ARIES-CS MAGNET CONDUCTOR AND STRUCTURE EVALUATION

X. R. Wang1, A.R. Raffray1, L. Bromberg2, J.H. Schultz2, L.P. Ku3, J. F. Lyon4, S. Malang5,

L. Waganer6, L. El-Guebaly7, C. Martin7 and the ARIES Team8

1- University of California San Diego, San Diego

9500 Gilman Drive, La Jolla, CA 92093-0417

Phone: (858) 534-7789

Fax: (858) 822-2120

xrwang@ucsd.edu

2- MIT Plasma Science and Fusion Center, Cambridge MA 02139

3- Princeton Plasma Physics Laboratory, Princeton N.J. 85440

4- Oak Ridge National Laboratory, Oak Ridge TN 37831

5- Fusion Nuclear Technology Consulting, Fliederweg, Linkenheim, Germany

6- The Boeing Company, St. Louis, MO 63166

7- University of Wisconsin, Madison WI 53706

8- ARIES Power Plant Studies, University of California, San Diego, CA, 92093

Keywords: Stellarator, fusion power plant, magnet conductor, coil structure Number of pages: 67

Number of tables: 6

Number of figures: 23

ARIES-CS MAGNET CONDUCTOR AND STRUCTURE EVALUATION

X. R. Wang1, A.R. Raffray1, L. Bromberg2, J.H. Schultz2, L.P. Ku3, J. F. Lyon4, S. Malang5, L.

Waganer6, L. El-Guebaly7, C. Martin7 and the ARIES Team8

ABSTRACT

The ARIES-CS study1 focused on the conceptual design and assessment of a compact

stellarator power plant to help identify the important advantages and key issues associated with a

compact stellarator design. The coil configuration and structural support approach represent key

design challenges, with the final design and material choices affected by a number of material

and geometry constraints. This paper describes the design configuration and analysis and

material choices of the ARIES-CS magnets and its structure. To meet aggressive cost and

assembly/maintenance goals, the magnets are designed as lifetime components. Due to the very

complex geometry, one of the goals of the study was to provide a robust operational design. This

decision has significant implications on cost and manufacturing requirements. Concepts with

both conventional and advanced superconductors have been explored. The adopted coil structure

design approach is to wind all the 6 modular coils of one-field period in grooves in one

monolithic coil structural shell (one per field-period). The coil structural shells are then bolted

together to form a strong structural shell to react the net radial forces. Extensive engineering

analyses of the coil system have been performed using ANSYS shell and solid modeling. These

include EM analyses to calculate the magnetic fields and EM forces, and structural analyses to

evaluate the structural responses and optimize the coil support system, which has a considerable

impact on the cost of the ARIES-CS power plant.

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I. INTRODUCTION

Recent stellarator power plant designs2, 3 have been large aspect ratio machines. These

designs explored direct extrapolations of experimental devices4, 5 to fusion devices. The magnet

systems of these reactor studies used similar materials and construction techniques as the

experiments, in order to investigate the implication of the state of the art technology and methods

of manufacturing in the design of stellarator-based fusion reactors. These designs were

characterized by large-radii power cores and high power.

The stellarator magnetic field structure is complex and requires unconventional (non-planar)

coils. The FFHR reactor design3 has continuous helical winding, similar to that of the LHD

device5, while the HELIAS reactor2 has modular coils, similar to that of the Wendelstein 7X

machine4. Both designs utilize NbTi superconductor, which is ductile and easy to wind.

Modular stellarators have multiple sets of coils that are highly shaped and non-planar,

resulting in complex EM forces that are difficult to react6. To minimize the introduction of field

errors, the usual approach is to design a stiff structure to minimize coil deformations and tightly

control the coil fabrication tolerances. A much less expensive approach is to analyze the EM

forces and predicted deformations of the coil structure and adjust the unloaded coil locations so

the steady state energized coil and structure are in the desired position7, 8. A stiff structure is

more attractive in either case to better predict deformed positions.

Traditionally, modular stellarator experiments6, 9, 10 and conceptual power plant designs2, 7

have a magnet system such that each coil is in its own casing, in shape similar to the coil shape,

with structural connections between adjacent coil structures to form a truss-like field period

structural assembly. Fabrication and assembly techniques on current stellarator experiments

have resulted in the coil structure being one of the more expensive power core components. It is

3

also difficult to analyze and optimize the coil structure, as the allowable stress and deformation

of the energized coils determine the required cross section and locations of the connecting

elements.

The ARIES-CS power plant study adopted a different approach and designed a monolithic

coil structure for each field period11 to better analyze the loaded structure and provide a much

lower cost solution. A continuous convoluted hollow toroidal segment supports the modular

coils within grooves on the internal surface of the monolithic coil structural shell. The coil

structural shell thickness can be continuously adjusted according to local stresses from the coil

winding packs. The thickness of the coil structural shell between coils is appropriately sized for

the local coil stresses and deflections. This approach allows the optimization of the toroidal coil

structure and minimizes its cost. Additional tailoring of the structure is accomplished for the

necessary access ports and support features12.

Even with the optimizing the thickness and mass of the coil structural shell, the large,

monolithic toroidal coil structure is still quite massive, around 1,000 tonnes per field period

element. The monolithic structure with continually varying curvature surfaces and thicknesses

would be very difficult, if not impossible, to economically fabricate with conventional methods.

Thus, advanced fabrication methods were investigated to more efficiently fabricate this unusual

and difficult shape. The adopted fabrication approach is documented in Ref. [11].

The ARIES-CS design investigates impacts of the use of a high performance superconductor

and aggressive coil design, which allows for an increase in the magnetic field and reduces the

reactor size. Winding the superconducting coil conductor in the monolithic structure in small

radii grooves is a challenging problem. Several superconductor options for the ARIES-CS

magnet have been evaluated by Bromberg13. Of the alternatives, wind-and-react Nb3Sn

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conductor, without the use of organic wrap insulation, followed by heat treatment, is selected as

the baseline. The process imposes requirements on the choices of coil structural materials that

are addressed in this paper.

Section 2 of this paper describes the material choices and the material selection used in the

ARIES-CS study. Section 3 describes the magnet definition and magnet construction. Section 4

describes the Finite Element calculations of the magnetic field, Lorenz loads, stresses and

deformations. Section 5 addresses the cost modeling. The findings are summarized in Section 6.

II. MATERIAL PROPERTIES

The Nb3Sn and JK2LB (Japanese austenitic steel) materials have been selected as the

superconductor and coil structure materials, respectively. The decision is justified in this section,

and implications of the choice are described.

The superconductor protection determines the design constraints that, in turn, determine the

inboard nuclear shielding requirements. The maximum radiation damage to the winding is

determined by the superconductor fast neutron fluence (~ 1019 n/cm2), dose to the insulator (~

1011 rads), and increased resistivity of the copper stabilizer (~ 0.006 dpa). Nuclear heating

limitations, determined by the refrigeration requirement, are less than 2 mW/cm3 for low

temperature superconductors. There is no practical nuclear heat limitation for the high

temperature superconductors.

The minimum bending radius of the coils is around 0.59 m. In addition, the present tolerance

in the accuracy of conductor positioning is ~ 1-1.5 cm.

II.1. Conductor Material Properties

5

For the compact stellarator applications, where the coils generate multipole-like fields that

decay rapidly with increasing distance to the coils, it is important to increase the current density

of the winding to minimize the distance from the coil centroid to the plasma. In order to increase

the average current density, the superconducting current density should be high, and the amount

of copper in the conductor should be minimized.

Previous stellarator reactor designs used ductile NbTi2, 3, 7 superconducting material. The

more compact stellarators require magnetic fields higher than those that can be generated with

NbTi, even with sub-cooling. A previous paper13 investigated the superconducting material

alternatives, and methods of manufacturing the coils and coil support structure. The conclusions

of that paper were that both Nb3Sn and High Temperature Superconductors (HTS) could be used

in compact stellarator designs, whereas NbTi could not be used.

Two options were identified13 for winding the Nb3Sn superconductor: wind-and-react of

conventional Cable-In-Conduit-Conductor (CICC) and react-and-wind of sheathed Rutherford

cable superconductor. Each of these methods has requirements that determine the design

approach. The baseline ARIES-CS design uses the former, using conventional CICC conductors.

However, the wind-and react approach requires special consideration of the electrical insulation,

as the chosen method of manufacturing of the structure and the winding pack makes it difficult to

apply insulation after the heat treatment, as in conventional magnet manufacturing process using

CICC.

The properties of high performance Nb3Sn superconductor14 were used in the design. This

material has high current density (~ 3000 A/mm2) at 12 T and 4K and can be manufactured in

relatively long lengths. In order to minimize the cost of the superconductor, low copper to non-

6

copper ratio in the strands is used. Any additional copper required for protection is added as

pure copper strands, arranged by appropriate bundling the strands in the sub-cable.

As in most high-field, high-stored-energy designs, the copper cross section is determined by

protection requirements. In order to allow for the largest current density, aggressive quench

protection has been used in the design. The design incorporates advanced quench techniques

(such as fiber optic sensors15) in addition to conventional voltage sensors, in order to increase the

signal-to-noise ratio and determine at an early stage the presence of normal zones in the

superconductor. Advanced quench protection techniques allows the activation of the external

dump system soon after the initiation of the quench. It is assumed that the quench detection

system generates a clean signal of quench with a delay of 0.5 s.

In addition, a fast energy dump is enabled by allowing 20 kV maximum voltages across the

coil, operating at high current, and increasing the number of electrical circuits. Each winding

pack consists of multiple separately driven circuits. In the baseline ARIES-CS design, the

magnet has 18 separate winding packs. Each of these winding packs is subdivided electrically

into 2 coils, effectively creating 36 coils. Each one of these coils has a dump-circuit, in order to

accelerate the removal of the magnet energy.

The CICC jacket material uses steels that are compatible with the superconductor. The wall

thickness is about 2 mm, and the conductor is square in cross section. The helium void fraction

in the cross section inside the jacket is 40%.

It is also assumed that the conductor is wrapped with an insulating tape that is about 1 mm

thick.

7

With the above constraints, it is possible to determine the effective current density over the

winding pack for a given peak field. Because of the complex field structure, it is assumed that

the same conductor characteristics are used throughout the winding. In principle it is possible to

grade the conductor, adjusting the conductor characteristics to the maximum field that section of

conductor will require. In the layer-wound ARIES design, the innermost layers have higher

fields and require additional superconductor, while the outer ones have lower fields, allowing

increased current density. This technique was used in previous ARIES designs, such as in the

ARIES-I16 magnets. However, the geometry of the stellarator magnets complicates the magnetic

fields, and grading, while possible, is not as simple as in tokamak TF coils.

Figure 1 shows the results of the calculations of the average current density over the winding

pack as a function of the peak field. The current density drops substantially after about 15 T,

when the superconducting cross-section starts to become a substantial fraction of the total cross-

section.

INSERT FIGURE 1

The unconventional winding method used in the ARIES-CS design is described in Section III.

The cost of the superconductor, the conductor and the winding process are provided in the

Section V.

II.2. Structural Material Properties

The choice of wind-and-react, using a winding method where the conductor needs to be heat

treated in place, requires a material with similar thermal contraction coefficients to the

superconductor to prevent strains due to differential thermal contraction. In the past, the US has

developed a nickel-based alloy, Incoloy 90817, which matches well the thermal contraction

8

between heat treatment temperature and operating temperature. Alternative low-carbon steels

have been developed in Europe and Japan. In particular, the JK2LB alloy18, 19 (developed by

Kobe Steel and considered for use in major components of the ITER device, including the central

solenoid) is sufficiently characterized for the analysis in this paper. Table I summarizes the

properties of the materials considered for the coil structure.

INSERT TABLE I

Incoloy 908 has some attractive features for magnet structure, including slightly higher

allowables, improved thermal match to the superconductor and improved fatigue performance.

However, Incoloy 908 is subject to Stress Accelerated Grain Boundary Oxidation21 (SAGBO), in

the presence of oxygen during the heat treatment process (or annealing). The JK2LB material is

either not sensitive to SAGBO, or much less so, simplifying the environmental conditions during

the heat treatment process (less requirement on the environmental control during heat treatment).

Because of the additive manufacturing method for the structure in ARIES-CS, described by

Waganer11, the use of material properties of welds are more appropriate that those of the base

metal, as the entire structure is effectively one very large weld. The properties of the weld

material of the alternative material, 9HA, are very good, The tensile strength and yield are

slightly lower than those of the base metal Incoloy 908, but the ductility and crack growth

properties (as indicated by the fracture toughness Kc and crack growth parameters (Paris law) m

and C), are outstanding. By comparison, as of the time of preparation of this manuscript, very

little information is available on the weld characterization of JK2LB. This is an area of active

development, although since JK2LB is close to conventional steels, it is not expected to raise

much concern. The material properties measurements including tensile, fracture toughness, and

fatigue crack growth rate of Incoloy 908 weld metals (9HA) at both room temperature and 4K

9

liquid helium temperature are shown in Table II22. The base metal used for welding is Incoloy

908, and the weld is 9HA weld wires. The cold work level was measured by the elongation in the

longitudinal direction. Aging heat treatment was achieved at 923K for 240 hours in a vacuum

furnace.

INSERT TABLE II

There are two additional drawbacks associated with Incoloy 908. In terms of the response of

the different alloying materials to neutron irradiation, the high 3 wt% Nb content makes Incoloy

908 less environmentally attractive than JK2LB23. Although the initial radiological response of

JK2LB is higher than that of Incoloy, after less than 1 day, they are comparable and thereafter

JK2LB decays much more rapidly than Incoloy. As a result, JK2LB can be released to the

commercial market for reuse after a short cooling period of ~ 1 year according to both U.S. and

IAEA clearance guidelines, while Incoloy cannot be cleared as a consequence of its high Nb

content. If it is desirable to recycle all materials, JK2LB can be recycled with hands-on after a

few months following shutdown, whereas Incoloy should be recycled remotely, again because of

the 3 wt% Nb content. The second drawback of Incoloy 908 is that, because of the high Ni

content, this material is substantially more expensive than specialty steels.

Based on the above discussion, it was decided to select an austenitic steel (such as JK2LB) as

the baseline material for the structure of the ARIES-CS magnets, and to keep Incoloy 908 as an

alternative.

For the stress and deformation calculations in section IV, the modulus of elasticity of the

JK2LB material for the structure is assumed to be 200 GPa, the Poisson’s ratio is 0.3, and the

maximum allowable bending + membrane stress is 845 MPa (assumed as 1.5 Sm, where Sm is

the lesser of 2/3 of the yield strength or 1/3 of the ultimate strength)24. Estimating the composite

10

material properties for the winding pack is challenging. The following average material

properties for the winding pack are assumed: Young’s modulus in the direction normal to the

conductor ~34 GPa; and Poisson's ratio ~0.3.

II.3. Insulation

As described above, the CICC winding pack cable is wound into grooves in the monolithic

structure, prior to the coil heat treatment. It is necessary to use insulation tape that will survive

the heat treatment. In conventional winding of CICC wind-and-react magnets, after heat

treatment the coil is slightly deformed to allow gaps between the coil turns/layers so that

insulation (consisting of glass tape and an organic insulation, such as kapton) can be wrapped

around the conductor, as the glass tape and organic material would not survive the heat

treatment25. This process is inadequate for ARIES-CS, as the conductor cannot be unwound from

the structure after heat treatment.

High performance inorganic/organic insulation has been developed by CDT26, which uses

ceramic pre-preg that are applied prior to the winding. The insulators, however, need to be

impregnated by an organic resin after heat treatment, limiting the radiation life to a few times

1010 rads.

The proposal insulation for ARIES-CS uses an inorganic tape impregnated with a ceramic

binder that is applied to the tape prior to application to the cable. Several types of tapes are

possible, including S2-glass that has been desized. The desizing process removes the organic

films from the glass fibers, preventing the pyrolysis of the organic material and the production of

carbon, which could short the coils. Alternatively, tapes of woven ceramic insulator have also

been proposed27, 28.

11

The ceramic-based tape is applied (wrapped around the conductor) during the winding

process, prior to heat treatment, using an inorganic clay-glass insulator such as that developed by

Puigsenur28. Puigsegur has developed means of applying the clay-glass insulator to the inorganic

tape that does not require an organic binder. The chosen ceramic binder tolerates the

temperatures required during heat treatment of the superconductor, after which it becomes a

monolithic solid. Melting of the glass during the low temperature heat treatment, followed by

solidification, achieves mechanical rigidity for the coil by binding to the cable to the structure,

thus obviating the need of a post impregnation.

In order to increase the dielectric strength of the winding needed because of the high voltage

during external dump following a quench, sheets of electric insulation can be placed between

conductor layers. The nature of the insulation is still being analyzed, but it could, in principle, be

made of the same material as the insulator wrapped around the conductor (such as desized S2-

glass or ceramic fabric, mica-based sheets). Section III describes in some detail the

manufacturing process of the winding pack.

The all-inorganic dielectric is still in the developing process; if adequate materials can not be

developed, the coils with turns wrapped with inorganic tapes and binder prior to the heat

treatment process, can be impregnated with an organic resin after the heat treatment. The effect

would be a decrease in radiation resistance of the coils; this would require an increase in

radiation shielding and some modification of the design point but without a major impact on the

conclusions from the present study.

III. DEFINITION OF THE MODULAR STELLARATOR MAGNET

12

Figure 2 shows the top view of the ARIES-CS coil and plasma configuration based on the

NCSX-like coil and plasma shape with three-field periodicity10. The ARIES-CS coil system

consists of 18 modular coils and 6 coils per field period. Due to the two-fold mirror symmetry of

the modular coils in the configuration of one field-period, only three different coil shapes are

needed to make up the complete coil set.

INSERT FIGURE 2

III.1. Coil Structural Assembly

The modular coil is subjected to three main forces when the coils are energized: (1) locally

outwardly directed forces away from the plasma, which result in a large net centering force

pulling coils within one field-period toward the center of the torus; (2) out-of plane forces acting

between neighboring coils inside a field-period; (3) weight of the cold coil system. There are

other loads, such as those during transients when PF coils are energized (which could be

supported by the structure), in addition to other equipment. Those loads are small compared

with the main Lorenz loads and have not been included in the analysis. The main challenges for

designing the complicated coil structure, considering the large forces between coils and the

requirements from the port maintenance scheme, include: (1) the design of the coil support to

react the centering forces pulling the coil field periods radially inward and the out-of-plane

forces between neighboring coils; (2) the connection between the cold coil system and the room

temperature support structure, which needs to carry the total weight of the coil and support

structure; and (3) the integration of the coil and coil supporting system with the modular

maintenance scheme and the power core configuration of the ARIES-CS power plant.

13

Previous designs of modular stellarator coils involve a large number of individual

components attached together. The NCSX coil supporting system consists of 18 independent

shell segments8, 9 (one shell structure per modular coil) bolted together. The Helias reactor

design2, 7 and Wendelstein 7X4, 6 have coils in individual casings supported by a superstructure

made of trusses. These design approaches are very difficult to analyze, time consuming to

assemble, and very costly.

To meet the design and cost challenges from both the coil supporting system and the power

core configuration and maintenance scheme12, a novel design approach and innovative

fabrication method11 has been investigated in the ARIES study. An entire field period magnet

structure is fabricated and the coil cables are wound inside the monolithic toroidal shell. The coil

structural shell provides casing and support for all 6 modular coils in a field period. The winding

packs are wound into internal grooves in the monolithic coil structural shell. Figures 3 and 4

show the coil supporting shell without and with the winding packs. The large ports required for

maintenance are in the large-major radius region between the coil structural shells, as shown in

Figures 3 to 4.

INSERT FIGURES 3 and 4

The coils system consists of 3 identical toroidal segments, bolted together, as shown in

Figure 5. The resulting structure behaves as a complete toroidal shell, capable to supporting the

loads while minimizing the deformation of the coil, because of the high rigidity of the structure.

The continuous monolithic structure allows a simple method of continuously tailoring the shell

thickness to contain and restrain the coils and provides cooling capability and additional neutron

14

shielding. In the outboard region of the coil, the structure is thicker near the region with the

winding pack in order to resist the outwardly directed (away from the plasma) Lorenz forces.

Figure 6 shows a section view cut through one of the coils and local structure to illustrate the

typical winding pack arrangement and structure thickness in the outboard section of the magnet.

The nominal structure thickness in the outboard region of the magnet is 0.2 m between winding

packs, with a strong-back of 0.28 m outboard of each winding pack. The thickness of these

components varies depending on the local stresses and deflections. Studies on the effects of

thinning the structure in regions of low stress and low deflection are given in Section IV.

Generally, the structure is thicker on the inboard region and thinner on the outboard region.

Given the local thicknesses and the configuration shown in Figures 3 to 5, the nominal mass of

the structure of each field period is roughly 1,000 tonnes.

INSERT FIGURES 5 and 6

Figure 7 shows the overall integration of the coil system with the modular maintenance

scheme and the power core configuration of the ARIES-CS12. In the resulting configuration, the

vacuum vessel is internal to the coils and serves as an additional shield for the protection of the

coils from neutron and gamma irradiation.

INSERT FIGURE 7

There are three main horizontal maintenance ports located toroidally at 0°, 120° and 240°,

corresponding to the end regions of the field periods. In addition there are three smaller ECH

ports also used for auxiliary maintenance12. All these ports penetrate through the coil structural

15

shell, and no disassembly of the coil system or the vacuum vessel is necessary for blanket

maintenance.

The weight of the coils and coil structure will rest on the warm foundation via three long cold

legs per field-period with high thermal resistance to keep the heat ingress into the cold system

within tolerable limits. There are penetrations through the coil structure in each field-period for

the warm legs to support the weight of the vacuum vessel and blanket/shield and to transfer the

weight of the warm components to the foundation. At least 3 warm legs are needed per period.

Thermal insulation between the cold structure and the warm supporting legs and the warm

vacuum vessel is provided. The thermal insulation includes reflecting multi-layer insulation

(MLI) as well as thermal stations at intermediate temperature to minimize the refrigerator power

requirements. The coil system is enclosed in a common cryostat as disassembly is not necessary

for blanket and divertor maintenance.

III.2. Fabrication Approaches for the Coil Structure

Several fabrication approaches could be used to fabricate the monolithic coil structure.

For ARIES-CS, additive manufacturing11 is chosen for fabrication method for this component.

In this approach, raw material is deposited in the correct position by a computer generated part

definition. Then the material is heated or activated to harden in place to form the part. This

process can build highly detailed, net shape components in plastic with minimal human

intervention other than the CAD part definition. This is a very useful means to quickly and

rather inexpensively build prototypes or test models. This approach evolved to use as raw

materials, metal powders sintered by the laser into the final piece part by creating a melted layer,

16

in the form of a continuous weld bead according to the CAD definition. This method has been

described by Waganer11 as means of cost-effectively building the large monolithic structure.

III.3. Winding Pack Manufacturing

The winding pack is manufactured by placing the coil conductor in the groove in the coil

structural shell. The conductor is wound from the inside of the coil structural shell, by using an

automatic winding machine which uses rails on the structure for manufacturing the coils and

structure11. The winding machine deforms the conductor such that when inserted in the groove it

fits next to the adjacent turn and above the previous conductor layer, with minimal stresses. The

conductor cannot be wound under tension, as it is being done from the inside of the structure.

The conductor is not reacted prior to winding in order to prevent strain during conductor

deformation from affecting the superconductor performance. The conductor is of square cross

section, with sides of 2 cm. The conductor is manufactured by wrapping a uniform cross section

jacket around the conductor. A linear seam weld along the length of the conductor seals the

conductor. Thus, the inner cross section is square, not circular as in the case of the ITER Center

Solenoid Model Coil (CSMC)25.

The relatively small conductor cross section is chosen in order to minimize the forces required

to shape the conductor during winding. Since the winding pack width is about 0.7 m wide, there

are approximately 35 turns per layer. A full spool for a single layer weighs about 3 tons. There

are 9 layers per coil. The actual turns per coil will be different for each type of coil. Because of

the high current density through the use of high performance superconductor and aggressive

quench techniques (with minimum copper), the conductor current is moderate at ~ 40 kA.

17

It is necessary to hold the conductor in place during the winding procedure. The first

approach includes tacking the conductor, as it is laid down, to the previously installed

conductors. The second approach uses automatic pneumatic actuators that disengage locally just

before the conductor is laid down, and re-engage afterwards. This is the preferred approach as it

faster and more reliable. The multiple actuator need to provide pressure both on both open faces

of the conductors, pressing it against the previously laid turns in the same layer, as well as

against the turn from the previous layer.

Inorganic fiber tape with an inorganic binder, is placed over the conductor after the conductor

has been shaped, but prior to insertion into the winding pack. Partial removal of the conductor

after fitting may be necessary for this operation.

Manifolding of the cooling circuits occurs at the outboard section of the magnet, where space

is more available. There is one inlet and one outlet per layer. The hydraulic path for the flowing

high pressure helium coolant is about 1.5 km.

After each layer is wound, additional insulation is placed to increase the dielectric strength of

the winding pack. Flat flexible inorganic insulation is used.

After all the cables are installed, another machine can secure the thin cover plate over the

winding pack. It is illustrated as being welded, although other fastening techniques might work.

These machining and cable installation steps are highly automated, which helps ensure part

consistency, accuracy, and low fabrication costs.

After the cover of the winding pack cover is installed, the conductor is heat treated, at

temperatures around 850-950 K for a period of about 100 hours.

18

If development of the inorganic insulation proves difficult, as discussed above, after heat

treatment the winding pack is impregnated, if needed, with an organic resin. It may be necessary

to make allowance in the inorganic insulating sheets, as well as the thin winding pack cover, in

order to allow the impregnation to penetrate uniformly through the winding pack. Distribution

rails would be used for each layer, at both sides of the winding, in order to ensure uniform

impregnation. The curing of the impregnation is quick and should not impact the construction

schedule, especially since the heating blankets and thermal insulation is already in place,

following the heat treatment process.

The electrical connections at each winding pack consist of two separately driven coils.

Although this approach increases the number of current leads, it minimizes the voltage required

for external dump of the magnetic energy in the case of quench.

IV. ELECTROMAGNETIC-STRUCTURAL ANALYSIS OF THE MAGNET

In this section, the forces and resulting stresses and deformation of the coils are presented. An

EM (electromagnetic) analysis was performed to calculate the magnetic flux density and EM

magnetic forces in the modular coils. The resulting EM forces are used as input for structural

analysis of the coil supporting tube. The results are used to determine the maximum field of the

magnet, as simple formulas are inappropriate for stellarator design.

The coil geometry has not been optimized, and neither has the structure. The purpose of the

effort in this section is to provide a quantitative estimation of the magnetic field characteristics at

the coils, as well as the stress and deformation of the coils. An optimized design that iterates on

the coil and structure geometry with the field and stress analysis presented in this section is

19

outside the scope of this work. The main goal was to assure that the configuration chosen

satisfies the conductor and material requirements, followed by a costing exercise.

Not all the features of the winding and structure configuration could be modeled even with the

relatively complex geometry of the FEM analysis. These issues are dealt with side calculations

to determine the magnitude of their effect.

IV.1. Peak Field Analysis

Finite Element Analysis (FEA), using the ANSYS code, is used to determine the magnetic

fields and the forces. The ANSYS code is also used for the stress calculations shown in the next

section. As a result of the threefold cyclic symmetry (three field-periods) of the coil

configuration, only the coils within a 120-degree region (one field-period) are modeled. Figure 8

shows a top view of the FEA (Finite Element Analysis) model. The three coils M1R, M2R, and

M3R are geometrically identical to the three coils M1L, M2L, and M3L, with a 180 degrees

rotation.

INSERT FIGURE 8

The geometry of the modular coils was imported from Pro/E CAD models. ANSYS

hexahedral elements SOLID5 were used in the EM model, and the 6 coils were meshed with

about 180,000 elements. The magnetic fields and the Lorenz forces were calculated for

maximum currents in the coils. The coil currents for the M1, M2 and M3 coils are 10.76 MA,

13.53 MA and 13.10 MA, respectively, flowing in the same direction. The fields due to the

plasma current and the PF coils (needed for flexibility during startup) have been neglected, as

20

they play a relatively small role in the Lorenz loads or peak magnetic field of compact

stellarators.

It has been difficult to generate winding pack models of the magnet that have large toroidal

extension. The NCSX design has large gaps between coil windings in the inboard section of the

magnet. Increasing the coil width and decreasing the gap has the advantage of substantially

decreased peak magnetic fields.

The coil cross section dimensions used for the analysis are ~ 0.194 m (thickness) and 0.743

m (width). Only about half of the space in the inboard of the coil is occupied by winding, with

large regions devoid of winding. This geometry is required in order to provide the required field

structure. The coil geometry is defined as in the ARE case of NCSX, scaled to the major radius

of 7.75 m and to a magnetic field on axis of 5.7 T.

The results from the model have been benchmarked by Williamson29 using the MAGFOR

code. The coil calculations have been performed by Long-Poe Ku of PPPL. The latter code is

used to determine the peak magnetic field for wide winding packs and to design the conductor.

The maximum local magnetic field is found in the inboard side (facing the plasma) in regions

where the modular coils have small bend radii of curvatures. The local maximum magnetic flux

densities are 14.6 T, 19.2 T and 18.5 T for the coil M1, M2, and M3 respectively. Figure 9

shows the contours of constant magnetic field on the modular coils.

INSERT FIGURE 9

The maximum fields for coils M2 and M3, 19.2 and 18.5 T respectively, occur in a very

small zone on the ARIES-CS coil. The field maxima occur in small bend radius locations.

21

However, the limiting value for Bmax in the ARIES-CS study is 16 T, or about 0.833 times the

highest field. The B = 16 T contours lie about 5/8 of the way into the orange areas on the inside

of a bend in Figure 9. Increasing the bend radius in these areas should reduce Bmax to <16 T.

Adjusting coil set to accomplish the field reduction is a time-consuming task, and the resources

required for the calculations were not available during the ARIES study. Adjustment of the coil

set to increase the minimum bend radius while preserving the good plasma properties and other

coil properties has been done in both the NCSX and QPS coil designs30, 31.

The high-field regions occur on the thin sides on the small-bend-radius part of the hairpin-

like bends in the coils. Brooks32 has modeled hairpin-like coils, shown in Figure 10, with

different bend radii to illustrate the dependence of Bmax on the minimum bend radius. The

calculations are for a section of coil with toroidal elongation (toroidal width/radial depth) of the

winding pack cross section of 4.8, similar to that for the ARIES-CS coils. Figure 11 shows the

|B| contours for a model hairpin-like coil with a bend radius of 20 cm (compared to the 200-cm

length of the straight leg of the hairpin model coil) to illustrate the effect of increasing the bend

radius of a coil. The B/Bmax = 0.833 contour lies about 5/8 of the way into the orange region on

the inside of the bend, as in the case of the M2 coil of ARIES-CS. Visual inspection suggests

that the best approximation is for an equivalent bend radius between 15 cm and 20 cm in this

model.

Figure 11 shows the peak magnetic field (normalized to the peak magnetic field for the 50-

cm bend radius) as a function of the hairpin-like coil bend radius. Decreasing Bmax by 0.833

(corresponding to the decrease of the peak magnetic field of the M2 coil from 19.2 T to 16 T)

corresponds to an increase in the normalized bend radius by ~ 45% for the rbend = 15 case. The

normalized field for a bend radius of 15 cm in this model is about 1.56; the bend radius

22

corresponding to a peak field of 1.3 (= 0.833 x 1.56) is about 21 cm, resulting in a ~45% increase

in the bend radius. The actual minimum bend radius for the reference ARIES-CS coil set is 58.5

cm, so it would have to be increased by 26 cm in this model. Similar percentage changes have

been made in the QPS coils while preserving the desired physics properties32.

INSERT FIGURES 10 and 11

IV.2. Lorenz Loads Analysis

The net Lorenz forces in the six modular coils are listed in Table III. As shown in Table III,

the maximum radial and vertical forces occur in the M2 coils (M2L and M2R). For left and right

coil sets, the net forces in the radial direction are identical in magnitude and acting in the same

direction, and the net forces in toroidal and vertical directions are equal in magnitude and acting

in opposite direction; therefore, there are no net forces in a field period in both toroidal and

vertical directions. Although no net toroidal forces need to be transferred from one field period to

the next, there are local moments and forces that are best restrained through mechanical

connection of adjacent coil structural shells. In addition, as the combined coil structural shells

form a shell, it is possible to couple responses, with tension along the coil generating shears in

other directions33. The sum of all 6 coils in the radial direction is 345 MN representing the

centering force pushing the coils inwards.

INSERT TABLE III

Figs. 12 to 14 show the nodal force vectors in the coil M1, M2 and M3, respectively. The

maximum nodal forces occur in the coil pair M2 that has the maximum current density, the

23

maximum magnetic field and smallest bend radii. The net magnetic forces acting in each

modular coil are outwardly directed, away from the plasma, and the coils need to be supported in

the region of the coils facing the plasma. This confirms that winding the coils into grooves from

inside of the modular coils is the preferred solution, and a thick coil strong-back (behind the

winding pack) is needed to react the radial forces against the structure. Figure 15 shows the

nodal force vectors in one field-period and the forces exhibit full symmetry in the coils of one

field-period from the top view. The toroidally directed forces within a field period are mainly

reacted by the coil structural shell. The vertically directed loads are reacted through tension in

the coil structural shell. And the net radial forces pulling the three coil structural shells towards

the center of the torus are reacted through wedging by hoop stresses in the closed ring formed by

bolting together the three coil structural shells.

INSERT FIGURES 12,13, 14 and 15

IV.3. Structural Analysis

Structural analyses were performed to evaluate the stresses and deformations and to help

optimize the design of the coil structure. The nodal forces obtained from the EM analysis were

used as input for the structural model. A sequential coupled EM-structural analysis was adopted,

so that the forces from the EM analysis could be transferred to the structural model by using

identical nodes and elements.

IV.3.1. Finite-Element Analysis: Shell Model

24

ANSYS shell elements for magnetic-structural analysis are really 2-D plane elements used to

model the mid-plane of thin structures. The shell model can be used in place of 3-D solid

elements and result in large savings in both set-up time and computational time, and is very

useful for parametric variations and parameter optimization. The thicknesses of the shell in the

intercoil structure and of the coil strong-back behind the winding pack are key parameters for the

magnet system: stress and deflection considerations favor thick structures whereas cost

minimization favor the use of thin structures. A parametric study used an ANSYS shell model to

optimize the thickness of the supporting shell and strong-back based on these considerations.

The coil structural shell configuration (including the modular coils) from Pro/E generated

files provided an accurate shape. Because of the threefold cyclic symmetries presented for both

the structural configuration and the EM loading, the model used a 120° field period, consisting of

6 modular coils and its coil structural shell. Cyclic boundary conditions were applied at both

ends of the coil structural shell.

INSERT FIGURE 16

Figure 16 shows the von Mises stresses calculated with the ANSYS shell model with a 0.35

m thick inter-coil structure and 0.3 m thick strong-back. These thicknesses were the initial case

conditions and were refined based on the analysis results. The results indicate a maximum

deformation of 2 cm at the outboard side of the coil structural shell. The peak von Mises stress is

536 MPa, occurring at the outboard of the coil structural shell. Both the peak deformation and

stress occur in very localized regions, and the stresses are much smaller over large areas of the

coil structure.

25

IV.3.2. Finite-Element Analysis: Solid Model

ANSYS solid structural elements are capable of modeling a general 3-D structure, allowing

the realistic modeling of boundary conditions and displacements. However, mesh preparation

effort and computing time are more demanding than for the shell model described in the previous

section. A few comparative runs using the more accurate but more time consuming 3-D solid

ANSYS model were done to confirm the results obtained from the ANSYS shell model and to

help better understand the effect of penetrations through the coil supporting tube. A number of

such penetrations and openings are required by the power core, for support, maintenance,

vacuum pumping, ECH/auxiliary maintenance and coolant access pipes. These openings in the

magnet structure could affect the local stress distribution and cause higher local stresses and

deformations in the coil structure.

INSERT TABLE IV

Table IV lists the major penetrations through the coil structure. The largest openings in the

coil structure are the three main maintenance ports. The maintenance ports at both ends of the

coil structural shell were included in the solid model in order to determine if enforcement ribs

would be needed.

The number of structural elements for the solid model was about 750,000. Figure 17 shows

the finite element model for the magnetic-structural analysis. The assumptions for the solid

model are the same as those used in the shell model, i.e., (1) the magnetic forces on the winding

pack are identical; (2) the winding packs are fully bonded to the grooves in the coil supporting

tube with no slip or movement relative to the grooves; (3) the cyclic symmetry boundary is

26

applied at both ends of the coil supporting tube. The nominal thicknesses of the coil structural

shell and strong-back are 0.20 m and 0.28 m, respectively.

INSERT FIGURE 17

The resulting deformation in the winding pack, the magnet structure and the stresses in the

magnet structure are shown in Figs. 18, 19 and 20, respectively. The maximum deformation of

the modular coils and the coil structure is about 2.0 cm and 2.1 cm, respectively, at the outboard

region of the magnet. The peak von Mises stress of 656 MPa occurs at the outboard side of the

coil structure caused by the net centering forces of the 6 modular coils in the field-period. Note

that this peak stress is only slightly higher than that from a similar solid model run but for a case

without any penetration (652 MPa). Overall, the displacements for the solid model case are

similar to those from the shell case, but the peak von Mises stress is higher (652 MPa from solid

modeling as compared to 525 MPa from shell modeling for cases without penetrations).

As in the shell case, the maximum stress occurs in small localized regions, with most of the

coil structure, including the inter-coil structure shell and coil strong-back, at a much lower stress

level. This provides the possibility of decreasing the thicknesses of the inter-coil structure shell

and the coil strong-back in these low-stress regions in order to reduce the material cost. A

detailed optimization study would include tailoring these thicknesses to minimize cost while

maintaining the local stresses and deflections within their allowable limits. The results indicate

also that the openings required for the main maintenance ports at 0°, 120° and 240° are not a

major concern since the deformations and stresses are very small in these regions (the effects on

the maximum stress and deflection in the coil system are also small as noted earlier). The results

27

also indicate the low stress regions where it would be preferable to position the

openings/penetrations required for the power core configuration and maintenance, for instance,

over toroidal spans of 0° to 40° and/or 80° to 120° in the outboard region of each field-period.

INSERT FIGURES 18, 19 and 20

Shear stress in the winding packs is a critical parameter to be used to qualify large-scale

electromagnets. Large shear stresses can result in structural/electrical failure of the insulation

system. The results for the winding packs indicate peak shear stresses of 45, 50 and 35 MPa in x-

z, y-z and x-y plane respectively. The peak shear stresses occur only in very small regions, and

the shear stresses in the most of the ARIES-CS winding packs are below 20 MPa, as illustrated

in the example results shown in Figs. 21 to 23. The NCSX shear stress test data indicate a failure

at 32 MPa34. No shear stress test data is available for our coil design.

INSERT FIGURES 21, 22 and 23

V. MAGNET COSTING

The magnet system, described in this paper, is only a part of the complete commercial power

plant design. For fusion electrical power plants to successfully compete with all other energy

sources, it must produce electricity at a competitive cost. Fusion power plants are certainly

capital cost intensive, so reasonable estimates of all major power core systems are vital in

understanding and controlling the cost of all the plant systems. Thus, there was an impetus to

28

correctly model the cost of the magnet systems for use in a 10th of a kind commercial power

plant.

The ARIES-CS costs were determined according to the cost model developed by J. Schultz

for superconducting magnet costing15. These models are sufficiently detailed and realistic to

determine the amount of superconductor, stabilizer, structure, insulation, and the complexity of

winding and assembly. These algorithms need to be modified to take into account 10th of a kind

costing, as opposed to first of a kind such as ITER or DEMO. In addition, substantial cost

reductions, compared to today’s costing, could be achieved through improved, more aggressive

manufacturing techniques and improved materials performance as a result of present and future

R&D activities.

The cost of the magnet conductor is determined from a bottom's-up estimate, with models for

the cost of the superconductor, conductor manufacturing, assembly, and manufacturing of the

magnet system. The cost of the continuous convoluted toroidal tube magnet structure is

presented in a separate paper11. As many characteristics of the magnet system are analyzed as

possible including superconductor type, number of independent pure copper strands (for quench

protection), material of the conduit, and structural material.

Table V shows the cost of the conductor for the magnet coils. There are 6 coils of each type,

two of each type in each field period. The cost of the strands is a substantial fraction (about

60%) of the cost of the magnet system winding pack.

INSERT TABLE V

29

The cost of the superconducting material has been assumed to be $500/kg, (2003 dollars)

slightly higher than some HEP experience35, 36, but substantially higher than what might be

expected in the future34. The cost of the stabilizer (copper) is $5/kg, with enough copper to

satisfy the protection requirements described above. The diffusion barrier, a thin coating of the

strands to minimize AC losses and to prevent the strands from sintering during the heat treatment

process, was estimated to be $220/kg. It was assumed that $100/m was the cost of cabling and

insulating the conductor. This cost includes the cost of the sheath material (thin plate), forming

the sheath around the conductor strands, and seam welding along the conductor. The cost

includes making and inspecting a long weld that should not leak during the life of the reactor.

The cabling and insulating cost can also be decreased substantially, as described below.

The above costs do not include Administration and Operating expenses. The values of

engineering and contingency are included in the overall system evaluation of the ARIES-CS37.

The ground rule adopted by the ARIES team is that the value-added capital costs will be

observing a 75% learning curve on the unit cost. The cost of value added tenth-of a kind

component is reduced by 10{ln(0.75)/ln(2)}~ 0.385 assuming the base cost is the first production unit.

The largest cost of the conductor is due to the superconducting strands and the insulating and

cabling. The cost of the superconductor strands and cable has been investigated by Cooley [35]

and others. It has been hoped that the cost of the superconducting strands can decrease to as low

as $1.5 / kA m (12 T, 4.2 K), through improvements in materials, use of inexpensive materials

instead of more expensive ones, and increased billet mass. The last column in Table VI shows

the results of the aggressive costing, compared to the more conventional one of Table V. The

cost of the winding pack, could be decreased to about 1/3 of that indicated in Table V, to ~ 30

M$.

30

INSERT TABLE VI

The cost of winding has been calculated by Waganer11, as well as the cost of heat treatment,

but these costs are substantially smaller than those presented in Tables V or VI due to highly

automated installation methods developed during prototype, demonstration, and production

power plant development.

VI. SUMMARY

The magnet system for the ARIES-CS has been described and analyzed. Innovative magnet

and structure design innovations result in a magnet system that is relatively simple and

inexpensive to construct and is operationally robust. The magnet system consists of 3-field

periods, each manufactured separately and then integrated into a full toroidal structure. The

magnet is wound with Cable-In-Conduit-Conductor, using wind-and-react high performance

Nb3Sn superconductor materials. A representative low carbon steel (JK2LB) has been selected as

structural material and conductor jacket in great part due to its low activation characteristics and

lower cost (as compared to Incoloy 908).

The structure is made by low cost and highly automated additive manufacturing techniques.

The conductor is wound directly into the coil structure, and the conductor heat treatment

involves warming the entire field period with the installed conductors.

The magnetic fields, Lorenz loads, stresses and deformations are calculated using finite

element methods, both shell and solid model. The highest fields are very localized, and means of

decreasing the peak value have been proposed. It is estimated that the peak field will be slightly

higher than 15 T, which is below the design value. The peak stresses and peak deformations are

31

also very localized, and the method of manufacturing allows for tailoring of the structure

thickness (to minimize its mass and cost) to match the allowable stress and deformation.

The cost methodology for the coil conductors has been described, including means of

evaluating future implications of improved winding and superconductor manufacturing and

performance.

ACKNOWLEDGEMENT

This work was supported under U.S. Department of Energy Grant No. DE-FC03-95-

ER54299.

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32

[7] E. HARMEYER, J. KIßLINGER, “Improved Support Concept for the Helias Reactor Coil

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33

[15] J.H. SCHULTZ, S. POURRAHIMI, S. SMITH, P.W. WANG, “Principles Of Advanced

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Superalloy,” PhD Thesis, MIT, 1995.

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Room Temperature and 4K,” ITER-USMIT-KIM-050706-01 (5/07/2006).

34

[23] B.J. MERRILL, L. EL-GUEBALY, C. MARTIN, R. L. MOORE, A. R. RAFFRAY, and the

ARIES-CS Team, “Safety Assessment of the ARIES Compact Stellarator Design,” Fusion

Sci. & Technol., this issue.

[24] P.H. TITUS, “Magnet, Magnet Structure, and Cryostats Structural Analysis,” MECO

Magnet System Safety Review, June 3, 2003.

[25] N. MITCHELL, K. OKUNO, R. THOME et al., “ITER CS Model Coil project,”

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[27] A. DEVRED, “Insulation Systems for Nb3Sn Accelerator Magnet Coils Manufactured by

the Wind and React Technique,” presented at 17Th International Conference on Magnet

Technology, Geneva (Switzerland), 2001.

[28] A. PUIGSEGUR et al., “Development Of An Innovative Insulation For Nb3sn Wind And

React Coils,” Advances in Cryogenic Engineering, Transaction of the 2003 International

Cryogenic Materials Conference ICMC 50, AIP Conference Proceedings 711, U.

Balachandran, ed. 2004.

[29] DAVID WILLIAMSON (ORNL), private communication.

[30] D. STRICKLER, L.A. BERRY, S.P. HIRSHMAN, “Designing Coils for Compact

Stellarators,” Fusion Sci. & Technol., 41 107 (2002).

35

[31] D. STRICKLER, S.P. HIRSHMAN, D.A. SPONG, et al., “Development of a Robust Quasi-

Poloidal Compact Stellarator,” Fusion Sci. & Technol., 45 15 (2004).

[32] A. BROOKS (PPPL), private communication.

[33] W.H. GRAY, W.C.T. STODDART, J.E. AKIN, “Derivation Of Bending Free Toroidal

Shell Shapes For Tokamak Fusion Reactors,” Journal of Applied Mechanics, Transactions

ASME, 46, n 1, Mar, 1979, p 120-124.

[34] L. MYATT, D. E. WILLIAMSON AND H. M. FAN, “Electromagnetic and Linear

Structural Analysis of the National Compact Stellarator Experiment (NCSX) Modular Coil

System,” Fusion Sci. & Technol., 47 (2005) 916-920.

[35] L.D. COOLEY, A.K. GHOSH AND R.M. SCANLAN, “Costs of High-field

Superconducting Strands for Particle Accelerator Magnets,” Supercond. Sci. Technol, 18

(2005) R51–R65.

[36] A. DEVRED, S.A. GOURLAY AND A. YAMAMOTO, “Future Accelerator Magnet

Needs,” IEEE Trans Applied Superconductivity, 15 (2005) 1192.

[37] J.F. LYON, L-P. KU, L. EL-GUEBALY et al., “Determination of ARIES-CS Plasma and

Device Parameters and Costing,” submitted for publication, Nuclear Science and

Technology.

36

TABLE I. Material properties of the jacket alloys20

(a) estimated; (b) preliminary; (c) not measured; (d) only plane stress values (not applicable

to CICC conduit) have been measured

Property T(K) Incoloy 908 316ELN JK2LB HA242Base metal, no treatment

Young’s modulus (GPa) 295 188 196 221b

4 191a 207 238b

density (g/cc) 295 8.1 8.0 ~9.5magnetic state 4 ferromagnetic diamagnetic ?

Base metal, after cold work and agingYoung’s modulus (GPa) 295 179 (c) (c) (c)

4 182 (c) (c) (c)tensile yield strength (MPa) 295 1260 370 490 1100

4 1460 1170 1420 1340tensile ultimate strength (MPa) 295 1450 710 750 1530

4 1890 1600 1690 1970tensile elongation (%) 295 20 51 44 34

4 26 38 25 26fracture toughness (MPa . m1/2) 4 160 (d) 75 (d)fatigue crack growth rate:

c (10-15m/cycle) 4 70 5000d 1.4 40d

n 4 3.8 2,7d 5.1 4.0d

thermal contraction (%) 295-4 0.17 0.33 0.19 0.23 1000-4 1.15 1.63 (c) 1.28

37

Table II. Properties of weld metal (9HA) developed for Incoloy 908

FCGR Material

condition Test

Temperature

Yield Strength (MPa)

Tensile Strength (MPa)

Elongation (%)

KJc

(MPa⋅m0.5) C (m/cycle) m

RT 989.91 1228.04 8.77 170.67 1.56e-13 3.69J.H. Kim [21]

10%CW +

Aging (650oC

& 240h) 4K 1088.89 1523.72 14.32 169.8 5.44e-16 5.07

RT 991 1210 8.8 170 NA NA CH Jang [16]

9%CW + Aging (650oC

& 200h) 4K 1251 1690 13.2 121 NA NA

38

TABLE III. Net Forces in the Modular Coils

Fr, MN Fθ, MN Fz, MNM1L -57.8 376.1 22.6M1R -57.8 -376.1 -22.6M2L -254.3 177.5 -151.2M2R -254.3 -177.5 151.2M3L 141.5 50.2 -141.5M3R 141.5 -50.2 141.5

Sum of all 6 coils -341.2 0 0

39

Table IV. Major openings through vacuum vessel and coil structure

40

Table V. Cost of winding packs for ARIES-CS with present day costing assumptions

M1 M2 M3

Modified coils (T) 14.6 15.1 15.1Coil currents (MA) 10.8 13.5 13.1

Single turn length (m) 45.8 45.1 41

Number of turns 270 338 328Length of conductor (m) 12366 15221 13428

Superconductor cost $/kg 500SC m^3/m 4.8E-05

kg/m 0.3888Cost @ 12 T, 4.2 K 194.4

Stabilizer cost $/m 8.54Diffusion barrier cost $/m 1.65Insulating and cabling $/m 100Total conductor $/m 305

$/kA m @12 T 4.2 K 7.61

Scaled $/kA m 10.2 10.5 10.5Cost of coils, all periods M$ 30 38 34Total conductor cost (direct) M$ 102

41

Table VI. Present day and future costs of the conductor

42

List of Figures

Fig. 1. Average winding pack current density as a function of peak field, for conductor with

characteristics as described in the text.

Fig. 2. ARIES-CS coil configuration.

Fig. 3. Coil supporting shell structure. Grooves where the winding packs are located are

indicated on the inner surface of the structure.

Fig. 4. Coil supporting shell structure with winding packs.

Fig. 5. ARIES-CS coil supporting system.

Fig. 6. TF coil cross-section through the coils.

Fig. 7. Layout of the ARIES-CS power core configuration at 0o, the location corresponding to the

region between toroidal segments.

Fig. 8. FEA model for EM analysis.

Fig. 9. Plot of the magnetic field (T) in the coils.

Fig.10. Geometry and contours of constant magnetic field (T) for hairpin-like coil with a

normalized bend radius of 20.

Fig. 11. Normalized magnetic field as a function of hairpin-like coil normalized bend radius.

Fig. 12. Plot of the nodal forces (N) in coil M1.

Fig. 13. Plot of the nodal forces (N) in coil M2.

Fig. 14. Plot of the nodal forces (N) in coil M3.

43

Fig. 15. Plots of the nodal forces (N) in one field-period.

Fig. 16. An example of the ANSYS shell modeling results showing the stress (MPa) distribution.

Fig. 17. The solid finite element model.

Fig. 18. Deformation (m) of the winding pack.

Fig. 19. Deformation (m) of the coil supporting tube.

Fig. 20. Von Mises stress (MPa) distribution in the coil supporting tube.

Fig. 21. Shear stresses (MPa) of the winding packs (in x-z plane).

Fig. 22. Shear stresses (MPa) of the winding packs (in y-z plane).

Fig. 23. Shear stresses (MPa) of the winding packs (in x-y plane).

44

0

20

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0 5 10 15 20

Peak field (T)

Curr

ent

den

sity

(M

A/m

^2)

Nb3Sn @ 4.2K

Figure 1

45

Figure 2

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Figure 3

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Figure 4

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Figure 5

49

igure 6

Nominally 28 cm thick

Nominally 20 cm thick

2 cm x 74 cm coverplate

Superconducting winding 9 layers of 37 turns each Square conductor, 2 cm x 2 cm

F

50

Figure 7

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igure 8

F

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igure 9

F

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igure 10

F

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igure 11

F

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igure 12

F

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igure 13

F

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igure 14

F

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igure 15

F

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igure 16

F

60

Figure 17

61

igure 18

F

62

igure 19

F

63

igure 20

F

64

igure 21

F

65

igure 22

F

66

igure 23

F

67