CCS Method to Reproduce Tokamak Plasma Shape

(Cauchy Condition Surface)

F. Wang*1, K. Nakamura2, O. Mitarai3, K. Kurihara4, Y. Kawamata4, M. Sueoka4, K. N. Sato2, H. Zushi2, K. Hanada2, M. Sakamoto2,

H. Idei2, M. Hasegawa2, S. Kawasaki2, H. Nakashima2, A. Higashijima2

1) IGSES, Kyushu University(Interdisciplinary Graduate School of Engineering Sciences)

2) RIAM, Kyushu University3) Kyushu Tokai University

4) Japan Atomic Energy Agency

Prepared and Presented by Wang Feng in ITC-16

Modified and Presented by Kazuo Nakamura in ASIPP

Outline Conventional Tokamak and Spherical Tokamak

CPD Cauchy Condition Surface Method

Main Principle of CCS Method Equations of Numerical Calculation

Motivation Configuration of CPD Magnetic Sensor Dependence Cauchy-Condition Dependence Plasma Current Profile Dependence Summary and Future Work Application of CCS Method to EAST

1. Conventional Tokamak and Spherical Tokamak

Spherical Tokamak (ST)

Small Aspect Ratio (A=R/a) < 2

High natural elongation

High natural triangularity

Equilibrium and stability properties are much

different with the conventional tokamaks

R

Conventional Tokamak

Spherical Tokamak

a

R a

Plasma major radius: 0.3 m Plasma minor radius: 0.2 m Toroidal field: 0.3 T @ R =

0.25 m Operation period: 1.00 sec

for Bt = 0.3 T Operation cycle: 5 min Plasma current: 150 kA

CPD (Compact PWI Experimental Device)

Main parameters of CPD:

RIAM, Kyushu University

2. Cauchy Condition Surface Method

Shape reproduction is important for plasma control in a tokamak, especially for non-circular and triangular plasmas.

Cauchy-Condition Surface (CCS) method [1] is a numerical approach to reproduce plasma shape. Its main features are as follows:

1) The CCS method can reproduce plasma shape with high precision corresponding to the number and types of available sensors.

2) The CCS method can identify plasma current with an error of less than 2%.

3) The CCS position and shape are insensitive to reproduction accuracy. This is advantageous in the application to the real-time plasma control.

[1] K. Kurihara, Nuclear Fusion, Vol.33, No.3 (1993) 399-412.CCS method was proposed by Dr. Kurihara and tested on JT-60U.

Cauchy-Condition SurfaceDirichlet (Φ) ?Neumann (B) ?

Magnetic Measurements

Cauchy-Condition SurfaceDirichlet (Φ)Neumann (B)

Flux Distribution Outside CCS

Actual Plasma Shape

Main Principle of CCS Method

R

Z

Flux Loops

Poloidal Field Coils

Magnetic Probes

Actual Plasma Surface

CCS

B = grad

Vacuum field

R

Z

Flux Loops

Poloidal Field Coils

Eq (2)

Magnetic Probes

Eq (3)

Eq (4)

Equations of Numerical Calculation

(1)

(2)

(3)

(4)

1 1

( ) 1( , ) ) 1( , ) ) 1( )M M

f f i i f i i fi i

x WF x z z WB x z t z WC x

Flux Loops CCS && PF Coils

1 1

( ) 2( , ) ) 2( , ) ) 2( )M M

B B i i B i i Bi i

Bt x WF x z z WB x z t z WC x

Magnetic Probes CCS && PF Coils

2

( ) ( )( ) [ ( ) ( , ) ( , ) ( )] ( ) ( , )

cz y

dS z dV yx z gradG x z G x z grad z j y G x y

r r

1 1

1( ) 3( , ) ) 3( , ) ) 3( )

2

M M

i i i ii i

x WF x z z WB x z t z WC x

CCS CCS && PF Coils

Dirichlet Neumann

Vacuum field

3. Motivation

Motivation

As for the spherical tokamak, the aspect ratio is much smaller than normal tokamaks, so the shape reproduction precision of CCS method under a spherical tokamak device is checked.

In order to apply it in real-time plasma shape control, magnetic sensor dependence and current profile dependence is also studied.

Main Steps of Comparison

1. Various ideal flux surfaces corresponding to different plasma profiles are made by equilibrium code.

2. These plasma shapes are reproduced by using CCS method.

3. The original and reproduced shapes are compared.

R: +0.1 ~ +0.8Z: -0.7 ~ +0.7

PF Coils: 7

Flux Loops: 45

Mesh Size (RxZ): 140x280Mesh Precision: 0.005m

Ellipse for CCS Small radius: 0.03mLarge radius: 0.05m

4. Configuration of CPD

Reproduction with 45 flux loops Reproduction with 26 magnetic probes

5. Magnetic Sensor Dependence

The CCS method can reproduce plasma shape of spherical tokamak solely with the measurements of flux loops.

CCS (M=6) CCS (M=8) CCS (M=10)

6. Cauchy-Condition Dependence

In case of much elongated and triangular plasmas in spherical tokamak CPD, good precision can be achieved by changing the degrees of parametric freedom of Cauchy-Condition Surface.

7. Plasma Current Profile Dependence (1)

In case of circular plasma shape, normally the shape difference of circular plasma shape is less than 1% compared with major radius R.

li=0.8 li=0.9 li=1.0

7. Plasma Current Profile Dependence (2)

(Ip = 100kA, IPF1=10kA, βp=0.5, li=0.7, κ=2.1)

X Point difference

Shape Difference

Typical plasma shape reproduction

Difference of X Point and Plasma Shape

The differences between CCS method and ECODE are compared. In case of large elongated and triangular double-null plasma of CPD, normally the X point difference is less than 2%, and shape difference is less than 3% compared with major radius R.

Difference of X Point Difference of Plasma Shape

8. Summary and Future Work

Summary1. The CCS method can reproduce plasma shape of spherical tokamak in good p

recision solely with the measurements of flux loops or magnetic sensors.

2. In case of much elongated and triangular plasmas in spherical tokamak, good precision can be achieved by increase in degrees of parametric freedom representing the Cauchy condition.

3. The CCS method can reproduce spherical tokamak plasma shape with good precision in different plasma current profiles (li=0.5 ~ 1.0). In case of large elongated and triangular double-null plasma, normally the X point difference is less than 2%, and shape difference is less than 3%.

Future WorkIn the real plasma discharge experiment, eddy current effect is important, especially at ramp-up stage of plasma current. The effect of eddy current will be taken into account in Cauchy Condition Surface method in future.

Application of CCS Method to EAST

Reproduction of plasma shapeConsideration of eddy current in startupReal-time reproduction and display