Proceedings of ITC/ISHW2007

Design studies on split-type helical coils for FFHR-2S
Nagato Yanagi, Kiyohiko Nishimura, Akio Sagara, Osamu Motojima
National Institute for Fusion Science, 322-6 Oroshi-cho, Tok, Gifu 509-5292, Japan
Configuration optimization is being carried out for the LHD-type fusion energy reactor FFHR. One of thepresent issues is to find a sufficient clearance between the ergodic layers of the magnetic field lines and the blankets
so that direct loss of alpha particles is minimized and the heat flux on the first wall is reduced. It has been newly
found that by having the combination of splitting the helical coils in the poloidal cross-section and adopting a small
pitch parameter for the winding law of the helical coils, a large gap is clearly obtained. Here, splitting of the helicalcoils means that they have higher current density at the inboard side of the torus and lower at the outboard side,which contributes in enhancing the helical symmetry. A small value of the pitch parameter such as 1 is adopted in
the configuration named FFHR-2S, and the plasma volume is almost the same as that with the original design of
FFHR-2m1 that has the pitch parameter of 1.15. Various physical parameters of the vacuum magnetic surfaces areinvestigated with the new configuration, such as the rotational transform, specific volume and the drift orbits ofhelically trapped particles.
Keywords: FFHR, LHD, heliotron, split-type helical coils, forbidden zone, ergodic layers, blanket space,configuration optimization

1. Inroduction
Based on the successful progress of fusion relevant
plasma experiments performed for 10 years in the Large
Helical Device (LHD) [1], the conceptual design studieson the LHD-type fusion energy reactor (FFHR) are beingconducted both on physics and engineering issues, andthe recent design activities are summarized in [2]. ForFFHR, a heliotron magnetic configuration similar to thatof LHD will be employed so that the confined plasma iscurrent free and the steady-state operation is realized.
Though the further optimization of the configuration isstill being carried out, the basic parameters give thetoroidal magnetic field of 6 T with a major radius in therange 14-18 m in order to generate 3 GW fusion power.
By having the machine size approximately four times
bigger than that of LHD, the stored magnetic energy ofthe superconducting coil system is in the range 120-150
GJ.
In these studies, the coil pitch parameter, γ, definedby (m/l)(ac/Rc) for continuous helical coils (having thetoroidal pitch number m, poloidal pole number l, averageminor radius ac and major radius Rc), has been chosen to
be lower than 1.25 adopted for the present LHD. This
choice is made for the purpose of reducing theelectromagnetic hoop-force on the helical coils while
ensuring larger blanket space between the core plasma
and the helical coils [3]. The latest standard configuration,
named FFHR-2m1, has γ = 1.15 with m = 10, l = 2, ac =3.22 m and Rc = 14 m.
The vacuum magnetic surfaces of FFHR-2m1 isauthor’s e-mail: yanagi@LHD.nifs.ac.jp

shown in Fig. 1(a). One of the most difficult issues withthis configuration is found in the still observed
interferences between the ergodic layers of the magnetic
field lines and the blankets (thickness: ~1.1 m) especiallyat the inboard side of the torus. In order to reduce the heat
flux on the blankets, the concept of “helical x-point
divertor (HXD)” was proposed [4]. However, this choicegives a high heat flux on the limiter-like structures, andmoreover, a recent study shows that the confinement ofalpha particles is deteriorated. Since the alpha particles
are lost finally along the magnetic field lines in theergodic regions, the loss rate is substantially reduced if
the ergodic layers are not cut by metallic materials.
In this connection, we are seeking for anotherapproach of ensuring much clearer blanket space bymodifying the coil configuration while keeping the major
radius below 16-17 m. As was found in the previous
study [5], the symmetry of magnetic surfaces around themagnetic axis is significantly improved, without shifting
the magnetic axis inward, by increasing the current
density at the inboard side of the helical coils while
decreasing at the outboard side. Modulation of the current
density can be practically realized by splitting the helicalcoils in the poloidal cross-section. Using this feature by
splitting the helical coils, we found a new configurationthat assures sufficient clearance between the ergodic
layers and the blankets. For the new configuration,
various physics properties of the magnetic field areinvestigated and the initial results of the parameter
surveys are introduced in this paper.

Proceedings of ITC/ISHW2007

(a)

(b)

(c)

Fig.1 Plan views of the coils and magnetic surfaces at two cross-sections for (a) FFHR-2m1, (b) FFHR-2S (γ = 1.0,
α = +0.1) and (c) FFHR-2S (γ = 1.0, α = -0.1). The coil currents are assumed by 16 filaments in one helical coil. For
splitting a helical coil, the half portion of the coil is assumed by 8 filaments.

2. Vacuum magnetic surfaces of FFHR-2S andtheir properties
Using the remarkable properties of improving thehelical symmetry by splitting the helical coils in thepoloidal cross-sections, new magnetic configurations
were surveyed. However, it was found that the ergodic
layers could not be easily removed from the blanket areaat the inboard side by simply splitting the helical coils
while maintaining the original pitch parameter of γ = 1.15.

In order to overcome this difficulty, we newly found thata drastically larger gap is obtained by reducing the pitch
parameter to be as low as γ = 1.0 together with splittingof the helical coils. Figure 1(b) and (c) show examples ofthe vacuum magnetic surfaces with γ = 1.0 configurations.
Two examples are shown with the pitch modulation
parameter α of +0.1 and –0.1. The major radius is 16.1 m
for both cases by keeping the minor radius of the helicalcoils to be 3.22 m, the same as that for FFHR-2m1. As isProceedings of ITC/ISHW2007
seen in these figures, the outermost ergodic layers areclearly displaced from the blankets. Here, the shapes andthe positions of the blankets are adjusted in these figuresin order to avoid any interference.
Here we should note that such a low pitch parameterof γ = 1.0 has never been examined so far, as it has been
well known that one is already in the so-called
forbidden-zone for generating magnetic surfaces with a l= 2 heliotron configuration [6]. We understand that thelow pitch parameter is effective for making the ergodiclayers compact, while the splitting of helical coils ensurelarger closed magnetic surfaces. Figure 2 shows thedistance between the helical coils and the ergodic layers.
The magnetic configuration of FFHR-2m1 has aninterference with the blankets unless it is with a muchlarger major radius. For FFHR-2S, much wider space isassured with a smaller major radius. Here it is assumed thatthe distance between the helical coils and vacuum vessel isconstant at 110 mm, which is the same as that for LHD.
The basic physical quantities of the vacuum
magnetic surfaces are evaluated, such as the rotationaltransform and specific volume as a function of theaverage minor radius. The radial variation of the rotationaltransform is shown in Fig. 3(a). Even with the lower pitch
parameter, a larger plasma minor radius is expected for
FFHR-2S. At the same time, a larger shear of the rotationaltransform is expected, which is good for MHD stability.
On the contrary, the specific volume shows that a magnetic
hill is formed all over the magnetic surfaces. It is expectedthat magnetic well is introduced by the plasma beta andthis should be calculated in our future study. It should also
be stressed, on the other hand, that by having a smaller
pitch parameter, the helical coils experience lesselectromagnetic forces, which is one of the fundamental
benefits of the FFHR concept [3].

Fig.2

Distance between the vacuum vessel and theergodic layers of magnetic field lines for
FFHR-2m1 and FFHR-2s.

Fig.3 (a) Rotational transform and (b) specific volume
for FFHR-2m1 and FFHR-2S with α = +0.1 and–0.1 as a function of the average minor radius.

3. Drift orbits of helically trapped particles
One of the important properties of magnetic
configuration for helical devices is the particle orbits
especially in terms of the direct loss of particles trappedin helical mirrors. Another advantage of the new
configuration of FFHR-2S is found with its particle orbits
for the pitch modulation parameter α of –0.1. A
comparison of the orbits of perpendicularly injected
deuterons is given for FFHR-2m1 and FFHR-2S in Fig. 4.
As is always observed for conventional heliotron
configurations such as LHD, the drift orbits of thehelically trapped particles are shifted inward compared tothe magnetic surfaces (with the magnetic axis at thecenter of the helical coils) as is seen in Fig. 4(a) for
FFHR-2m1. The drift orbits for FFHR-2S has a similartendency for the particles starting from the core region,
however, the confinement of particles are better up to theplasma periphery, as is seen in Fig. 4(b).
In order to clarify the difference about particle orbits,
the helical ripples are compared for the two
configurations. Figure 5 shows the variation of themagnetic field strength along magnetic field lines.
Compared to FFHR-2m1, the helical ripples in FFHR-2S

Proceedings of ITC/ISHW2007
are mitigating the toroidal ripples, which lead to the better
confinement of helically trapped particles. Figure 6 shows
the variation of the amplitude of the helical ripples as afunction of the minor radius. The helical ripple ofFFHR-2S is almost the same as that for FFHR-2m1 near
the magnetic axis, however, it remains less than half at alarger minor radius. The small helical ripple should
contribute in a better confinement of plasma not only interms of neoclassical transport but also of anomalous one.

4. Conclusions
A new magnetic configuration for the LHD-type
fusion energy reactor FFHR is examined by splitting thehelical coils in the poloidal cross-section. It was found thatby employing a low pitch parameter of γ = 1.0, a large
clearance is obtained between the ergodic layers andblankets. This configuration with a negative pitch
modulation parameter of α = -0.1 has good properties forthe drift orbits of helically trapped particles. The
optimization of the coil configuration is being carried out
also from the engineering viewpoint.

Fig.5Variation of the magnetic field strength along thefield lines for FFHR-2m1 and FFHR-2S (α =-0.1) on the magnetic surfaces having the averageminor radius of 1 m for both cases.

Fig.6

Variation of helical ripples as a function of theaverage minor radius for FFHR-2m1 andFFHR-2S (α = -0.1).

Acknowlegments
The authors are grateful to many other staff in theFFHR design group for valuable discussion and support.

References
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[2]
[3]

Fig.4 Drift orbits of deuterons for (a) FFHR-2m1 and(b) FFHR-2S. Deuterons with 500 keV energy are
injected with a pitch angle of 90 degrees atvarious locations on the magnetic surfaces.

[4]
[5]
[6]

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