1. The Hangzhou International Stellarator Workshop
(HISW2018)
The Advanced Configuration and Coil System Design for the Chinese First Quasi-axisymmetric Stellarator
Haifeng Liu1,4,*, Akihiro Shimizu2,**, Mitsutaka Isobe2,3, Shoichi Okamura2
Yuhong Xu1, Changjian Tang1,4, Xin Zhang1, Bing Liu1, Hai Liu1, Jie Huang1, Xianqu Wang, Dapeng Ying5, Yi Wang5 and CFQS team1,2
1 Institute of Fusion Science, School of Physical Science and Technology,
Southwest Jiaotong University, Chengdu, China
2 National Institute for Fusion Science, National Institutes of Natural Sciences, Toki , Japan 3 SOKENDAI (The Graduate University for Advanced Studies), Toki , Japan 4 School of Physical Science and Technology, Sichuan University, Chengdu , China
5 Hefei Keye Electro Physical Equipment Manufacturing Co., Ltd, Hefei, , China
Mar 26th-28th, 2018, Hangzhou, China

2. SWJTU and NIFS Joint Project Perspective improvement
The aim of the joint project:
SWJTU and NIFS design and operate cooperatively the Chinese First Quasi-axisymmetric Stellarator (CFQS) based on the CHS-qa configuration.
Basic optimization strategy of CFQS
Focused property
Perspective improvement
Quasi-axisymmetric configuration
Reducing neoclassical transport
Magnetic well
Good MHD stability
Low aspect ratio
Large plasma volume
Low toroidal viscosity
(high toroidal rotation)
Suppressing anomalous transport by shear flow

3. Quasi-axisymmetric stellarator (QAS)
What is the quasi-axisymmetric configuration?
Tokamak
Helical
Requires plasma current Major disruption
Reduced neoclassical transport and good particle orbit by axisymmetry
No plasma current
Steady-state operation
Large neoclassical transport (1/n regime) by ripple diffusion loss
Combined
Quasi-axisymmetric stellarator (QAS)
QAS is a tokamak-like stellarator in the magnetic configuration.
Advantages of QAS:
No requirement of inductive plasma current
Steady-state operation
Reduced neoclassical transport (tokamak like diffusion)
High toroidal rotation

4. Outline 1. Quasi-axisymmetric configuration of CFQS
2. Engineering design for CFQS-coil system
3. Physics of CFQS configuration
4. Schedule plan
5. Summary

5. Quasi-axisymmetric configuration of CFQS
R0(m)
Ap(R0/a)
BT(T)
Toroidal period(N)
Vp(m3)
1.0
4.0 2
1.1
Fourier spectrum of B in the Boozer coordinates
Distribution of magnetic field strength
Toroidal ripple B10
Mirror ripple B01
Helical ripples B11 , B12
B: Poloidal angle
B: Toroidal angle
Plasma boundary
Expression of magnetic field strength
(𝜓, 𝜃 𝐵 , 𝜑 𝐵 ) are the Boozer coordinates.

6. Quasi-axisymmetric configuration of CFQS
Magnetic well
Magnetic well structure in entire region
Iota/2  profile
Low shear iota profile
MHD stability   

7. Outline 1. Quasi-axisymmetric configuration of CFQS
2. Engineering design for CFQS-coil system
3. Physics of CFQS configuration
4. Schedule plan
5. Summary

8. Engineering design for CFQS coil system
Parameter optimization for the filament-coil design by NESCOIL code:
Weight
Realized value of a property
Target value of a property
Average of normal magnetic field
Minimum radius of curvature
Minimum distance of adjacent coils
𝐵∙𝑛 𝐵
When the above objective parameters are satisfied, including both physics requirements and engineering constraints, the filament coils are generated.

9. Scan of modular-coil numbersAp
R0（m）
a (m)
Num of modular coils
Min. distance
between coils (filament) (cm)
Min. radius of curvature (filament) (cm)
B∙n/|B|
Cross section of coils (cm2)
4.0
1.0
0.25 20
17.0
18.2
1.11%
17×9 16
18.5
21.5
0.97%
18×10 12
14.2
14.7
1.21%
19×13
Properties of 16-coil system:
The minimum interval between adjacent filament coils is the widest .
The minimum radius of curvature is the largest.
The magnetic flux surface generated is the closest to the target surface.

10. Comparison among three types of coil systems with finite coil cross sections
Without the coil-coil overlaps
Narrow distance between adjacent coils
High cost of coil fabrication
Cross section:17×9 cm2
16-coil system
Without the coil-coil overlaps
Wide distance between adjacent coils
Simple-shaped coils
Matched magnetic configuration
Cross section:18×10 cm2
12-coil system
With the coil-coil overlaps
Narrow distance between adjacent coils
Complex-shaped coils
Cross section:19×13 cm2

11. Properties of magnetic configuration generated
by 16-coil system
1.0
-1.0
0.0
2.0
=0o
1.0
-1.0
0.0
2.0
=90o
The coil-induced flux surface matches the target plasma boundary.
The rotational transform profile generated from coils is consistent with the targeted profile.
The Fourier spectrum induced by coils is almost the same as the targeted one (VMEC).
Z(m)
R(m)
Helical ripples
Toroidal ripple
Mirror ripple
Bmn induced by coils
Target Bmn(VMEC)
Toroidal ripple
Mirror ripple
Helical ripples

12. Team of the CFQS fabrication
Hefei Keye Electro Physical Equipment Manufacturing Co., Ltd. (Hefei, China)
Abundant
fabrication
experiences:
KTX in USTC
ITER, PF6 coil
ASDEX-U, ICRF antenna
Engineering model of M4 coil
16-coil system for CFQS
Four pairs of symmetric coils for a period.
M4 (green) is the most complex-shaped coil.
Cross section: 64 x 96mm2,
96 (8x12) hollow Cu conductors

13. Outline 1. Quasi-axisymmetric configuration of CFQS
2. Engineering design for CFQS-coil system
3. Physics of CFQS configuration
4. Schedule plan
5. Summary

14. Shafranov shift in the CFQS configuration
Beta=0%
Beta=2%
=0o
=90o
=0o
=90o
𝑃∝ 1− 𝜌 2 2
The VMEC code with the free boundary is employed to estimate the Shafranov shift.
When volume averaged beta equals 1.7%, the Shafranov shift is about the half of the minor radius.
By applying the vertical field, Shafranov shift can be reduced and beta limit increases.
Shafranov shift (Dr) at the bean shaped cross section
Dr/a
Beta limit=1.7%
1.7%

15. Mercier stability in the CFQS configuration
Stable region(Dmerc>0)
Unstable region(Dmerc<0)
𝑃∝ 1− 𝜌 2 2
r=0.7
The Mercier stability criterion is expressed as: Dmerc=Dshear+Dwell+Dcurr+Dgeod >0.
Up to beta=2%, the interchange mode is stable.
The stabilizing effect from the magnetic well (Dwell > 0) is stronger than the destabilizing effect from the geodesic curvature term (Dgeod < 0).

16. Neoclassical transport in the CFQS configuration
|B| on the plasma boundary （Target） B B
|B| on the plasma boundary with 16 coils B B
Comparison of neoclassical transport
The mirror ripple induced by discrete coils increases neoclassical transport.
The effective ripple of CFQS is three orders less than that of the CHS.
As for the CFQS, the neoclassical diffusion properties of 16-coil and 20-coil are similar, therefore 16-coil system is preferable.
Diffusion coefficient（NEO code）
Monoenergetic neoclassical
diffusion Coefficient D  eeff3/2/n

17. Ballooning stability in the CFQS configuration
Unstable region
𝑃∝ 1− 𝜌 2 2
Stable region
Unstable region
There are two regions of ballooning stability existing :
One region: up to beta=1%, the ballooning mode is stable.
The other one: high beta region from beta= 3.0%-3.5%.
Cobravmec
Stable region

18. Outline 1. Quasi-axisymmetric configuration of CFQS
2. Engineering design for CFQS-coil system
3. Physics of CFQS configuration
4. Schedule plan
5. Summary

19. Planned schedule FY-17 FY-18 FY-19 FY-20 FY-21 FY-22 Phase 
Physics design and main machine design
Phase 
Fabrication Project
Transfer heating systems and diagnostic systems for first plasma from NIFS to SWJTU
Phase Ⅲ
Commissioning first
plasma
Phase Ⅳ
Operation
Phase Goals
Phase : Physics design (configuration, neoclassical transport, MHD) and main machine design (modular coils and vacuum vessel) .
Phase : Fabrication of CFQS and transfer essential heating systems and diagnostic systems from NIFS to SWJTU, such as gyrotron, interferometer, X-ray diagnostic, etc.
Phase Ⅲ: Verify construction accuracy and obtain first plasma.
Phase Ⅳ: Magnetic configuration studies and heating experiments.

20. Summary
SWJTU and NIFS design and operate collaboratively the Chinese First Quasi-axisymmetric Stellarator.
The candidate parameters of the CFQS configuration are as follows: toroidal periodic number, aspect ratio, magnetic field strength and major radius are 2, 4.0, 1.0 T and 1.0 m, respectively.
The 16 modular coil system is advantageous.
The neoclassical transport in the CFQS is excepted to be equivalent to that in tokamaks.
The equilibrium of configuration is almost stable up to beta = 1%. More accurate analysis and optimization (pressure profile scan, vertical field control, kink mode driven by bootstrap current etc.) of beta limit are coming issues.

21. Thank you for your attention!

22. Backup
Mission
Quasi-axisymmetric configuration （Electron gun and CCD camera）
Flexible magnetic configuration (poloidal field coils, independent power supply, ECCD, etc.)
Optimization of neoclassical transport………..
3D plasma physics
3D plasma shaping, MHD stability
Rotational transform sources (int., ext.)
tokamak-like fundamental transport properties
3D divertors: effects on boundary plasma, plasma-material interactions
Hutch Neilson, 2006, Annual Symposium

23. Current Carrying Surface
Inner limit surface, d=20cm
Outer limit surface, d=40cm

26. Answering critical fusion science questions, e. g
Answering critical fusion science questions, e.g. • How does magnetic field structure impact plasma confinement? – plasma shaping? internal structure? self-generated currents? • How much external control vs. self-organization will a fusion plasma require? Role in burning plasma research • Provide tools, database, strategies for understanding 3D effects • Contribute to ITER experimental planning.