1

Physical and Engineering Designs for Chinese First Quasi-axisymmetric Stellarator (CFQS)

Yuhong Xu1, Haifeng Liu1,4, Guozhen Xiong1, Akihiro Shimizu2, Shigeyoshi Kinoshita2,

Mitsutaka Isobe2,5, Shoichi Okamura2, Motoki Nakata2,5, Dapeng Yin3, Yi Wan3, Wilfred

Anthony Cooper2,6, Caoxiang Zhu7, Hai Liu1, Xin Zhang1, Jie Huang1, Xianqu Wang1,

Changjian Tang1,4 and the CFQS team1,2

1 Institute of Fusion Science, School of Physical Science and Technology, Southwest Jiaotong University,

Chengdu 610031, China 2 National Institute for Fusion Science, National Institutes of Natural Sciences, Toki 509-5292, Japan 3 Hefei Keye Electro Physical Equipment Manufacturing Co., Ltd, Hefei, 230000, China 4 Physics Department, Sichuan University, Chengdu 610041, China 5 SOKENDAI (The Graduate University for Advanced Studies), Toki 509-5292, Japan 6 Ecole Polytechnique Fédérale de Lausanne, Swiss Plasma Center, Station 13, CH-1015 Lausanne, Switzerland 7 Princeton Plasma Physics Laboratory, Princeton University, P O Box 451, NJ 08543, USA

E-mail contact of main author: xuyuhong@swjtu.edu.cn

Abstract. The Chinese First Quasi-axisymmetric Stellarator (CFQS) is a joint project of international

collaboration. It is designed and fabricated by the Southwest Jiaotong University (SWJTU) in China

and the National Institute for Fusion Science (NIFS) in Japan. The target parameters of CFQS are

chosen as follows: the toroidal period number Np = 2, major radius R0 =1.0 m and magnetic field

strength Bt =1.0 T. Via the scan of major radius, aspect ratio and coil numbers, the target parameters

of the CFQS configuration are determined by comprehensively considering physical and engineering

constrains on equilibrium, MHD instabilities, neoclassical and turbulent transport, etc. It turns out that

the configuration for a 16-coil system with Np =2, R0 =1.0 m, a=0.25 m, Bt =1.0 T and aspect ratio Ap

=4.0 is the most preferable. In addition, the engineering design for the modular coils, the vacuum

vessel and support structures of the CFQS has also been preliminarily performed.

1. Introduction

The quasi-axisymmetric stellarator offers novel solutions for confining high-β plasmas by

combining the best features of advanced tokamaks and optimized stellarators [1, 2]. Using the

3D shaping freedom available in a stellarator, configurations can be designed that exhibit

stable MHD behaviors without external current drive requirements at high β. The quasi-

axisymmetry yields well-confined particle orbits and hence neoclassical transport, which is

equivalent to that in tokamaks. To this end, the Southwest Jiaotong University (SWJTU) in

China and the National Institute for Fusion Science (NIFS) in Japan are making collaboration

for constructing a new quasi-axisymmetric stellarator in China [3, 4]. In this paper, the

physical and engineering designs for the CFQS are introduced. The calculations show that a

16-coil system with Np =2, R0=1.0 m, a=0.25 m, Bt =1.0 T and Ap = 4.0 represents the

optimum configuration for the CFQS stellarator.

2. Physical design of CFQS

2.1 Equilibrium

The equilibrium of the magnetic field configuration of the CFQS is obtained with the VMEC

code, which calculates the MHD equilibrium from the given geometry of the outermost

2

magnetic flux surface and the radial profiles of plasma pressure and toroidal current [5, 6].

The geometry of the torus outermost magnetic flux surface can be parameterized by Fourier

series as follows:

𝑅(𝜃, 𝜙, 𝑠) = ∑𝑅𝑚𝑛(𝑠) cos(𝑚𝜃 − 𝑁𝑝𝑛𝜙),

𝑍(𝜃, 𝜙, 𝑠) = ∑𝑍𝑚𝑛(𝑠) sin(𝑚𝜃 − 𝑁𝑝𝑛𝜙),

Here, 𝜃, 𝜙, 𝑠 are the poloidal angle, toroidal angle, and the radial flux coordinate, m and n

denote the poloidal and toroidal mode numbers, and Np is the toroidal period number of the

magnetic field configuration. In stellarator optimization, we consider Rmn and Zmn as control

parameters to be varied for achieving physics properties desired. For the numerical

optimization, the characteristics of the magnetic field configuration are expressed

quantitatively, e. g., the sum of non-axisymmetric components of magnetic field in the

Boozer coordinates [7], the Mercier criteria of DI and the effective helical ripple 𝜀𝑒𝑓𝑓, etc. are

used for the numerical evaluation of the magnetic configuration. The guiding center drift

orbits of charged particles in the Boozer coordinate in stellarators depend only on the

geometry through the absolute value of the magnetic field strength B [7, 8]. The design of B

such that it varies dominantly with s and 𝜃, but weakly with 𝜙 yields a configuration that is

called quasi-axisymmetric. This type of system recovers the favorable neoclassical transport

properties of the exactly axisymmetric tokamak despite its 3D geometry.

The physical design of CFQS is based on the earlier designed 2b32 configuration of

CHS-qa at NIFS, which has a good quasi-axisymmetry with favorable magnetic well and

ballooning mode stability [9]. For the CFQS, Np = 2, B =1.0 T and the major radius R0 = 1.0

m were chosen initially. The low aspect ratio Ap =3.2 of CHS-qa constitutes a practical

technical challenge. We therefore select Ap = 4 so that the coil system is easier to realize from

an engineering point of view. Plotted in Fig. 1 are the equilibrium magnetic flux surfaces

calculated with the VMEC code for plasma pressure-free case at three different toroidal

angles. The radial profiles of the rotational transform (iota) and the magnetic well are

depicted by red and green curves in Fig. 3(d). The iota profile has a low shear and the value

between 2/6 and 2/5 is favorable to avoid low-order rational surfaces in the plasma. The

magnetic well extends across the entire plasma radius, which is beneficial to stabilize MHD

instabilities and reduce the island width [10]. The Fourier spectrum of the magnetic field

R (m)

Z (

m)

= 0 = 45 = 90

Fig. 1 Poloidal cross-sections of CFQS vacuum magnetic surfaces calculated with the

VMEC code at three different toroidal angles (𝜙=0o, 45o and 90o).

3

strength, Bmn, further indicates that the B10 component plays a dominant role at all flux

surfaces (see Fig. 4(a)) and the large axisymmetric crescent, elongation and triangularity may

enhance stability of ballooning and kink modes.

2.2 Coil system

In order to achieve the target magnetic configuration, a modular coil system is necessary

to be designed to reproduce the plasma boundary. According to the Neumann boundary

condition, the accuracy of the magnetic configuration induced by the coil system depends on

the normal component of the magnetic field on the plasma boundary, which is expressed as

nB , where B is the vacuum magnetic field generated from the coil system at the plasma

boundary and n is the normal unit

vector of this surface. Via the

minimization of nB on the plasma

boundary, the modular coil

geometry is optimized. Meanwhile,

the engineering constraints are also

taken into account, i. e., the

minimum interval between adjacent

coils and the maximum curvature.

They are imposed to avoid the coil-

coil overlap and to reduce

complexity of the coil shape. This

optimization process is

accomplished with the NESCOIL

code [11]. In the design of the

CFQS coil system, the coil numbers,

major radius and the aspect ratio have been scanned to achieve an optimum modular coil

system. The corresponding parameters are listed in Table 1. Totally, we have calculated for

R0 (m) Ap a (m) Bt (T) Number of modular coils

1.5 3.2 0.47 1.0 20

1.5 3.9 0.38 1.0 20

1.5 4.0 0.38 1.0 20

1.5 5.0 0.30 1.0 20

1.2 4.0 0.30 1.0 24,20,16,12

1.0 3.2 0.31 1.0 20,16,12

1.0 3.6 0.28 1.0 20,16,12

1.0 4.0 0.25 1.0 20,16,12

Total Number of configurations: 10, Number of coil systems: 17

Table 1 Parameters for 10 different magnetic configurations and 17 coil systems designed. It

turns out that the configuration with Np =2, R0=1.0 m, a=0.25 m, Bt =1.0 T and Ap = 4.0 is the

most optimal along with 16 coils.

Fig. 2 Top view of modular coils of CFQS. The

coil system comprises four different shapes.

4

10 different magnetic configurations and 17 coil systems. Finally it turns out that the

configuration with Np =2, R0=1.0 m, a=0.25 m, Bt =1.0 T and Ap = 4.0 is the most optimum.

For the coil numbers, the comparison of the physical and engineering constraints among 12,

16, 20 and 24 coils demonstrates that the 16-coil system is most preferable [12]. Figure 2

displays the 16 modular coil system, consisting of four different shape modular coils due to

Np =2 and the stellarator symmetry. The centerline of each finite sized coil is assigned by the

corresponding filament coil [11]. The coil cross section is rectangular and the area is

13.2×6.9 cm2 which includes copper conductor, insulation and coil casing.

For evaluating the accuracy of the magnetic configuration induced by the 16-coil system,

the magnetic flux surfaces, rotational transform and Fourier spectrum of the magnetic field

strength generated by the coils are calculated, assuming that the coils are filamentary ones. In

Fig. 3, the Poincaré plots of magnetic surfaces at cross sections of 𝜙=0o, 45o and 90o and the

iota and magnetic well profiles induced by the modular coils are illustrated. In Figs. 3(a)-(c),

the red curves indicate the target plasma boundary calculated with VMEC. The shapes of the

coil-generated flux surfaces are quite coincident with the target boundary. The average of

|B|n/B at the plasma boundary is below 1%, which cannot be reduced further from the

engineering viewpoint. The comparisons of iota and magnetic well in Fig. 3(d) also show

good agreement between the coil-induced and the target profiles. It should be noted that the

radial extent of the outermost flux surface produced by the modular coils is larger than that of

target plasma boundary, which is beneficial to increase the plasma volume with movable

limiters. In order to precisely estimate the quasi-axisymmetry of the configuration, the coil-

generated magnetic field strength is decomposed into a Fourier spectrum in the Boozer

coordinates and compared with the target spectrum. The Bmn components calculated with the

VMEC code and the coil-induced magnetic field are shown in Fig. 4(a) and 4(b), respectively.

Fig. 3 (a)-(c) Poincaré plots

of coil-generated magnetic

flux surfaces at cross

sections with 𝜙=0o

, 45o

and

90o

. The red curves indicate

the target plasma boundary

calculated with the VMEC

code. (d) Comparison of the

radial profiles of iota and

magnetic well generated with

the modular coils and their

corresponding targets.

(a) (b)

(c) (d)

5

To visualize small-amplitude components, the largest B00 is omitted. The results are quite

similar in the two cases. The B10 component is dominant, while the others, such as the mirror

ripple (B01) and helical ripples (B11, B12), are much smaller than B10, indicating a tokamak-

like or quasi-axisymmetric configuration.

With respect to the MHD instabilities, the Mercier and ballooning modes have been

calculated to evaluate the property of the CFQS configuration. When is enhanced up to 1%,

the MHD equilibrium of the configuration remains stable and the bootstrap current estimated

by the BOOTSJ code in the collision-less limit reaches ~ 30 kA [13, 14]. To investigate the

influence of finite with bootstrap currents on the neoclassical transport, the effective

helical ripple 𝜀𝑒𝑓𝑓 is calculated with the NEO

code [15]. Figure 5 plots the radial profile of

𝜀𝑒𝑓𝑓3/2

, which is proportional to the neoclassical

diffusion coefficient. As a reference, the 𝜀𝑒𝑓𝑓3/2

profile in the CHS is also shown, and the value

of 𝜀𝑒𝑓𝑓3/2

in CFQS is about 2 order lower than that

in CHS at the location of 0.5. Meanwhile, the

degradation of 𝜀𝑒𝑓𝑓3/2

due to finite is rather small

for CFQS. It is expected that the neoclassical

transport in the 1/𝜈 regime of CFQS is less than

that in W7-X [12, 14].

The characteristics of turbulent transport in

CFQS have also been studied recently using the

electromagnetic gyrokinetic Vlasov simulations

with GKV [16]. The impacts of quasi-axisymmetry

on the linear ion temperature gradient (ITG)

instability, turbulent transport and zonal flow

Fig. 4 Comparison of Fourier spectrum of the magnetic field strength, Bmn, in the

Boozer coordinate frame for the CFQS (a) target spectrum calculated with the

VMEC code, (b) Bmn generated with the modular coils.

Fig. 5 Radial profiles of 𝜀𝑒𝑓𝑓3/2

for

various and the corresponding

bootstrap currents. The profile of

𝜀𝑒𝑓𝑓3/2

in the CHS (R0 = 92.1 cm, =

0.0%) is also shown as a reference.

Target Bmn(VMEC)

Helical ripples

Toroidal ripple

Mirror ripple

Toroidal ripple

Mirror ripple

Helical ripples

Bmn induced by coils

Fig. 4 Comparison of Fourier spectrum of the magnetic field strength, Bmn, in the

Boozer coordinate frame for the CFQS (a) target spectrum calculated with the

VMEC code, (b) Bmn generated with the modular coils.

6

generation are investigated. It is shown that the quasi-axisymmetric stellarator has more

unstable ITG modes in comparison with the equivalent tokamak. However, the turbulent

transport level is comparable or less in the nonlinear phase, and hence, strong zonal flows

could be excited in CFQS [17]. Finally at the plasma periphery, a novel island bundle

divertor configuration may emerge, which is favorable for the distribution of heat load at the

plasma boundary of CFQS [18].

3. Engineering design of CFQS

Based on all of above analyses, the

16-coil system with Np =2, R0=1.0 m, Bt

=1.0 T and Ap = 4.0 we proposed for

CFQS constitutes a very feasible

engineering design, which has been

performed preliminarily for the modular

coils, vacuum vessel and support

structures, as depicted in Fig. 6.

3.1 Modular coils

The 16 modular coils of CFQS

consists of four different types of coils,

which are classified as M1, M2, M3 and

M4, as shown in Fig. 7. The engineering

design of the modular coil has been

preliminarily completed. The coil has 72

turns, with 12 and 6 layers in the radial and other directions, respectively (see Fig. 7(b)). The

material of the conductor is oxygen free copper. It is a 8.58.5 mm2 square (1 mm rounded

corner) with a diameter = 4 mm hollow for the water cooling channel. The thickness of the

insulation layer wrapping around the conductor is 1 mm. And the thickness of the grounding

insulation wrapping around the coil winding is 3 mm.

Fig. 6 Schematic drawing of the CFQS

modular coils, vacuum vessel, and support

structures.

(a)

(b)

Fig. 7 (a) Modular coils of CFQS; (b) hollow conductor and insulation for the CFQS

coil with 612 layers.

7

The electromagnetic analysis and the calculation of the electromagnetic force of the

modular coils have been performed with ANSYS for the CFQS modular coils [19]. The

maximum magnetic field located at the inner side of the coil is about 2.5 T, and the magnetic

field strength at the magnetic axis is about 1 T. The maximum electromagnetic force volume

density is about 1.44108 N/m3 and the maximum force of 168 KN is on the M1 coil. The

error field analysis has also been done with a Hessian matrix approach for determining the

error field sensitivity to coil deviations in CFQS coils using the FOCUS code [20].

3.2 Vacuum vessel

The Vacuum Vessel (VV) is also an important part of CFQS. To meet physical and

engineering constraints, the VV structure, good performance of conductivity, fine vacuum,

appropriate loop resistance and adequate supporting strength should be all considered [21].

The VV is a single layer and thin wall

structure of SUS316L material baked

under 150℃ temperature to ensure

favorable vacuum characteristics. As

shown in Fig. 8, numerous ports are

provided for vacuum pumping, plasma

diagnostics and heating apparatus.

Two large rectangular ports are

provided for NBI and the Thomoson

scattering diagnostic system. One of

them also serves as an entrance to the

VV for maintenance. Considering the

limited space around the VV, welding

of split part and large diameter ports

will be done from inside of VV. The

structure of the VV is sufficient strong

to withstand the barometric pressure and gravity. And the thermal stress caused by the

temperature gradient during the baking process have also been considered.

3.3 Structural support

Based on the magnitude and direction of the electromagnetic force of the modular coils in

CFQS, the support system has been designed preliminarily. The support includes the main

structural support and the coil support plate. The main structural support is designed to

provide a support for the VV and coils while the coil support plate is designed to withstand

the outward expanding force on each coil. The reliability of the support structures is under

investigation.

Fig. 8 Structure of the CFQS vacuum vessel

with numerous ports designed for the access

of diagnostics and heating apparatus, etc.

8

4. Summary

The Southwest Jiaotong University in China and National Institute for Fusion Science in

Japan are collaborating to construct a new quasi-axisymmetric stellarator CFQS in China.

The physical and engineering designs of CFQS have been performed by deliberately

considering various constraints on equilibrium, MHD instabilities, neoclassical and turbulent

transport, etc. Via the scan of major radius, aspect ratio and coil numbers, it turns out that the

configuration of a 16-coil system with Np =2, R0=1.0 m, a=0.25 m, Bt =1.0 T and Ap = 4.0 is

the most preferable. In addition, the engineering design for modular coils, the vacuum vessel

and the support structures has also been preliminarily fulfilled.

References:

[1] S. Okamura, K. Matsuoka, S. Nishimura et al., Nucl. Fusion 44 (2004) 575.

[2] Y. Xu, Matter and Radiation at Extremes 1 (2016) 192.

[3] H. Liu, A. Shimizu, M. Isobe et al., 45th EPS Conference on Plasma Physics, P1.1039

(2018).

[4] M. Isobe, A. Shimizu, H. Liu et al., 45th EPS Conference on Plasma Physics, P2.1043

(2018).

[5] J. Nuhrenberg, R. Zille, Phys. Lett. A 129 (1988) 113.

[6] S. P. Hirshman, J. C. Whitson, Phys. Fluids 26 (1983) 3553.

[7] A. H. Boozer, Phys. Fluids 23 (1980) 904.

[8] A. H. Boozer, Phys. Fluids 24 (1981) 1999.

[9] S. Okamura et al., Nucl. Fusion 41 (2001) 1865.

[10] J. R. Cary and M. Kotschenreuther, Phys. Fluids 28, (1985) 1392.

[11] M. Drevlak, Fusion Technology 33 (1998) 106.

[12] H. Liu et al., Plasma and Fusion Research 13 (2018) 3405067.

[13] K. C. Shaing et al., Phys. Fluids B1 (1989) 148.

[14] A. Shimizu et al., 45th EPS Conference on Plasma Physics, P1.1053 (2018).

[15] V. V. Nemov, S. V. Kasilov et al., Phys. Plasmas 6 (1999) 4622.

[16] T. H. Watanabe et al., Nucl. Fusion 46, (2006) 24.

[17] M. Nakata et al., 27th International Toki Conference (2018), oral presentation.

[18] S. Okamura et al., 45th EPS Conference on Plasma Physics, P5.1034 (2018).

[19] D. P. Yin, Y. Wan et al., 1st Hangzhou International Stellarator Workshop (2018).

[20] C. X. Zhu, D. A. Gates et al., 60th APS Conference on Plasma Physics (2018).

[21] B. E. Nelson, L.A. Berry et al., Fusion Engineering and design 66-68 (2003) 169.