aries-cs magnet conductor and structure evaluation · aries-cs magnet conductor and structure...

ARIES-CS MAGNET CONDUCTORAND STRUCTURE EVALUATIONX. R. WANG,*a A. R. RAFFRAY,a L. BROMBERG,b J. H. SCHULTZ,b L. P. KU,c

J. F. LYON,d S. MALANG,e L. WAGANER,f L. EL-GUEBALY,g, C. MARTIN,g

and ARIES TEAMh

aUniversity of California, San Diego, 9500 Gilman Drive, La Jolla, California 92093bMIT Plasma Science and Fusion Center, Cambridge, Massachusetts 02139cPrinceton Plasma Physics Laboratory, Princeton, New Jersey 85440dOak Ridge National Laboratory, Oak Ridge, Tennessee 37831eFusion Nuclear Technology Consulting, Fliederweg, Linkenheim, GermanyfThe Boeing Company, St. Louis, Missouri 63166gUniversity of Wisconsin, Madison, Wisconsin 53706hARIES Power Plant Studies, University of California, San Diego, California 92093

Received April 16, 2007Accepted for Publication October 5, 2007

The ARIES-CS study focusing on the conceptual de-sign and assessment of a compact stellarator power plantidentified the important advantages and key issues asso-ciated with such a design. The coil configuration andstructural support approach represent key design chal-lenges, with the final design and material choices af-fected by a number of material and geometry constraints.This paper describes the design configuration and analy-sis and material choices for the ARIES-CS magnets andits structure. To meet aggressive cost and assembly/maintenance goals, the magnets are designed as lifetimecomponents. Due to the very complex geometry, one ofthe goals of the study was to provide a robust operationaldesign. This decision has significant implications on costand manufacturing requirements. Concepts with both con-ventional and advanced superconductors have been ex-plored. The coil structure design approach adopted is to

wind all six modular coils of one field period in groovesin one monolithic coil structural shell (one per field pe-riod). The coil structural shells are then bolted togetherto form a strong structural shell to react the net radialforces. Extensive engineering analyses of the coil systemhave been performed using ANSYS shell and solid mod-eling. These include electromagnetic (EM) analyses tocalculate the magnetic fields and EM forces and struc-tural analyses to evaluate the structural responses andoptimize the coil support system, which has a consider-able impact on the cost of the ARIES-CS power plant.

KEYWORDS: electromagnetic-structural analysis, compactstellarator, superconductor

Note: Some figures in this paper are in color only in the electronicversion.

I. INTRODUCTION

Recent stellarator power plant designs1,2 have beenlarge–aspect ratio machines. These designs explored di-rect extrapolations of experimental devices3,4 to fusiondevices. The magnet systems of these reactor studies usedmaterials and construction techniques similar to those ofthe experiments in order to investigate the implication of

the state-of-the-art technology and methods of manufac-turing in the design of stellarator-based fusion reactors.These designs were characterized by large-radii powercores and high power.

The stellarator magnetic field structure is complexand requires unconventional ~nonplanar! coils. The FFHRreactor design2 has continuous helical winding, simi-lar to that of the LHD device,4 whereas the HELIASreactor1 has modular coils, similar to those of the Wen-delstein 7X machine.3 Both designs utilize NbTi super-conductor, which is ductile and easy to wind.*E-mail: [email protected]

818 FUSION SCIENCE AND TECHNOLOGY VOL. 54 OCT. 2008

Modular stellarators have multiple sets of coils thatare highly shaped and nonplanar, resulting in complexelectromagnetic ~EM! forces that are difficult to react.5

To minimize the introduction of field errors, the usualapproach is to design a stiff structure to minimize coildeformations and tightly control the coil fabrication tol-erances. A much less expensive approach is to analyzethe EM forces and predicted deformations of the coilstructure and adjust the unloaded coil locations so thatthe steady-state energized coil and structure are in thedesired position.6,7 A stiff structure is more attractive ineither case to better predict deformed positions.

Traditionally, modular stellarator experiments5,8,9 andconceptual power plant designs1,6 have a magnet systemsuch that each coil is in its own casing, in shape similarto the coil shape, with structural connections betweenadjacent coil structures to form a trusslike field periodstructural assembly. Fabrication and assembly tech-niques on current stellarator experiments have resulted inthe coil structure being one of the more expensive powercore components. It is also difficult to analyze and opti-mize the coil structure, since the allowable stress anddeformation of the energized coils determine the re-quired cross section and locations of the connectingelements.

The ARIES-CS power plant study adopted a differ-ent approach and designed a monolithic coil structure foreach field period10 to better analyze the loaded structureand provide a much lower-cost solution. A continuousconvoluted hollow toroidal segment supports the modu-lar coils within grooves on the internal surface of themonolithic coil structural shell. The coil structural shellthickness can be continuously adjusted according to localstresses from the coil winding packs. The thickness of thecoil structural shell between coils is appropriately sizedfor the local coil stresses and deflections. This approachallows the optimization of the toroidal coil structure andminimizes its cost. Additional tailoring of the structure isaccomplished for the necessary access ports and supportfeatures.11

Even with the optimizing of the thickness and massof the coil structural shell, the large, monolithic toroidalcoil structure is still quite massive, around 1000 tonnesper field period element. The monolithic structure withcontinually varying curvature surfaces and thicknesseswould be very difficult, if not impossible, to economi-cally fabricate with conventional methods. Thus, ad-vanced fabrication methods were investigated to moreefficiently fabricate this unusual and difficult shape. Theadopted fabrication approach is documented in Ref. 10.

The ARIES-CS design investigates impacts of theuse of a high-performance superconductor and aggres-sive coil design, which allows for an increase in the mag-netic field and reduces the reactor size. Winding thesuperconducting coil conductor in the monolithic struc-ture in small-radii grooves is a challenging problem. Sev-eral superconductor options for the ARIES-CS magnet

have been evaluated by Bromberg et al.12 Of the alterna-tives, wind-and-react Nb3Sn conductor, without the useof organic wrap insulation, followed by heat treatment, isselected as the baseline. The process imposes require-ments on the choices of coil structural materials that areaddressed in this paper.

Section II of this paper describes the material choicesand the material selection used in the ARIES-CS study.Section III describes the magnet definition and magnetconstruction. Section IV describes the finite element cal-culations of the magnetic field, Lorenz loads, stresses,and deformations. Section V addresses the cost model-ing. The findings are summarized in Sec. VI.

II. MATERIAL PROPERTIES

The Nb3Sn and JK2LB ~Japanese austenitic steel!materials have been selected as the superconductor andcoil structure materials, respectively. The decision is jus-tified in this section, and implications of the choice aredescribed.

The superconductor protection determines the de-sign constraints that, in turn, determine the inboard nu-clear shielding requirements. The maximum radiationdamage to the winding is determined by the supercon-ductor fast neutron fluence ~;1019 n0cm2!, dose to theinsulator ~;1011 rads!, and increased resistivity of thecopper stabilizer ~;0.006 displacements per atom!. Nu-clear heating limitations, determined by the refrigerationrequirement, are less than 2 mW0cm3 for low-temperaturesuperconductors. There is no practical nuclear heat lim-itation for the high-temperature superconductors.

The minimum bending radius of the coils is around0.59 m. In addition, the present tolerance in the accuracyof conductor positioning is ;1 to 1.5 cm.

II.A. Conductor Material Properties

For the compact stellarator applications, where thecoils generate multipole-like fields that decay rapidlywith increasing distance to the coils, it is important toincrease the current density of the winding to minimizethe distance from the coil centroid to the plasma. Toincrease the average current density, the superconductingcurrent density should be high, and the amount of copperin the conductor should be minimized.

Previous stellarator reactor designs1,2,6 used ductileNbTi superconducting material. The more compact stel-larators require magnetic fields higher than those that canbe generated with NbTi, even with subcooling. A previ-ous paper12 investigated the superconducting materialalternatives and methods of manufacturing the coils andcoil support structure. The conclusions of that paper werethat both Nb3Sn and high-temperature superconductorscould be used in compact stellarator designs, whereasNbTi could not be used.

Wang et al. ARIES-CS MAGNET SYSTEM

FUSION SCIENCE AND TECHNOLOGY VOL. 54 OCT. 2008 819

Two options were identified12 for winding the Nb3Snsuperconductor: wind-and-react of conventional cable-in-conduit conductor ~CICC! and react-and-wind ofsheathed Rutherford cable superconductor. Each of thesemethods has requirements that determine the design ap-proach. The baseline ARIES-CS design uses the former,using conventional CICC. However, the wind-and-reactapproach requires special consideration of the electricalinsulation, since the method chosen for manufacturingthe structure and the winding pack makes it difficult toapply insulation after the heat treatment, as in the con-ventional magnet manufacturing process using CICC.

The properties of high-performance Nb3Sn super-conductor13 were used in the design. This material hashigh current density ~;3000 A0mm2! at 12 T and 4 Kand can be manufactured in relatively long lengths. Tominimize the cost of the superconductor, low-copper tononcopper ratio in the strands is used. Any additionalcopper required for protection is added as pure copperstrands, arranged by appropriate bundling of the strandsin the subcable.

As in most high-field, high-stored-energy designs,the copper cross section is determined by protection re-quirements. To allow for the largest current density, ag-gressive quench protection has been used in the design.The design incorporates advanced quench techniques ~suchas fiber-optic sensors14! in addition to conventional volt-age sensors in order to increase the signal-to-noise ratioand determine at an early stage the presence of normalzones in the superconductor. Advanced quench protec-tion techniques allow the activation of the external dumpsystem soon after the initiation of the quench. It is as-sumed that the quench detection system generates a cleansignal of quench with a delay of 0.5 s.

In addition, a fast energy dump is enabled by allow-ing 20-kV maximum voltages across the coil, operatingat high current, and increasing the number of electricalcircuits. Each winding pack consists of multiple sepa-rately driven circuits. In the baseline ARIES-CS design,the magnet has 18 separate winding packs. Each of thesewinding packs is subdivided electrically into 2 coils, ef-fectively creating 36 coils. Each of these coils has a dumpcircuit to accelerate the removal of the magnet energy.

The CICC jacket material uses steels that are com-patible with the superconductor. The wall thickness isabout 2 mm, and the conductor is square in cross section.The helium void fraction in the cross section inside thejacket is 40%.

It is also assumed that the conductor is wrapped withan insulating tape that is about 1 mm thick.

With the above constraints, it is possible to deter-mine the effective current density over the winding packfor a given peak field. Because of the complex fieldstructure, it is assumed that the same conductor charac-teristics are used throughout the winding. In principle, itis possible to grade the conductor, adjusting the conduc-tor characteristics to the maximum field that section of

conductor will require. In the layer-wound ARIES de-sign, the innermost layers have higher fields and requireadditional superconductor, while the outer ones have lowerfields, allowing increased current density. This techniquewas used in previous ARIES designs, such as in theARIES-I ~Ref. 15! magnets. However, the geometry ofthe stellarator magnets complicates the magnetic fields,and grading, while possible, is not as simple as in toka-mak toroidal field coils.

Figure 1 shows the results of the calculations of theaverage current density over the winding pack as a func-tion of the peak field. The current density drops substan-tially after about 15 T, when the superconducting crosssection starts to become a substantial fraction of the totalcross section.

The unconventional winding method used in theARIES-CS design is described in Sec. III. The cost of thesuperconductor, the conductor, and the winding processare provided in Sec. V.

II.B. Structural Material Properties

The choice of wind-and-react, using a winding methodin which the conductor needs to be heat treated in place,requires a material with thermal contraction coefficientssimilar to those of the superconductor to prevent strainsdue to differential thermal contraction. In the past, theUnited States has developed a nickel-based alloy, Inco-loy� 908 ~Ref. 16!, which matches well the thermal con-traction between heat treatment temperature and operatingtemperature. Alternative low-carbon steels have been de-veloped in Europe and Japan. In particular, the JK2LBalloy17,18 ~developed by Kobe Steel and considered foruse in major components of the ITER device, includingthe central solenoid! is sufficiently characterized for theanalysis in this paper. Table I summarizes the propertiesof the materials considered for the coil structure.

Fig. 1. Average winding pack current density as a function ofpeak field, for conductor with characteristics as de-scribed in the text.



Incoloy� 908 has some attractive features for mag-net structure, including slightly higher allowables, im-proved thermal match to the superconductor, and improvedfatigue performance. However, Incoloy� 908 is subjectto stress-accelerated grain boundary oxidation20 ~SAGBO!in the presence of oxygen during the heat treatment pro-cess ~or annealing!. The JK2LB material is either notsensitive to SAGBO or much less so, simplifying theenvironmental conditions during the heat treatment pro-cess ~less requirement on the environmental control dur-ing heat treatment!.

Because of the additive manufacturing method forthe structure in ARIES-CS, described by Waganer et al.,10

the use of material properties of welds are more appro-priate than those of the base metal, since the entire struc-ture is effectively one very large weld. The properties ofthe weld material of the alternative material, 9HA, arevery good. The tensile strength and yield are slightlylower than those of the base metal Incoloy� 908, but theductility and crack growth properties @as indicated by thefracture toughness Kc and crack growth parameters ~Parislaw!m and C# , are outstanding. By comparison, as of thetime of preparation of this manuscript, very little infor-mation is available on the weld characterization of JK2LB.

This is an area of active development, although sinceJK2LB is close to conventional steels, it is not expectedto raise much concern. The material properties measure-ments including tensile, fracture toughness, and fatiguecrack growth rate of Incoloy� 908 weld metals ~9HA! atboth room temperature and 4 K liquid helium tempera-ture are shown in Table II ~Ref. 21!. The base metal usedfor welding is Incoloy� 908, and the weld is 9HA weldwires. The cold work level was measured by the elonga-tion in the longitudinal direction. Aging heat treatmentwas achieved at 923 K for 240 h in a vacuum furnace.

There are two additional drawbacks associated withIncoloy� 908. In terms of the response of the differentalloying materials to neutron irradiation, the high 3 wt%Nb content makes Incoloy� 908 less environmentallyattractive than JK2LB ~Ref. 22!. Although the initial ra-diological response of JK2LB is higher than that of In-coloy�, after less than 1 day they are comparable, andthereafter JK2LB decays much more rapidly than Inco-loy�. As a result, JK2LB can be released to the commer-cial market for reuse after a short cooling period of;1 yraccording to both U.S. and International Atomic EnergyAgency clearance guidelines, whereas Incoloy� cannotbe cleared as a consequence of its high Nb content. If it

TABLE I

Material Properties of the Jacket Alloys*

PropertyT~K! Incoloy� 908 316ELN JK2LB HA242

Base metal, no treatmentYoung’s modulus ~GPa! 295 188 196 221a

4 191b 207 238a

Density ~g0cm3 ! 295 8.1 8.0 ;9.5Magnetic state 4 Ferromagnetic Diamagnetic 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 11004 1460 1170 1420 1340

Tensile ultimate strength ~MPa! 295 1450 710 750 15304 1890 1600 1690 1970

Tensile elongation ~%! 295 20 51 44 344 26 38 25 26

Fracture toughness ~MPa{m102 ! 4 160 d 75 d

Fatigue crack growth ratec ~10�15 m0cycle! 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 0.231000-4 1.15 1.63 c 1.28

*Reference 19.aPreliminary.bEstimated.cNot measured.dOnly plane stress values ~not applicable to CICC! have been measured.



is desirable to recycle all materials, JK2LB can be re-cycled with hands-on after a few months following shut-down, whereas Incoloy� should be recycled remotely,again because of the 3 wt% Nb content. The second draw-back of Incoloy� 908 is that because of the high Ni con-tent, this material is substantially more expensive thanspecialty steels.

Based on the above discussion, it was decided toselect an austenitic steel ~such as JK2LB! as the baselinematerial for the structure of the ARIES-CS magnets andto keep Incoloy� 908 as an alternative.

For the stress and deformation calculations in Sec. IV,the modulus of elasticity of the JK2LB material for thestructure is assumed to be 200 GPa, Poisson’s ratio is0.3, and the maximum allowable bending � membranestress is 845 MPa ~assumed as 1.5 Sm, where Sm is thelesser of two-thirds of the yield strength or one-third ofthe ultimate strength!.23 Estimating the composite ma-terial properties for the winding pack is challenging.The following average material properties for the wind-ing pack are assumed: Young’s modulus in the directionnormal to the conductor ;34 GPa and Poisson’s ratio;0.3.

II.C. Insulation

As described, the CICC winding pack cable is woundinto grooves in the monolithic structure, prior to the coilheat treatment. It is necessary to use insulation tape thatwill survive the heat treatment. In conventional windingof CICC wind-and-react magnets, after heat treatmentthe coil is slightly deformed to allow gaps between thecoil turns0layers so that insulation ~consisting of glasstape and an organic insulation, such as kapton! can bewrapped around the conductor, since the glass tape andorganic material would not survive the heat treatment.24

This process is inadequate for ARIES-CS since the con-ductor cannot be unwound from the structure after heattreatment.

High-performance inorganic0organic insulation hasbeen developed by CDT ~Ref. 25!, which uses ceramic

prepregs that are applied prior to the winding. The insu-lators, however, need to be impregnated by an organicresin after heat treatment, limiting the radiation life to afew times 1010 rads.

The proposed insulation for ARIES-CS uses an in-organic tape impregnated with a ceramic binder that isapplied to the tape prior to application to the cable. Sev-eral types of tapes are possible, including S2 glass thathas been desized. The desizing process removes the or-ganic films from the glass fibers, preventing the pyrol-ysis of the organic material and the production of carbon,which could short the coils. Alternatively, tapes of wovenceramic insulator have also been proposed.26,27

The ceramic-based tape is applied ~wrapped aroundthe conductor! during the winding process, prior to heattreatment, using an inorganic clay-glass insulator such asthat developed by Puigsegur.27 Puigsegur has developedmeans of applying the clay-glass insulator to the inor-ganic tape that does not require an organic binder. Thechosen ceramic binder tolerates the temperatures re-quired during heat treatment of the superconductor, afterwhich it becomes a monolithic solid. Melting of the glassduring the low-temperature heat treatment, followed bysolidification, achieves mechanical rigidity for the coilby binding to the cable to the structure, thus obviating theneed of a postimpregnation.

To increase the dielectric strength of the windingneeded because of the high voltage during external dumpfollowing a quench, sheets of electric insulation can beplaced between conductor layers. The nature of the in-sulation is still being analyzed, but in principle, it couldbe made of the same material as the insulator wrappedaround the conductor ~such as desized S2 glass or ce-ramic fabric, mica-based sheets!. Section III describes insome detail the manufacturing process of the windingpack.

The all-inorganic dielectric is still in the develop-ment process; if adequate materials cannot be developed,the coils with turns wrapped with inorganic tapes andbinder prior to the heat-treatment process can be impreg-nated with an organic resin after the heat treatment. The

TABLE II

Properties of Weld Metal ~9HA! Developed for Incoloy� 908

Fracture CrackGrowth Rate

Material Condition Test Temperature

YieldStrength~MPa!

TensileStrength~MPa!

Elongation~%!

KJc

~MPa{m0.5!C

~m0cycle! m

Kim21 10% cold work � aging Room temperature 989.91 1228.04 8.77 170.67 1.56 � 10�13 3.69~6508C and 240 h! 4 K 1088.89 1523.72 14.32 169.8 5.44 � 10�16 5.07

Jang16 9% cold work � aging Room temperature 991 1210 8.8 170 NA NA~6508C and 200 h! 4 K 1251 1690 13.2 121 NA NA



effect would be a decrease in radiation resistance of thecoils; this would require an increase in radiation shield-ing and some modification of the design point but with-out a major impact on the conclusions from the presentstudy.

III. DEFINITION OF THE MODULAR

STELLARATOR MAGNET

Figure 2 shows the top view of the ARIES-CS coiland plasma configuration based on the NCSX-like coiland plasma shape with three-field periodicity.9 TheARIES-CS coil system consists of 18 modular coils and6 coils per field period. Because of the twofold mirrorsymmetry of the modular coils in the configuration ofone field period, only three different coil shapes are neededto make up the complete coil set.

III.A. Coil Structural Assembly

The modular coil is subjected to three main forceswhen the coils are energized:

1. locally outwardly directed forces away from theplasma, which result in a large net centering forcepulling coils within one field period toward thecenter of the torus

2. out-of-plane forces acting between neighboringcoils inside a field period

3. the weight of the cold coil system.

There are other loads, such as those during transientswhen poloidal field ~PF! coils are energized ~which couldbe supported by the structure!, in addition to other equip-ment. Those loads are small compared with the mainLorenz loads and have not been included in the analysis.The main challenges for designing the complicated coilstructure, considering the large forces between coils andthe requirements from the port maintenance scheme, in-clude the following:

1. the design of the coil support to react the center-ing forces pulling the coil field periods radiallyinward and the out-of-plane forces between neigh-boring coils

2. the connection between the cold coil system andthe room temperature support structure, whichneeds to carry the total weight of the coil andsupport structure

3. the integration of the coil and coil supporting sys-tem with the modular maintenance scheme andthe power core configuration of the ARIES-CSpower plant.

Previous designs of modular stellarator coils involvea large number of individual components attached to-gether. The NCSX coil supporting system consists of 18independent shell segments7,8 ~one shell structure permodular coil! bolted together. The Helias reactor de-sign1,6 and Wendelstein 7X ~Refs. 3 and 5! have coils inindividual casings supported by a superstructure made oftrusses. These design approaches are very difficult toanalyze, time consuming to assemble, and very costly.

To meet the design and cost challenges from both thecoil supporting system and the power core configurationand maintenance scheme,11 a novel design approach andinnovative fabrication method10 has been investigated inthe ARIES study. An entire field period magnet structureis fabricated and the coil cables are wound inside themonolithic toroidal shell. The coil structural shell pro-vides casing and support for all six modular coils in afield period. The winding packs are wound into internalgrooves in the monolithic coil structural shell. Figures 3and 4 show the coil supporting shell without and with thewinding packs. The large ports required for maintenanceare in the large major radius region between the coilstructural shells, as shown in Figs. 3 and 4.

The coil system consists of three identical toroidalsegments, bolted together, as shown in Fig. 5. The re-sulting structure behaves as a complete toroidal shell,capable of supporting the loads while minimizing thedeformation of the coil, because of the high rigidity ofthe structure. The continuous monolithic structure al-lows a simple method of continuously tailoring the shellthickness to contain and restrain the coils and providescooling capability and additional neutron shielding. Inthe outboard region of the coil, the structure is thickernear the region with the winding pack in order to resistFig. 2. ARIES-CS coil configuration.



the outwardly directed ~away from the plasma! Lorenzforces. Figure 6 shows a section view cut through oneof the coils and local structure to illustrate the typicalwinding pack arrangement and structure thickness inthe outboard section of the magnet. The nominal struc-ture thickness in the outboard region of the magnet is0.2 m between winding packs, with a strongback of0.28 m outboard of each winding pack. The thicknessof these components varies depending on the localstresses and deflections. Studies on the effects of thin-ning the structure in regions of low stress and low de-flection are given in Sec. IV. Generally, the structure isthicker on the inboard region and thinner on the out-board region. Given the local thicknesses and the con-figuration shown in Figs. 3, 4, and 5, the nominal mass ofthe structure of each field period is roughly 1000 tonnes.

Figure 7 shows the overall integration of the coilsystem with the modular maintenance scheme and thepower core configuration of the ARIES-CS ~Ref. 11!. Inthe resulting configuration, the vacuum vessel is internalto the coils and serves as an additional shield for theprotection of the coils from neutron and gamma irradiation.

There are three main horizontal maintenance portslocated toroidally at 0, 120, and 240 deg, correspondingto the end regions of the field periods. In addition, thereare three smaller electron cyclotron heating ~ECH! portsalso used for auxiliary maintenance.11 All of these portspenetrate through the coil structural shell, and no disas-sembly of the coil system or the vacuum vessel is nec-essary for blanket maintenance.

The weight of the coils and coil structure will rest onthe warm foundation via three long cold legs per fieldperiod with high thermal resistance to keep the heat in-gress into the cold system within tolerable limits. Thereare penetrations through the coil structure in each fieldperiod for the warm legs to support the weight of thevacuum vessel and blanket0shield and to transfer theweight of the warm components to the foundation. Atleast three warm legs are needed per period. Thermalinsulation between the cold structure and the warm sup-porting legs and the warm vacuum vessel is provided.The thermal insulation includes reflecting multilayer in-sulation as well as thermal stations at intermediate tem-perature to minimize the refrigerator power requirements.The coil system is enclosed in a common cryostat sincedisassembly is not necessary for blanket and divertormaintenance.

III.B. Fabrication Approaches for the Coil Structure

Several fabrication approaches could be used to fab-ricate the monolithic coil structure.

For ARIES-CS, additive manufacturing10 is the fab-rication method chosen for this component. In thisapproach, raw material is deposited in the correct posi-tion by a computer-generated part definition. Then thematerial is heated or activated to harden in place to

Fig. 3. Coil-supporting shell structure. Grooves where the wind-ing packs are located are indicated on the inner surfaceof the structure.

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

Fig. 5. ARIES-CS coil-supporting system.



form the part. This process can build highly detailed, netshape components in plastic with minimal human inter-vention other than the computer-aided design ~CAD! partdefinition. This is a very useful means to quickly and

rather inexpensively build prototypes or test models. Thisapproach evolved to use as raw materials metal powderssintered by the laser into the final piece part by creatinga melted layer, in the form of a continuous weld bead

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

Fig. 7. Layout of the ARIES-CS power core configuration at 0 deg, the location corresponding to the region between toroidalsegments.



according to the CAD definition. This method has beendescribed by Waganer et al.10 as a means of building thelarge monolithic structure cost effectively.

III.C. Winding Pack Manufacture

The winding pack is manufactured by placing thecoil conductor in the groove in the coil structural shell.The conductor is wound from the inside of the coil struc-tural shell, by using an automatic winding machine thatuses rails on the structure for manufacturing the coils andstructure.10 The winding machine deforms the conductorsuch that when inserted in the groove, it fits next to theadjacent turn and above the previous conductor layer,with minimal stresses. The conductor cannot be woundunder tension, since it is being done from the inside of thestructure.

The conductor is not reacted prior to winding inorder to prevent strain during conductor deformationfrom affecting the superconductor performance. The con-ductor is of square cross section, with sides of 2 cm.The conductor is manufactured by wrapping a uniformcross-section jacket around the conductor. A linear seamweld along the length of the conductor seals the con-ductor. Thus, the inner cross section is square, not cir-cular as in the case of the ITER center solenoid modelcoil.24

The relatively small conductor cross section ischosen in order to minimize the forces required to shapethe conductor during winding. Since the winding packwidth is about 0.7 m, there are approximately 35 turnsper layer. A full spool for a single layer weighs about3 tonnes. There are nine layers per coil. The actualturns per coil will be different for each type of coil.Because of the high current density through the use ofhigh-performance superconductor and aggressive quenchtechniques ~with minimum copper!, the conductor cur-rent is moderate at ;40 kA.

It is necessary to hold the conductor in place duringthe winding procedure. The first approach includes tack-ing the conductor, as it is laid down, to the previouslyinstalled conductors. The second approach uses auto-matic pneumatic actuators that disengage locally just be-fore the conductor is laid down and reengage afterward.This is the preferred approach since it is faster and morereliable. The multiple actuator needs to provide pressureon both open faces of the conductors, pressing it againstthe previously laid turns in the same layer as well asagainst the turn from the previous layer.

Inorganic fiber tape with an inorganic binder is placedover the conductor after the conductor has been shapedbut prior to insertion into the winding pack. Partial re-moval of the conductor after fitting may be necessary forthis operation.

Manifolding of the cooling circuits occurs at the out-board section of the magnet, where space is more avail-able. There is one inlet and one outlet per layer. The

hydraulic path for the flowing high-pressure helium cool-ant is about 1.5 km.

After each layer is wound, additional insulation isplaced to increase the dielectric strength of the windingpack. Flat flexible inorganic insulation is used.

After all the cables are installed, another machinecan secure the thin cover plate over the winding pack. Itis illustrated as being welded, although other fasteningtechniques might work. These machining and cable in-stallation steps are highly automated, which helps ensurepart consistency, accuracy, and low fabrication costs.

After the cover of the winding pack is installed, theconductor is heat treated, at temperatures around 850 to950 K, for a period of about 100 h.

If development of the inorganic insulation provesdifficult, as discussed above, after heat treatment the wind-ing pack is impregnated, if needed, with an organic resin.It may be necessary to make allowance in the inorganicinsulating sheets, as well as the thin winding pack cover,in order to allow the impregnation to penetrate uniformlythrough the winding pack. Distribution rails would beused for each layer, at both sides of the winding, to en-sure uniform impregnation. The curing of the impregna-tion is quick and should not impact the constructionschedule, especially since the heating blankets and ther-mal insulation are already in place, following the heattreatment process.

The electrical connections at each winding pack con-sist of two separately driven coils. Although this ap-proach increases the number of current leads, it minimizesthe voltage required for external dump of the magneticenergy in the case of quench.

IV. ELECTROMAGNETIC-STRUCTURAL ANALYSIS

OF THE MAGNET

In this section, the forces and resulting stresses anddeformation of the coils are presented. An EM analysiswas performed to calculate the magnetic flux density andEM magnetic forces in the modular coils. The resultingEM forces are used as input for structural analysis of thecoil supporting shell. The results are used to determinethe maximum field of the magnet, since simple formulasare inappropriate for stellarator design.

The coil geometry has not been optimized, and nei-ther has the structure. The purpose of the effort in thissection is to provide a quantitative estimation of the mag-netic field characteristics at the coils, as well as the stressand deformation of the coils. An optimized design thatiterates on the coil and structure geometry with the fieldand stress analysis presented in this section is outside thescope of this work. The main goal was to ensure that theconfiguration chosen satisfies the conductor and materialrequirements, followed by a costing exercise.

Not all the features of the winding and structureconfiguration could be modeled even with the relatively



complex geometry of the finite element analysis ~FEA!.These issues are dealt with in side calculations to deter-mine the magnitude of their effect.

IV.A. Peak Field Analysis

FEA, using the ANSYS code, is used to determinethe magnetic fields and the forces. The ANSYS code isalso used for the stress calculations shown in the nextsection.As a result of the threefold cyclic symmetry ~threefield periods! of the coil configuration, only the coilswithin a 120-deg region ~one field period! are modeled.Figure 8 shows a top view of the FEA model. The threecoils M1R, M2R, and M3R are geometrically identical tothe three coils M1L, M2L, and M3L but with a 180-degrotation.

The geometry of the modular coils was importedfrom Pro0E CAD models. ANSYS hexahedral elementsSOLID5 were used in the EM model, and the six coilswere meshed with about 180 000 elements. The magneticfields and the Lorenz forces were calculated for maxi-mum currents in the coils. The coil currents for the M1,M2, and M3 coils are 10.76, 13.53, and 13.10 MA, re-spectively, flowing in the same direction. The fields dueto the plasma current and the PF coils ~needed for flex-ibility during start-up! have been neglected, since theyplay a relatively small role in the Lorenz loads or peakmagnetic fields of compact stellarators.

It has been difficult to generate winding pack modelsof the magnet that have large toroidal extension. TheNCSX design has large gaps between coil windings inthe inboard section of the magnet. Increasing the coilwidth and decreasing the gap has the advantage of sub-stantially decreased peak magnetic fields.

The coil cross section dimensions used for the analy-sis are ;0.194 m ~thickness! and 0.743 m ~width!. Onlyabout half of the space in the inboard of the coil is occu-

pied by winding, with large regions devoid of winding.This geometry is required in order to provide the requiredfield structure. The coil geometry is defined as in theARE case of NCSX, scaled to the major radius of 7.75 mand to a magnetic field on-axis of 5.7 T.

The results from the model have been benchmarkedby Williamson28 using the MAGFOR code. The coil cal-culations have been performed by Long-Poe Ku of Prince-ton Plasma Physics Laboratory. The latter code is used todetermine the peak magnetic field for wide winding packsand to design the conductor.

The maximum local magnetic field is found in theinboard side ~facing the plasma! in regions where the mod-ular coils have small bend radii of curvatures. The localmaximum magnetic flux densities are 14.6, 19.2, and18.5 T for coils M1, M2, and M3, respectively. Figure 9shows the contours of constant magnetic field on themodular coils.

The maximum fields for coils M2 and M3, 19.2 and18.5 T, respectively, occur in a very small zone on theARIES-CS coil. The field maxima occur in small bendradius locations. However, the limiting value for Bmax inthe ARIES-CS study is 16 T, or about 0.833 times thehighest field. The B � 16 T contours lie about five-eighths of the way into the orange areas on the inside ofa bend in Fig. 9 ~color on-line!. Increasing the bend ra-dius in these areas should reduce Bmax to ,16 T. Adjust-ing the coil set to accomplish the field reduction is atime-consuming task, and the resources required for thecalculations were not available during the ARIES study.Adjustment of the coil set to increase the minimum bendradius while preserving the good plasma properties andother coil properties has been done in both the NCSX andQPS coil designs.29,30

The high-field regions occur on the thin sides on thesmall-bend-radius part of the hairpin-like bends in thecoils. Brooks31 has modeled hairpin-like coils, shown inFig. 10, with different bend radii to illustrate the depen-dence of Bmax on the minimum bend radius. The calcu-lations are for a section of coil with toroidal elongation~toroidal width0radial depth! of the winding pack crosssection of 4.8, similar to that for the ARIES-CS coils.Figure 11 shows the 6B 6 contours for a model hairpin-like coil with a bend radius of 20 cm ~compared to the200-cm length of the straight leg of the hairpin modelcoil! to illustrate the effect of increasing the bend radiusof a coil. The B0Bmax � 0.833 contour lies about five-eighths of the way into the orange region on the inside ofthe bend, as in the case of the M2 coil of ARIES-CS.Visual inspection suggests that the best approximation isfor an equivalent bend radius between 15 and 20 cm inthis model.

Figure 11 shows the peak magnetic field ~normal-ized to the peak magnetic field for the 50-cm bendradius! as a function of the hairpin-like coil bend ra-dius. Decreasing Bmax by 0.833 ~corresponding to thedecrease of the peak magnetic field of the M2 coil fromFig. 8. FEA model for EM analysis.



19.2 to 16 T! corresponds to an increase in the normal-ized bend radius by ;45% for the rbend � 15 case. Thenormalized field for a bend radius of 15 cm in thismodel is about 1.56; the bend radius corresponding toa peak field of 1.3 ~� 0.833 � 1.56! is about 21 cm,resulting in an ;45% increase in the bend radius. Theactual minimum bend radius for the reference ARIES-CScoil set is 58.5 cm, so it would have to be increased by26 cm in this model. Similar percentage changes havebeen made in the QPS coils while preserving the de-sired physics properties.31

IV.B. Lorenz Loads Analysis

The net Lorenz forces in the six modular coils arelisted in Table III. As shown in Table III, the maximum

radial and vertical forces occur in the M2 coils ~M2L andM2R!. For left and right coil sets, the net forces in theradial direction are identical in magnitude and acting inthe same direction, and the net forces in toroidal andvertical directions are equal in magnitude and acting inopposite direction; therefore, there are no net forces ina field period in both toroidal and vertical directions.Although no net toroidal forces need to be transferredfrom one field period to the next, there are local momentsand forces that are best restrained through mechanicalconnection of adjacent coil structural shells. In addition,since the combined coil structural shells form a shell, it ispossible to couple responses, with tension along the coilgenerating shears in other directions.32 The sum of all six

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 radiusof 20.

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



coils in the radial direction is 345 MN, representing thecentering force pushing the coils inward.

Figures 12, 13, and 14 show the nodal force vectorsin coils M1, M2, and M3, respectively. The maximumnodal forces occur in the coil pair M2 that has the max-imum current density, the maximum magnetic field, andthe smallest bend radii. The net magnetic forces acting ineach modular coil are outwardly directed, away from theplasma, and the coils need to be supported in the regionof the coils facing the plasma. This confirms that windingthe coils into grooves from inside the modular coils is thepreferred solution, and a thick coil strong-back ~behindthe winding pack! is needed to react the radial forcesagainst the structure. Figure 15 shows the nodal forcevectors in one field period, and the forces exhibit fullsymmetry in the coils of one field period from the topview. The toroidally directed forces within a field periodare mainly reacted by the coil structural shell. The ver-

tically directed loads are reacted through tension in thecoil structural shell. And the net radial forces pulling thethree coil structural shells toward the center of the torusare reacted through wedging by hoop stresses in the closedring formed by bolting together the three coil structuralshells.

IV.C. Structural Analysis

Structural analyses were performed to evaluate thestresses and deformations and to help optimize the de-sign of the coil structure. The nodal forces obtained fromthe EM analysis were used as input for the structuralmodel. A sequential coupled EM-structural analysis wasadopted so that the forces from the EM analysis could betransferred to the structural model by using identical nodesand elements.

TABLE III

Net Forces in the Modular Coils

Fr~MN!

Fu~MN!

Fz~MN!

M1L �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 �50.2 141.5Sum of all six coils �341.2 0 0

Fig. 12. Plot of the nodal forces ~N! in coil M1.





IV.C.1. FEA: Shell Model

ANSYS shell elements for magnetic-structural analy-sis are really two-dimensional plane elements used tomodel the midplane of thin structures. The shell modelcan be used in place of three-dimensional ~3-D! solidelements and result in large savings in both setuptime and computational time, and it is very useful forparametric variations and parameter optimization. Thethicknesses of the shell in the intercoil structure and ofthe coil strongback behind the winding pack are keyparameters for the magnet system: Stress and deflectionconsiderations favor thick structures, whereas cost min-imization favors the use of thin structures. A parametricstudy used an ANSYS shell model to optimize the thick-ness of the supporting shell and strongback based onthese considerations.

The coil structural shell configuration ~including themodular coils! from Pro0E-generated files provided anaccurate shape. Because of the threefold cyclic symme-tries presented for both the structural configuration andthe EM loading, the model used a 120-deg field period,consisting of six modular coils and their coil structuralshell. Cyclic boundary conditions were applied at bothends of the coil structural shell.

Figure 16 shows the von Mises stresses calculatedwith the ANSYS shell model with a 0.35-m-thick inter-coil structure and 0.3-m-thick strongback. These thick-nesses were the initial case conditions and were refinedbased on the analysis results. The results indicate a max-

imum deformation of 2 cm at the outboard side of the coilstructural shell. The peak von Mises stress is 536 MPa,occurring at the outboard of the coil structural shell. Boththe peak deformation and stress occur in very localizedregions, and the stresses are much smaller over largeareas of the coil structure.

IV.C.2. FEA: Solid Model

ANSYS solid structural elements are capable of mod-eling a general 3-D structure, allowing the realisticmodeling of boundary conditions and displacements.However, mesh preparation effort and computing timeare more demanding than for the shell model describedin the previous section. A few comparative runs usingthe more accurate but more time-consuming 3-D solidANSYS model were done to confirm the results ob-tained from the ANSYS shell model and to better un-derstand the effect of penetrations through the coilsupporting shell. A number of such penetrations andopenings are required by the power core, for support,maintenance, vacuum pumping, ECH0auxiliary mainte-nance and coolant access pipes. These openings in themagnet structure could affect the local stress distribu-tion and cause higher local stresses and deformations inthe coil structure.

Table IV lists the major penetrations through the coilstructure. The largest openings in the coil structure arethe three main maintenance ports. The maintenance portsat both ends of the coil structural shell were included in

Fig. 15. Plots of the nodal forces ~N! in one field period.



the solid model to determine if enforcement ribs wouldbe needed.

The number of structural elements for the solid modelwas about 750 000. Figure 17 shows the finite elementmodel for the magnetic-structural analysis. The assump-tions for the solid model are the same as those used in theshell model:

1. The magnetic forces on the winding pack areidentical.

2. The winding packs are fully bonded to the groovesin the coil supporting shell with no slip or movementrelative to the grooves.

3. The cyclic symmetry boundary is applied at bothends of the coil supporting tube.

The nominal thicknesses of the coil structural shell andstrongback are 0.20 and 0.28 m, respectively.

The resulting deformation in the winding pack andthe magnet structure and the stresses in the magnet struc-ture are shown in Figs. 18, 19, and 20, respectively. Themaximum deformations of the modular coils and the coilstructure are about 2.0 and 2.1 cm, respectively, at theoutboard region of the magnet. The peak von Mises stressof 656 MPa occurs at the outboard side of the coil struc-ture, caused by the net centering forces of the six mod-ular coils in the field period. Note that this peak stress isonly slightly higher than that from a similar solid modelrun but for a case without any penetration ~652 MPa!.Overall, the displacements for the solid model case aresimilar to those from the shell case, but the peak vonMises stress is higher ~652 MPa from solid modeling as

Fig. 16. An example of the ANSYS shell modeling results showing the stress ~Pa! distribution.

TABLE IV

Major Openings Through Vacuum Vessel and Coil Structure

Number ofOpenings Opening in the Vacuum Vessel

Opening in the Coil Structure Tube~Vacuum Vessel ;0.1 m; Insulation ;0.1 m!

Maintenance port 3 1.8 m ~toroidal!� 4.0 m ~poloidal! 2.2 m ~toroidal!� 4.4 m ~poloidal!ECH0auxiliary port 3 1.24 m ~toroidal!� 1.54 m ~poloidal!

~waveguide: 0.24 m � 0.54 m!1.92 m ~toroidal!� 1.94 m ~poloidal!

Diverter access pipe 24 D � 0.6 m D � 0.8 mVacuum pumping duct 12 1.0 m ~toroidal!� 1.25 m ~poloidal! 1.4 m ~toroidal!� 1.65 m ~poloidal!He0PbLi pipe connecting

to heat exchangers 6 � 6 D � 0.74 m D � 0.94 mHot supporting leg 9 D � 1.0 m D � 1.2 mCold supporting leg 9 D � 0.75 m D � 0.95 m



compared to 536 MPa from shell modeling for caseswithout penetrations!.

As in the shell case, the maximum stress occurs insmall localized regions, with most of the coil structure,including the intercoil structure shell and coil strong-back, at a much lower stress level. This provides thepossibility of decreasing the thicknesses of the intercoilstructure shell and the coil strongback in these low-stressregions to reduce the material cost. A detailed optimiza-

tion study would include tailoring these thicknesses tominimize cost while maintaining the local stresses anddeflections within their allowable limits. The results in-dicate also that the openings required for the main main-tenance ports at 0, 120, and 240 deg are not a majorconcern since the deformations and stresses are very smallin these regions ~the effects on the maximum stress anddeflection in the coil system are also small, as notedearlier!. The results also indicate the low-stress regions

Fig. 17. The solid finite element model.

Fig. 18. Deformation ~m! of the winding pack.



where it would be preferable to position the openings0penetrations required for the power core configurationand maintenance, for instance, over toroidal spans of 0 to40 deg and0or 80 to 120 deg in the outboard region ofeach field period.

Shear stress in the winding packs is a critical param-eter to be used to qualify large-scale electromagnets. Largeshear stresses can result in structural0electrical failure ofthe insulation system. The results for the winding packsindicate peak shear stresses of 45, 50, and 35 MPa in x-z,y-z, and x-y planes, respectively. The peak shear stressesoccur only in very small regions, and the shear stresses inmost of the ARIES-CS winding packs are below 20 MPa,as illustrated in the example results shown in Figs. 21,22, and 23. The NCSX shear stress test data indicate afailure at 32 MPa ~Ref. 33!. No shear stress test data areavailable for our coil design.

V. MAGNET COSTING

The magnet system described in this paper is only apart of the complete commercial power plant design. Forfusion electrical power plants to successfully competewith all other energy sources, they must produce elec-tricity at a competitive cost. Fusion power plants arecertainly capital cost intensive, so reasonable estimatesof all major power core systems are vital in understand-ing and controlling the cost of all the plant systems. Thus,there was an impetus to correctly model the cost of themagnet systems for use in a tenth-of-a-kind commercialpower plant.

The ARIES-CS costs were determined according tothe cost model developed by Schultz et al.14 for super-conducting magnet costing. These models are suffi-ciently detailed and realistic to determine the amount of

Fig. 19. Deformation ~m! of the coil supporting tube.

Fig. 20. Von Mises stress ~Pa! distribution in the coil supporting tube.



superconductor, stabilizer, structure, and insulation andthe complexity of winding and assembly. These algo-rithms need to be modified to take into account tenth-of-a-kind costing, as opposed to first-of-a-kind such as ITERor DEMO. In addition, substantial cost reductions, com-pared to today’s costing, could be achieved through im-proved, more aggressive manufacturing techniques andimproved materials performance as a result of presentand future research and development activities.

The cost of the magnet conductor is determined froma bottom-up estimate, with models for the cost of thesuperconductor, conductor manufacturing, assembly, andmanufacturing of the magnet system. The cost of thecontinuous convoluted toroidal tube magnet structure ispresented in a separate paper.10 As many characteristicsof the magnet system as possible are analyzed, includingsuperconductor type, number of independent pure cop-

per strands ~for quench protection!, material of the con-duit, and structural material.

Table V shows the cost of the conductor for the mag-net coils. There are six coils of each type, two of eachtype in each field period. The cost of the strands is asubstantial fraction ~about 60%! of the cost of the magnetsystem winding pack.

The cost of the superconducting material has beenassumed to be $5000kg ~2003 dollars!, slightly higherthan some HEP experience34,35 but substantially higherthan what might be expected in the future.33 The cost ofthe stabilizer ~copper! is $50kg, with enough copper tosatisfy the protection requirements described above. Thediffusion barrier, a thin coating of the strands to mini-mize ac losses and to prevent the strands from sinteringduring the heat treatment process, was estimated to be$2200kg. It was assumed that $1000m was the cost of

Fig. 21. Shear stresses ~Pa! of the winding packs in the x-z plane.

Fig. 22. Shear stresses ~Pa! of the winding packs in the y-z plane.



cabling and insulating the conductor. This cost includesthe cost of the sheath material ~thin plate!, forming thesheath around the conductor strands, and seam weldingalong the conductor. The cost includes making and in-specting a long weld that should not leak during the lifeof the reactor. The cabling and insulating cost can also bedecreased substantially, as described below.

The above costs do not include administration andoperating expenses. The values of engineering and con-tingency are included in the overall system evaluation ofthe ARIES-CS ~Ref. 36!.

The ground rule adopted by theARIES team is that thevalue-added capital costs will be observing a 75% learn-

ing curve on the unit cost. The cost of value-added tenth-of-a-kind component is reduced by 10@ln~0.75!0ln~2!# ; 0.385,assuming the base cost is the first production unit. Thelargest cost of the conductor is due to the superconduct-ing strands and the insulating and cabling. The cost of thesuperconductor strands and cable has been investigatedby Cooley et al.34 and others. It has been hoped that thecost of the superconducting strands can decrease to aslow as $1.50kA{m ~12 T, 4.2 K! through improvementsin materials, use of inexpensive materials instead of moreexpensive ones, and increased billet mass. The final col-umn in Table VI shows the results of the aggressive cost-ing, compared to the more conventional one of Table V.The cost of the winding pack could be decreased to aboutone-third of that indicated in Table V, to ;30 M$ ~mil-lion dollars!.

The cost of winding has been calculated by Waganeret al.,10 as well as the cost of heat treatment, but these

Fig. 23. Shear stresses ~Pa! of the winding packs in the x-y plane.

TABLE V

Cost of Winding Packs for ARIES-CS withPresent-Day Costing Assumptions

M1 M2 M3

Modified coils ~T! 14.6 15.1 15.1Coil currents ~MA! 10.8 13.5 13.1Single turn length ~m! 45.8 45.1 41Number of turns 270 338 328Length of conductor ~m! 12 366 15 221 13 428Superconductor cost ~$0kg! 500Superconductor cost~m30m! 4.8 � 10�5

~kg0m! 0.3888~cost at 12 T, 4.2 K! 194.4

Stabilizer cost ~$0m! 8.54Diffusion barrier cost ~$0m! 1.65Insulating and cabling ~$0m! 100Total conductor~$0m! 305~$0kA{m at 12 T, 4.2 K! 7.61

Scaled ~$0kA{m! 10.2 10.5 10.5Cost of coils, all periods ~M$! 30 38 34Total conductor cost ~direct!~M$! 102

TABLE VI

Present-Day and Future Costs of the Conductor

Present By 2016

Superconductor cost ~$0kg! 500 120Superconductor cost~m30m! 4.80 � 10�5 4.80 � 10�5

~kg0m! 0.3888 0.3888~cost at 12 T, 4.2 K! 194.4 46.7

Stabilizer cost ~$0m! 8.5 8.5Diffusion barrier cost ~$0m! 1.6 1.6Insulating and cabling ~$0m! 100 38Total conductor~$0m! 304.6 94.8~$0kA{m at 12 T, 4.2 K! 7.6 2.4

Scaled ~$0kA{m! 10.2 3.2Cost of coils, all periods ~M$! 30.2 9.4Total conductor cost ~direct! ~M$! 102 32



costs are substantially smaller than those presented inTables V or VI because of the highly automated instal-lation methods developed during prototype, demonstra-tion, and production power plant development.

VI. SUMMARY

The magnet system for the ARIES-CS has been de-scribed and analyzed. Innovative magnet and structuredesign innovations result in a magnet system that is rel-atively simple and inexpensive to construct and is oper-ationally robust. The magnet system consists of threefield periods, each manufactured separately and then in-tegrated into a full toroidal structure. The magnet is woundwith CICC using wind-and-react high-performance Nb3Snsuperconductor materials. A representative low-carbonsteel ~JK2LB! has been selected as the structural materialand conductor jacket in great part due to its low activa-tion characteristics and lower cost ~as compared to Inco-loy� 908!.

The structure is made by low-cost and highly auto-mated additive manufacturing techniques. The conductoris wound directly into the coil structure, and the conduc-tor heat treatment involves warming the entire field pe-riod with the installed conductors.

The magnetic fields, Lorenz loads, stresses, and de-formations are calculated using finite element methods,both shell and solid model. The highest fields are verylocalized, and means of decreasing the peak value havebeen proposed. It is estimated that the peak field will beslightly higher than 15 T, which is below the design value.The peak stresses and peak deformations are also verylocalized, and the method of manufacturing allows fortailoring of the structure thickness ~to minimize its massand cost! to match the allowable stress and deformation.

The cost methodology for the coil conductors hasbeen described, including means of evaluating future im-plications of improved winding and superconductor man-ufacturing and performance.

ACKNOWLEDGMENT

This work was supported under U.S. Department of En-ergy grant DE-FC03-95-ER54299.

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