23P055-P
Helical Ferritic Steel Inserts for Resonant Magnetic Perturbation to Suppress
ELMs in Tokamak DEMO Reactor
トカマクDEMO炉のELM抑制共鳴磁場擾乱用ヘリカル状フェライト鋼設置	 
Tomonori Takizuka1,2, Naoyuki Oyama2 and Takeshi Fukuda1
滝塚知典1,2, 大山直幸2，福田武司1
1

2

Osaka University, 2-1, Yamadaoka, Suita 565-0871, Japan
Japan Atomic Energy Agency, 801-1, Mukoyama, Naka 311-0193, Japan1
大阪大学 〒565-0871 吹田市山田丘2-1
2
日本原子力研究開発機構 〒311-0193 那珂市向山801-1

Edge localized mode (ELM) must be eliminated which enhances the erosion of divertor plates in theH-mode operation of tokamak reactors. Suppression of ELM has been experimentally achieved by theresonant magnetic perturbation (RMP) with multipartite coils. In a DEMO reactor with strong neutron flux,
however, it is desired the coils near the first wall not to be put in. We propose an innovative concept of theRMP for tokamak DEMO reactors without installing coils but inserting ferritic steels of the helicalconfiguration. Helically perturbed magnetic field is naturally formed in the axisymmetric toroidal magnetic
field through the helical ferritic steel inserts (FSI).

1. Introduction
Edge localized modes (ELMs) in H-mode
plasmas intermittently produce large heat load on
the plasma facing components (PFC), especiallyon the divertor plate, and enhances erosion of thePFC materials [1,2]. To maintain long lifetime ofdivertor plates, ELM must be eliminated in theH-mode operation of tokamak reactors. Suppression of the ELM has been experimentally achievedby the resonant magnetic perturbation (RMP) withmultipartite coils in DIII-D [3]. Figure 1 shows anRMP coil system placed on the low-field-side firstwall in DIII-D. This coil system generates theperturbed field with the main toroidal mode number
n = 3 and the broad spectra of poloidal mode
number m. The maximum perturbation for an m/nmode is about 10 gauss. When the safety factor atthe 95% poloidal flux surface is q95 ~ 3.5, the RMP
is remarkable and magnetic filed lines behavestochastic near the plasma edge region. The
pedestal plasma pressure is decreased by this RMP,
and resultantly the ELM can be suppressed.

Based on this experimental demonstration, ITER isplanning to install the RMP coil system to suppress
ELM [4], while discussing about its additional cost.
In order to generate magnetic perturbation
effectively, the coil system is better to put near theplasma surface. On the other hand, in the DEMO/
Commercial reactors with strong neutron flux, it isdesired such coil systems near the first wall not tobe put in. In this paper, we propose an innovative
concept of the RMP for tokamak DEMO reactors
without installing coils but inserting ferritic steelsof the helical configuration. Helically perturbed
magnetic field is naturally formed in the axisymmetric toroidal magnetic field through the helical
ferritic steel inserts (FSI).
2. Helical magnetic field by helical FSI
Consider a cylindrical system (r, θ, z), where alongitudinal (toroidal) uniform magnetic field Hext
is externally given in the z direction. A hollow
ferritic tube is put at aF – d < r < aF + d. This ferritic
steel inserts (FSI) creates the perturbed magnetic
field H1(v) in the vacuum region. The perturbed field
is expanded to the Fourier modes in θ and zdirections. A single helical mode of the magneticfield H1(v) = H1(v)(r) exp i(mθ – nz/R) is described bythe solution to the set of equations,rot H1(v) = 0Fig.1. RMP coil system in DIII-D [3]anddiv µ0H1(v) = 0.

Note the relation to magnetic flux density B1(v) =µ0H1(v) (µ0: permeability of vacuum). The solution
is H1z(v) ~ Im(nr/R) for the inner region r < aF – d,and H1z(v) ~ Km(nr/R) for the outer region r > aF + d

(Im, Km: modified Bessel functions of the 1st kindand 2nd kind). For the high m mode, the equations
are approximated as those in the Cartesian
coordinates (x, y, z) with x = r – aF. The solution ofthe form H1(v) = H1(v)(x) exp i(kyy – kzz) becomes
simple as
H1z(v) ~ exp (k x)
H1z(v) ~ exp (– k x)

for x < 0 ,for x > 0,

where ky = m/aF, kz = n/R, and the inverse decay
length is k = (ky2 + kz2)1/2. When we choose the RMP
mode, n ~ 3 and m ~ 9, the decay length is about 0.3
m for a DEMO device with aF ~ 3 m. This lengthseems appropriate, not much decaying from thewall but decaying enough in the plasma core. Theabove inner and outer solutions are continued
through the ferritic region, aF – d < r < aF + d.
The magnetization of the ferritic steel is saturated
for the strong magnetic flux density B > Bsat ~ 1.5 T.
The permeability of the ferritic steel can be approximated as µF/ µ0 ≈ (Bsat + Bext) / Bext = 1.1~1.3 in thetokamak DEMO reactor condition Bext = 5~10 T.
Now we insert ferritic steels ideally so that thepermeability distribution become helical,µ = <µ> + µ1 exp i(ky y – kz z)
in the region – d < x < d. Here the average <µ> =(µF + µ0) / 2 and the amplitude µ1 = (µF – µ0) / 2.
Figure 2 is a sample of the FSI configuration with asingle helical mode m/n = 9/3.

Fig.2. Helical FSI configuration with m/n = 9/3. FSs areplaced on the wall at r = aF (φ: toroidal angle and θ:
poloidal angle)

The set of equations in ferritic region, rot H = 0 anddiv µH = 0, is solved by assuming the smallness ofhelical permeability amplitude; µ1/<µ> << 1. The
first order equation becomes∂2Hz1(F)/∂x2 – k2 Hz1(F) + <µ>–1 (∂2µ/∂z2) Hext = 0,
and its solution isHz1(F) + (kz2/ k2) (µ1/<µ>) Hext
= C{ exp(k x) + exp(– k x) } ,Hx1(F) = (i / kz) ∂Hz1(F)/∂x .
At the ferritic steel boundary, x = ± d, the tangential
component of the magnetic field H// is continuous,
while the normal component of the magnetic flux
density B⊥ is continuous;
Hz1(v) = Hz1(F)andµ0 Hx1(v) = µ Hx1(F) .

We obtain the magnitude of the perturbation
Hx1(v) = (kz / k) (µ1/<µ>) Hext / ( 1 + µ0/f <µ>)where f is a function on the ferritic thickness 2d,
f = {exp(kd) – exp(–kd)}/{exp(kd) + exp(–kd)}.
It is confirmed that the helically perturbed magnetic
field is naturally formed in the axisymmetrictoroidal magnetic field through the helical FSI. We
estimate the helical magnetic perturbation on theferritic boundary, for the typical parameter ofDEMO condition, kz/k ≈ naF/mR ~ 0.2 (n/m ~ 1/3,aF/R ~ 1/2) and µ1/<µ> ~ 0.1 (µF/µ0 ~ 1.2):
H1 / Hext ≈ 0.02 f / (1 + f ) .
The f value is easily designed in the range f = 0~0.7
with 2d = 0~0.6 m (k d = 0~1), and consequently themaximum perturbation is up to ~1% of the toroidal
field strength. This amplitude can be more thanenough for the RMP to suppress ELM.
3. Summary and discussion
The RMP is a promising method to suppress
ELM in H-mode plasmas. In DEMO/Commercial
reactors with strong neutron flux, it is desired theRMP coil system near the first wall not to be put in.
We propose an innovative concept of the RMP for
tokamak DEMO reactors without installing coils
but inserting ferritic steels of the helical configuration. Helically perturbed magnetic field is naturally formed in the axisymmetric toroidal magnetic
field through the FSI. The perturbation amplitude
can easily be set ~1% of the toroidal field strength.
Ferritic steels will be employed for the blanket
structural materials in a DEMO reactor. The helical
FS configuration, therefore, can also be attained by
the helical arrangement of blanket modules.
References[1] A. Loarte et al.: Progress in the ITER Physics Basis,Chapter 4, Nucl. Fusion 47 (2007) S203.
[2] Y. Liang: ELM control in tokamak plasmas, 4th
ITER Int. Summer School (Austin, USA, 2010)
http://w3fusion.ph.utexas.edu/ifs/iiss2010/.
[3] T.E. Evans et al.: Phys. Plasmas 13 (2006) 056121.
[4] H. Takatsu: Nucl. Fusion 51 (2010) 094002.