andshape. On the other hand, in the equilibrium
calculation part of the simulator, the position andshape of the plasma is obtained as a result of

Equilibrium calculation
Calculate the imaginary magnetic field needed for a given
plasma position and given internal parameters taking into
account eddy currents
Adjust plasma position to minimize imaginary magnetic field

Superconducting and in-vessel coils

Position and shape controller

Fig.1. Calculation flow of control simulator.

equilibrium calculation. To do this, we introduced
an imaginary magnetic field. We assume a plasma
position and calculate the equilibrium by adjusting
the imaginary field. In the equilibrium calculation,
plasma internal parameters (poloidal beta andinternal inductance) are also fixed to given values
by adjusting the plasma pressure and current profile.
The eddy current induced in the conductingstructures around the plasma (the in-vessel
stabilizing plate and the vacuum vessel) is
calculated using the voltage induced by change inthe magnetic field and is taken into account for theequilibrium calculation (calculating the necessary
imaginary field). The plasma position is adjusted tominimize the imaginary magnetic field and then an
equilibrium realized for a given set of coil currents
is obtained. In the controller part, the ‘isoflux’
technique is employed as the position and shapecontrol. A set of locations that defines the desired
plasma separatrix is specified as the referencepositions. The poloidal field coil currents areadjusted to keep the poloidal flux is equal at all ofthese locations. The controller modifies the coilcurrent according to the follow equation,

dI   M (G  G  dt  G (d/dt)) dt (1)
1

jP

I

Di

(a)

0.9p

 , li0.8
0.7

 inputp0.6

 calculation

0.5

li inputli calculationpR-inner[m]1.82(b)

4.16
R-inner

R-outer

1.8

4.14

1.78

4.12

4-1 104.1
CS2
EF1(c)FPPCC1FPPCC2100450404-50-1.25 10-1.5 10-1.75 104-2 10-100
CS2EF1(d)FPPCC1FPPCC2600

1530000-15-300-301441 101618

FPPCC Voltage[V]CS, EF Voltage[V]CS, EF Current[A]1.76

FPPCC Current[A]Fig.2. Flux contour and control points at the initial time.

GP[1] GI[1/s] GD[s]Reference Point(CS and EF) 0.5 1.0
X point(CS and EF)
0.1 0.8
FPPCC- 0.005

R-outer[m]3. Simulation Result
The position and shape control has been simulated
during heating phase in which the plasma positionand shape were attempted to be fixed while thepoloidal beta and internal inductance are changing.
Figure 2 shows the flux contour and input control
points at the initial time. A typical JT-60SA lower
single null equilibrium with IP=5.5 MA is shown.
There are 10 poloidal field coils and 2 fast plasma
position control coils (FPPCCs) in JT-60SA. The
poloidalfieldcoilsandFPPCCs
aresuperconducting and in-vessel copper coils,respectively. The poloidal field coils consist ofcentral solenoid (CS) modules and equilibrium field(EF) coils. The input control points as the referenceof position and shape are 6 points (P1 to P6). TheP0 is the X point. The value of control gain isshown in Table I. The controller modifies thecurrent of CS and EF to adjust the flux at thereference and X points. The controller modifies thecurrent of FPPCC with reference to the flux of P1and P2. The vacuum vessel and stabilizing plate aremodeled as 71 and 27 toroidal conducting elements,respectively. Figure 3 shows waveforms of internalparameter, plasma position, coil current, coilvoltage and eddy current.

Table I. Value of control gain

Total Eddy Current[A]where, i is the difference between flux and its
reference value at the control point, dIj is theamount of modification in the coil current and M-1
is the control matrix which is the inverse of Green’s
function M calculated by use of singulardecomposition method, respectively. The GP, GIand GD are the proportional (P), integral (I) andderivative (D) control gains for modifying the coilcurrent, respectively. The superconducting coils use
the P-I control, and the in-vessel coils use the Dcontrol.

20(e)

5000
0-5000Stabilizing PlateVacuum Vessel

4-1 10141618
Time[sec]

20Fig.3. Waveform of (a) input and calculation value of thepoloidal beta and internal inductance. (b) inner and outer
position of the separatrix in the major radius direction.
(c) coil current of CS2, EF1, FPPCC1 and FPPCC2. (d)voltage of CS2, EF1, FPPCC1 and FPPCC2. (e) total
eddy current on the stabilizing plate and vacuum vessel.

The poloidal beta increased exponentially fromabout 0.5 to 0.75 with a time constant of 1 sec. Theinternal inductance decreased linearly from about0.85 to 0.75 with time. The internal parameters areconverged at each time step. The outer position
increased from about 4.11 to 4.13 m initially due toan increase in the poloidal beta. The current of EF1
slowly increased (in the negative direction) to movethe outer position inward, to the reference position.
The plasma position and shape have been
approached to the input reference values at 21.6 sec.
It was possible to simulate the position and shapecontrol in response to prescribed change in thepoloidal beta and internal inductance with a small
number of coils. The position and shape control of
the transition from limiter to diverter configurationis also reported. The control characteristics inducedby changing the control gain are discussed.