J. Plasma
J.
Plasma Fusion
Fusion Res.
Res. SERIES,SERIES,Vol.
Vol.6 6(2004)(2004)303–305
000–000

Parameter Requirements for D-3He Helical Reactors
MITARAI Osamu, SAGARA Akio1, IMAGAWA Shinsaku1, TOMITA Yukihiro1,
WATANABE Kiyomasa1 and WATANABE Tsuguhiro1
Kyushu Tokai University, Toroku 862-8652, Japan
National Institute for Fusion Science, Toki 509-5292, Japan

1(Received: 9 December 2003 / Accepted: 12 February 2004)

Abstract
Parameter requirements are studied for D-3He helical reactors with three sizes based on the shifted large helicaldevice (LHD) plasma (the major radius R = 3.6 m) with R = 14.5~18.5 m, and for a compact reactor based on aquasi-poloidal stellarator with R = 10.36 m. To achieve ignition in a D-3He helical reactor with the magnetic fieldstrength Bo = 6 T, the confinement should be improved up to >2.4 times larger than the present LHD confinement,and the volume averaged beta 〈β 〉 = 14~21 %, the hot ion mode with the peak ion to electron temperature ratio Ti /Te >1.5 and the heating power of 200~300 MW are necessary. The lower beta would be obtained in a larger machine
and the neutron power can be reduced to 60 ~ 90 MW for 3 GW fusion power.
Keywords:
D-3He fusion, Helical reactor, Ignition, Low neutron power, LHD, Quasi-poloidal stellarator

1. Introduction

the operating density by 2 %. Fusion power is regulated by aproportional-integration-derivative (PID) controller with thefusion power signal, and fuel ratio of D and 3He is controlled
by a proportional-integration (PI) controller with fuel ratio
signal. This D and 3He fuel ratio control is important toachieve the low neutron power mode. We employ theconfinement factor γLHD over the present LHD confinement
time of 1.6 × τISS95 in this study with τISS95 being theconfinement time given by ISS95 scaling. This ISS95 scaling
created for a helical system is the second different point fromthe tokamak reactor analysis. The effective minor radius a–expressing the helical plasma makes a helical system analysis
similar to a tokamak reactor analysis. All the effective particle
confinement time ratios of the deuterium, helium-3, tritium,
14 MeV proton and 3.7 MeV alpha particle to the energy
confinement time are assumed to be 2, and the prompt lossof all the fusion products to be zero. The density andtemperature profiles are assumed as parabolic. As the beta
value is lower than that in ST, ignition is sensitive to the wall
reflectivity (Reff), then Reff = 0.99 has been chosen.

A D-3He fusion is attractive for achieving a safer andcleaner fusion reactor. Therefore, ARTEMIS studies had been
conducted using the field reverse configuration (FRC) forachieving D-3 He fusion by Momota et al. [1]. Recent
demonstration of feasibility of a D-3He spherical tokamakreactor [2] also urges studies of a D-3He helical reactor, which
has not been explored yet. To see the future prospect of LHD
type experiments and other type of helical machine, it isimportant to study parameter requirements in a D-3He helical
reactor. In contrast to a D-3He tokamak system requiring thelarge plasma current more than 50 MA, the possible plasma
current-free operation in a helical system is advantageous
because of no risk of the disruption. In this paper, we examine
parameters to be necessary for D-3He helical reactors basedon the 0-dimensional analysis and the international stellaratorscaling (ISS95 scaling) [3] for three sizes of helical reactors
and a quasi-poloidal stellarator (QPS) [4].

2. Formalism and ignition control
algorithm

3. Temporal evolution of the plasma
parameters to ignition

We have used the 0-dimensional particle and power
balance equations for D-3He, D-D and D-T fusions. The hot
ion mode of Ti /Te = 1.5 is assumed in the power balance
equation. As clear transition from L to H mode in LHD has
not been observed, the density limit has been used for controlof the heating power [5], which is mainly different from thetokamak reactor analysis. Therefore, the applied external
heating power is set to expand the density limit larger than

D-3He ignition is possible for a helical reactor with R =14.5 m, a– = 2.6 m, Bo = 6 T, and the high beta of 〈β 〉 ~ 18 %.
Confinement factor with γLHD = 2.4 provides ignition with theexternal heating power of PEXT = 300 MW for the fuel ratioof D:3He = 2:1, leading to high neutron power of Pn = 184
MW.

Corresponding author’s e-mail: omitarai@ktmail.ktokai-u.ac.jp1303©2004 by The Japan Society of Plasma
Science and Nuclear Fusion ResearchMitarai O. et al., Parameter Requirements for D-3He Helical Reactors

The lower neutron power of Pn = 61 MW is achieved
after switching the fuel ratio setting value to the helium richstate of D:3He = 0.45:0.55 at 70 sec as shown in Fig.1. The
external heating power is lowered to PEXT = 200 MW in thecase of higher confinement factor of γLHD = 3. The final beta
reaches 〈β 〉 ~ 21 %, and the peak electron density n(0) is
3.92×1020 m-3 and the peak ion temperature Ti (0) is 115 keV.
The total Bremsstrahlung loss power PB = 0.9 GW to the firstwall and the total plasma conduction loss PL~1.8 GW todivertor should be converted to the electricity. For the thermal
conversion efficiency of 40 %, the electrical power output
may be 1.1 GW. Average heat flux to the first wall (Γh) is
0.74 MW/m2 which is manageable in the present technology
and the average neutron wall loading (Γn) is 0.04 MW/m2,
where the blanket could be used for a reactor life time. The
divertor heat flux Pdiv to the assumed wetted area with 1 m
width of two legs is ~10 MW/m2, which is calculated by Pdiv
= PL /(2 πR × 1m × 2 legs), providing a challenging task
especially for the shorter wetted width [6]. The detailed
parameters are listed in Table 1. As the ratio of thebremsstrahlung and conduction loss power, which determines
the divertor heat flux, depends on the confinement law itself(the power law of the density and the external heating powerin the ISS95 scaling), it is difficult to change this ratio byconfinement improvement.
The larger machine such as R/ a– = 16.6 m/2.9 m can alsoreach ignition with γLHD = 3.0 and PEXT = 250 MW, and theslightly larger neutron power of Pn = 87 MW is obtained forthe fuel ratio of D:3He = 0.52:0.48 at 〈β 〉 ~ 16 %. For theFig. 1

Temporal evolution of the plasma parameters in the
low neutron power mode in the D-3He helical reactor
with R = 14.5 m. (a) The peak density n(0), density limitn(0)LMT and peak ion temperature Ti (0), (b) fusion power
Pf , fusion power set value Pf0 , and alpha and proton ash
fraction falpha , (c) the energy confinement time τE andthe total neutron power Pn , (d) beta value β and density
limit factor n(0)LMT /n(0) and (e) the external heatingpower PEXT and deuterium SD and helium-3 fueling rate
SHE3 .

Table 1. Parameters for LHD type D-3He Helical Reactors
Major radius:
Effective minor radius:
Toroidal field:
Plasma volume
Average plasma surface area
Blanket thickness:
Rotational transform:
Heating power:
Confinement factor:
Confinement time:
Ash density fraction:
Effective ion charge:
Fuel ratio:
Electron density:
Ion temperature:
Toroidal beta value:
Fusion power:
Neutron power:
Bremsstrahlung loss:
Synchrotron radiation loss
to the wall:for energy conv.:
Plasma conduction loss:
Electric power (ηc = 40 %)Average neutron wall loading
Average heat flux:
Divertor heat load

Ra–Bo
VoSo
∆BT
ι- 2/3PEXT
γLHD
τEfalphaZeff
nD:nHe3n(0)Ti (0)〈β 〉PfPnPB

14.47 m2.585 m
6.0 T
1908 m31476 m2
0.933 m0.92200 MW
2.4~3.0
4.7 s
5.1 %
1.73
0.45:0.55
3.92×1020
115
21.1%
3 GW
61 MW
906 MW

16.62
2.908
6.02774
1988
1.115
0.92
250 (300)
2.5~3.0
5.0
4.4
1.68
0.52:0.48
3.3×1020
100
15.9
387
818

18.46
3.232
6.0
3806
2355
1.297
0.92
250 (300)
2.5~3.0
6.3
4.9
1.68
0.52:0.48
2.72×1020
107
14.0386803

Psw
PsH
PLPeΓnΓhΓr89.3 MW99.2 MW1847 MW~1100 MW0.04 MW/m2
0.74 MW/m2~10 MW/m2

94.6
105.1
1897
~1000
0.046
0.539143158
1810~10000.036
0.47
7.82304

Mitarai O. et al., Parameter Requirements for D-3He Helical Reactors

smaller confinement factor of γLHD = 2.5, the larger heating
power of PEXT = 300 MW is required. For somewhat larger
machine such as R/ a– = 18.5 m/3.2 m, the beta value can be
reduced to 〈β 〉 ~ 14 % for similar performances as listed inTable 1. This is because that the longer confinement time inthe larger machine leads to the lower density, and hence lowerbeta.
We note that the same size of D-T reactor (R = 14.5 m,–a = 2.6 m, Bo = 6 T) does not require any improvement inconfinement (γLHD = 1.0) for D-T ignition in the case of ηα =1 (no prompt loss of alpha particles) and τα*/τE = 3 (alphaash confinement time to the energy confinement ratio). The
initial heating power is 70 MW, and the final beta is 〈β 〉 ~2.7 %, which is within the present experimental value. On
the other hand, a D-3He helical reactor is demanding in beta,
confinement factor and divertor heat flux when LHD type
machine is assumed. Therefore, we have further searched forthe other type of helical machines suitable for a D-3He fusion
such as quasi-poloidal stellarator proposed by Oak Ridge
National Laboratory group [4]. In this machine, the high betaof 〈β 〉 = 15~23 % and long confinement time of τE ~ 6 × τISS95= 3.75 × (1.6×τISS95) are expected for the aspect ratio of A =3.7. The large confinement factor compensates the relatively
low rotational transform of -ι = 0.4 at the center. We havecalculated the temporal evolution of the plasma parametersin the compact QPS D-3He reactor with R = 10.36 m, a– = 2.8m, and Bo = 6 T as shown in Fig. 2. For γLHD = 3.7, theconfinement fraction of the 14 MeV proton and 3.7 MeValpha particle ηp = ηα = 97 % and D:3He = 0.49:0.52, wehave obtained the following parameters such as Pn = 72 MW,
Γn = 0.06 MW/m2, Γh = 0.84 MW/m2, the alpha and proton
ash fraction falpha = 5.0 %, PL = 1.9 GW, PB = 0.88 GW, thetotal synchrotron radiation loss power PS = 0.15 GW, τE~4.1s, n(0)~4.29×1020 m-3, Ti (0)~111 keV and 〈β 〉 = 22.7 % in
the steady state phase.

Fig. 2

Temporal evolution of the plasma parameters in thecompact QPS D-3He helical reactor with R = 10.36 m.

density and larger confinement time. While these parameter
improvements are challenging for LHD type machine, QPS
is quite interesting for D-3He fusion.

Acknowledgments
One of authors (O.M.) thanks Prof. S. Okamura for
information on QPS.

References[1] H. Momota et al., in 7th International Conference onEmerging Nuclear Energy Systems, (Makuhari, Chiba,Japan, 1993) p16.
[2] O. Mitarai and Y. Tomita, to be submitted in “A D-3Hespherical tokamak reactor using efficient use of thevertical field and heating power”, (2004).
[3] U. Stroh et al., Nucl. Fusion 36, 1063 (1996).
[4] D.A. Spong et al., Nucl. Fusion 41, 711 (2001).
[5] S. Sudo et al., Nucl. Fusion 30, 11 (1990).
[6] A. Sagara et al., J. of Nucl. Matt. 313-316, 1 (2003).

4. Summary and issue
To achieve ignition in a D-3He helical reactor with R =14.5 m to 18.5 m and Bo = 6 T, the confinement should beimproved up to >2.4 times larger than the present LHD
confinement, and 〈β 〉 = 14~21 %, the hot ion mode of Ti /Te>1.5 and the heating power of 200~300 MW are necessary.
Neutron power is 60~90 MW. However, divertor heat load ischallenging. Larger machine has a lower beta due to the lower

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