24P139-P
Discharge optimization of micro-Tokamak device using Electron-cycrotron
heating
電子サイクロトロン加熱を用いた超小型トカマクにおける放電調整	 Yasuyuki TANAKA and Takeshi FUKUDA
田中靖之, 福田武司
Graduate school of engineering, Osaka University
2-1, Yamadaoka, Suita-shi, Osaka 565-0871, Japan
大阪大学大学院工学研究科 〒565-0871	  大阪府吹田市山田丘2-1
It is known that the loop voltage of a superconducting tokamak device is limited. In small tokamak devices,
error field, short connection length and misalignment of coils generally all lead to an increase of required
loop voltage. In order to elaborate a quantitative picture related to the equilibrium formation, anelectromagnetic theory-based model was developed. We have performed the detail comparison of thenumerical results with magnetic measurements. In addition, an influence of ECH that strongly modify thekinetic processes is presented in the poster.

2. Overview of micro-Tokamak device
Micro-Tokamak device has been developed for adevice processing, such as a semiconductor
manufacturing process, and designed with theequilibrium code TOSCA. The device parameters
are shown in Table 1[4] and Fig.1 shows the topview photo of the device. The device has toroidal
field coil (TF, 12 segments), the center solenoidcoil (ohmic heating coil: F, 56 turns) and 3 types ofpoloidal field coils (vertical coil: V, 14 turns,horizontal coil: H, 4 turns and divertor coil: D, 2turns). Fig.2 shows the alignment of confinement

field coils.
Table 1. Micro-Tokamak device parameter
Major radius R00.06 m
Minor radisu a0.02 m
Plasma current Ip~100A
Toroidal Field Bt
0.05T

Fig. 1 Top view photo of the device
0.10.05Z [m]

1. Introduction
In many large tokamaks, reduction of thebreakdown loop voltage has been investigatedusing ECH preionization and the electric field of
0.15Vm -1 achieved in DIII-D is the lowest
documented record for plasma breakdown underan externally applied loop voltage[1,2]. We have
performed reduction of the required loop voltage
in micro-Tokamak device[3]. As a result of ourprevious research, the ionization assists of theglow discharge and the thermal electron emitterare not able to be used for the method ofpreionization because of its high utilizable gaspressure (0.9~10Pa) and its produced error field.
Since plasma current ramp-up could not occur insimple calculation of the breakdown, we need toelaborate the comprehensive models. Therefore,
we have performed the model computation andintroduced ECH preionization to micro-Tokamak
device. We will present the detail comparison of
its numerical results with magnetic measurements
and the influence of ECH for the breakdown loop
voltage.

F-CS1
F-CS2
F1
F2
V1
V2
H1
H2
D0-0.05-0.1
0.04 0.06 0.08 0.1 0.12 0.14
R [m]Fig.2 The alignment of confinement field coils

3. Numerical results of vaccum magnetic andelectric field
In order to design the current waveform andestimate the misalignment of coils, we carried out

the model computation of poloidal magnetic field
and toroidal electric field in a poloidal cross section.
A poloidal flux based on the Green’s function for a
toroidal current source is given by[5]:µ0 I
Rc R #$( 2 − k 2 ) K ( k 2 ) − 2E ( k 2 )%&k22k 2 = 4RRc ( R + Rc ) + ( Z − Z c )(1)

Ψ ( R, Z ) =where Ψ is poloidal flux, I is coil current,(Rc,Zc) is the coil position, µ 0 is the magnetic
permeability and K and E are the elliptic integral of
the first kind and the second kind respectively. Themagnetic field calculation is based on its partial
derivative with respect to the coordinates (R,Z).
And the electric field calculation is based on its
partial derivative with respect to time. Thus, theelectric field is given by:
∂A
1 ∂Ψ
(2)
Eφ = − φ =∂t

2π R ∂t

The numerical results of magnetic field indicatedthe existence of the current condition of minimum
poloidal field. The perpendicular magnetic field atthat condition is shown in Fig.3 (a). It shows thewide area of small poloidal field (< 0.2mT).
(a)

(b)

Fig.3 Numerical results of magnetic (a) and electricfield(b)The electric field numerical result at dIF/dt =-1.0kA/ms in this current condition is shown inFig.3 (b). It shows the toroidal electric field is about
3 ~ 4 V/m at R=R0. The waveform used in themodel computation is shown in Fig. 5.
300
F coil
V coil
H coilD coilCoil current [A]200
1000-100-200-30004. Comparing both results of model computationand measurement
In order to introduce ECH in the device andestimate the model, we measured the toroidal fieldand compare the value of measurement with thecalculated result of toroidal field(shown in Fig.5)[6].
Fig.6 indicates that the measurement result(0.04T at
R=R0) is smaller than designed value(0.05T at
R=R0).

510Time [sec]15

Fig.4 Current waveform of the operation

20

Fig.5 Comparison result about toroidal field

In addition, by comparing numerical results withmagnetic measurements, we have verified thevalidity of the numerical model. Fig.6 shows thecomparison result of poloidal field BZ at mid planein the minimum poloidal field condition.

Fig.6 model validation about BZ at midplane(Z=0)

It indicates large differences exist between thenumerical result and the measured value for
R<70mm. In 70mm < R < 140mm region, themodelcomputation
could
describes
thecharacteristic of BZ. Moreover, It would be need tocompare the other current set and search better
condition in relating to the poloidal magnetic field.
References[1] R. Yoshino and M. Seki: Plasma Phys. Control.
Fusion 39 205-222 (1997).
[2] Lloyd B et al: Nucl. Fusion 31 2031(1991)[3] Y. Tanaka, T. Ito, and T. Fukuda et al. : 27th JSPF
Annual Metting (2010) 03P10.
[4] M. Inomoto, H. Nozato and T. Fukuda: Plasma Sci.
Symp. / Symp. on Plasma Processing 22nd (2005)
497.
[5] J. L. Johnson et al.: Journal of computational physics
32, 212-234 (1979).
[6] K. Miyamoto, “Fundamentals of Plasma Physics andControlled Fusion”, Iwanami Book Service (2001).