24D05
Core Plasma Design for Helical Fusion DEMO Reactor FFHR-d1
ヘリカル型核融合原型炉FFHR‑d1炉心プラズマの設計
Junichi Miyazawa, Takuya Goto, Ryuichi Sakamoto, Chihiro Suzuki, Yasuhiro Suzuki,Masayuki Yokoyama, Yoshitada Masaoka1), Sadayoshi Murakami1), Teruya Tanaka,
Nagato Yanagi, Hitoshi Tamura, Hiroshi Yamada, Akio Sagara, and the FFHR Design Group
宮澤順一, 後藤拓也, 坂本隆一, 鈴木千尋, 鈴木康浩, 横山雅之, 政岡義唯1), 村上定義1),
田中照也, 柳長門, 田村仁, 山田弘司, 相良明男, FFHR設計グループ
National Institute for Fusion Science, 322-6 Oroshi, Toki, Gifu 509-5292, Japan
核融合科学研究所 〒509-5292 岐阜県土岐市下石町322-61)
Department of Nuclear Engineering, Kyoto University, Sakyo-ku, Kyoto 606-8501, Japan
京都大学大学院工学研究科原子核工学専攻 〒606-8501 京都市左京区吉田本町
A conceptual design activity on the helical fusion DEMO reactor FFHR-d1 has been launched since 2010.
FFHR-d1 is based on the core plasma design extrapolated from experimental data of LHD using the direct
profile extrapolation (DPE) method. A confinement improvement effect due to the peaked heat deposition
profile that is expected in the reactor has been included in the DPE method. Radial profiles of temperatureand density in the reactor predicted by DPE make it possible to analyze detailed properties of the reactor
core plasma, e.g., MHD equilibrium, neoclassical transport, and alpha particle confinement.

1. Introduction
Since 2010, a conceptual design activity on thehelical thermonuclear fusion reactor named
FFHR-d1 has been started [1,2]. Technologicalfeasibilities and safety together with therobustness of core plasma design are emphasizedin FFHR-d1. Similar configuration of thesuperconducting magnet coils as LHD has been
adopted in FFHR-d1 to make the best use ofexperiences in both fields of technology andplasma physics obtained so far in LHD.
In traditional fusion reactor design activities,
radial profiles of density and temperature that
determine the fusion output have been assumed tobe, for example, parabolic. There remains a large
degree of freedom in determining the profiles thatcauses a large ambiguity in the fusion output.
Recently, the direct profile extrapolation (DPE)method has been developed to solve this problem[3]. In the DPE method, the radial profilesobserved in the experiment are directly
extrapolated to the reactor condition based on thegyro-Bohm model. Three enhancement factors forenergy confinement, density, and plasma beta
have been artificially given in the DPE method.
In this presentation, after introducing thedevice parameters provisionally adopted for
FFHR-d1, a new method to estimate the energy
confinement enhancement factor will bediscussed. Preliminary results from theoreticalanalysis on MHD equilibrium and neoclassicaltransport in the reactor will be also shown.

2. Design parameters of FFHR-d1
FFHR-d1 is a heliotron device as LHD, wherenested magnetic surfaces for plasma confinement
are produced by two continuously wound helicalcoils. Except a pair of poloidal coils, FFHR-d1 is alarge reproduction of LHD. Planar poloidal coils
that generate the vertical magnetic field for plasma
shaping and positioning are reduced from 6 in LHD
to 4 in FFHR-d1, to secure large ports formaintenance. The device size is 4 times enlarged
from LHD, i.e., the major radius of the helical coilcenter, Rc, is 15.6 m, and the magnetic field at thehelical coil center, Bc, is 4.7 T, in FFHR-d1. Due tothe reduction of poloidal coils, the averaged plasma
cross section becomes vertically elongatedcompared to the standard configurations in LHD.
To determine these device parameters, iterative
discussions have been carried out between the coreplasma, superconducting magnets, supporting
structures, and blankets. Then, the device
parameters have been fixed to keep the magnetic
stored energy to ~160 GJ, the minimum distancefrom the blanket to the plasma to ~0.7 m. The
self-ignition condition in FFHR-d1, where noauxiliary heating is needed, is foreseen by the DPE
method with an assumed energy confinement
enhancement factor of 1.3 [1]. More details about
the device parameters will be found in [2].
3. Energy confinement enhancement factor
It has been often observed in LHD that the global
energy confinement in the plasmas heated byExtrapolation from LHD (#96172, t = 6.966s)
to FFHR-d1 (B= 5.09 T, R= 14.4 m)(10(a)

19-3m )

reactor(b)40

4. Theoretical analysis
In the reactor, the MHD equilibrium will bedifferent from that in the present experiment, atleast in the cases with the beta enhancement factor,fβ, larger than 1. It will be also necessary to apply avertical magnetic field to control the plasma
position suffered from the Shafranov shift, which
possibly causes degradation in the energy
confinement and/or increase in the direct loss ofalpha particles. Therefore, it is necessary to
calculate the MHD equilibrium using the radial
profiles given by the DPE method. Then, it
becomes possible to concretely evaluate relevant
physics quantities, such as the neoclassical andanomalous transport, and the heat deposition byalpha particles. Preliminary results on the MHD
equilibrium reconstruction using the HINT2 code,
the neoclassical transport analysis using theGSRAKE code, and the alpha particle transport
analysis using the GNET code will be presented.
5. Summary
Typical profiles in the helical DEMO reactor
FFHR-d1 are extrapolated from experimental dataof LHD, using the DPE method and theconfinement enhancement factor as a function ofheating profile. It is already possible to design ahelical fusion reactor without assuming unknown(%)

f = 3.16nn10LHDTef = 7.72

Reactor

510SudocTLHD
Reactorβf = 7.13
βLHD3(MW/m )where Pdep = Pdep(ρ) is the volume-integrated NBpower deposition profile as a function ofnormalized minor radius, ρ, Pdep1 = Pdep(1), and(Pdep/Pdep1)avg is the line-average of Pdep(ρ)/Pdep1
inside ρ ≤ 1 that represents the peaking factor of theNB power deposition profile. The numerator of 0.6
in Eq. (1) is the assumed peaking factor of alphaheating in the reactor condition. The exponent of0.8 in Eq. (1) is determined according to theregression analysis of a dataset obtained in LHD.
Typical radial profiles in FFHR-d1 extrapolated
from LHD using the DPE method coupled with Eq.
(1) are depicted in Fig. 1.

(c)
(d)
(e)

(MW)

(1)

nereactor

Reactor

20

00.8

⎛
⎞
0.6
⎟⎟ ,γ DPE ≡ ⎜⎜⎝ (Pdep / Pdep1 )avg ⎠600(keV)

neutral beam (NB) injection degrades athigh-density. Qualitatively, this has been attributed
to the shallow penetration of NB at high-density,i.e., the NB heat deposition profile becomes peaked
to flat to shallow as the density increases. Thiseffect has been introduced to the DPE method using
the energy confinement enhancement factor, γDPE,defined by05432102000
1000γ

P 'αDPE= 1.29P 'B

P -PαP

BαP

reactorPB

01(f)0.50(Pdep/P)

dep1 avg= 0.721P

dep-1/P

LHD: 0.436

dep1-0.50ρ

0.51Fig. 1. Typical radial profiles in FFHR-d1, where (a)electron density, (b) electron temperature, (c) plasma
beta defined by 100 × 2neTe /(B02/(2μ0)), in LHD (opencircles) and reactor (closed circles), (d) alpha heating(birth profile) and Bremsstrahlung loss per unit volumein reactor, (e) the sum of volume-integrated alphaheating power and Bremsstrahlung loss in reactor, (f)normalized heat deposition profiles in LHD (opencircles) and reactor (closed circles), are shown from top
to bottom. Horizontal lines in (a), (e), and (f) denote thedensity limit of ncSudo in reactor, the conduction loss inreactor, and (Pdep/Pdep1)avg in LHD (broken line) andreactor (solid line, deduced from the alpha birth profile
shown in (d)). The enhancement factors of density,
plasma beta, and energy confinement are assumed to be
3.16, 7.13, and 1.29, respectively.

confinement improvement, although the discovery
of it is still desired. Theoretical studies using theextrapolated profiles have been started successfully.
Further endeavour to obtain better radial profiles for
FFHR-d1 design is, on the other hand, still
underway in LHD.
References[1] A. Sagara et al.: International Symposium on FusionNuclear Technology 10, 11–16 September, 2011,
Portland Oregon US. O38.
[2] T. Goto et al.: This conference, 24D09.
[3] J. Miyazawa et al.: Fusion Eng. Des., in press.