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TABLE IPERFORMANCES AT 17 T OF MULTISTAGE CABLES MADE OFSINGLE-STACKED-TAPE CONDUCTORS OF VARIOUS TAPE WIDTHS, BASED ONTHE CRITICAL CURRENT OF 180 A AT 17 T AND 4.2 K FOR A 4 MM WIDTH,0.1 MM THICKNESS REBCO TAPEFig. 6. (a) Illustration of one turn coil of a part of TF magnet. (b) A schematicdrawing of a single turn coil of a superconducting parallel-tapes conductor.cal fusion reactor composed of segmented conductors (STARS;Stacked Tapes Assembled in Rigid Structure) [8].For a high-field tokamak, a TSTC conductor can also be modified using the Stacked-Tape Twist-Winding (STTW) method[12] to allow a parallel-HTS-tape cable at the inner legs of aTF coil to provide enough support against Lorentz load and tomitigate AC losses such the coupling current is discussed next.From the no-cyclic load effect up to 6.0 kA at 17 T, we canconclude that a Lorentz load up to 102 kN/m (17 T 6.0 kA)does not degrade the critical currents for the TSTC cable. Theoverall engineering critical-current density Je is 117 A/mm2for the present conductor considering an overall averaged diameter of 8.1 mm, while it is 375 A/mm2 for the conductorcross-section of 4 mm 4 mm. The density Je considering thecircular envelop with 36% space around a TSTC conductor(5.7 mm diameter) gives a value of 239 A/mm2 .C. High Field and High Current ConductorsThe estimated performance of single-stacked TSTC conductors and its multiple-stage conductors at the magnetic field of17 T is shown in Table I for various tape widths between 4 mmand 12 mm. The values are estimated considering a tape criticalcurrent of 180 A for 4 mm width (450 A/cm) at 17 T at 4.2 K.As shown in Table I a single stack conductor of 12 mm width,120 tapes provides the critical current of 65 kA at 17 T and 4.2 Kwith a diameter of 22.2 mm, while the triplet conductor can get194 kA with the diameter of 48 mm. A TSTC conductor witha single stack of tapes provides 36% space around the REBCOtapes since they are twisted as mentioned earlier. This spacecan be used for the stabilizer. A hexa (6-in-1) conductor of six,6 mm 60-tape conductor carries the critical current of 97 kA withthe diameter 35 mm. Given those high currents cables options,a TSTC conductor can provide a very compact cable-in-conduitconductor for fusion magnets and other applications. But a magnet conductor can be exposed to severe electromagnetic forces;therefore the conductor has to be properly supported.III. METHOD TO MITIGATE COUPLING CURRENTS IN PARALLELSUPERCONDUCTING-TAPE CABLE FOR A TOKAMAK MAGNETIf REBCO flat tapes can be used in a cable without transpositions, a parallel-tape cable could be desirable in a high Lorentzload environment (high field and high current) as a tape canresist high loads on its wide face [15]. A parallel-tape HTSconductors has been developed for a specially designed heli-A. Conceptual DescriptionFig. 6 shows an illustration of a single turn of a D-shape TFcoil, composed of an inner straight section (S-section), an outersection (O-section) and two mid sections (M-sections). If thiscoil is made of a cable with a stack of tapes without twistingor transposition (parallel-tape) as shown in Fig. 6(b), an outertape (Tape A) would always be on the outside of the stack whilea Tape B would always be in the inside. This configurationwould cause significant issues due to magnetic flux coupling.To solve or mitigate this problem the cable is twisted except atthe S-section (where the EM load is largest), and the couplingcurrent of the S-section is compensated with coupling currentsof the other sections. Two options to compensate the couplingare discussed below: a) Two-turn coil mitigation method andb) Single coil mitigation method.B. Two-Turn Mitigation MethodIn the case of a TF coil magnet with multiple turns, thecoupling current on a tape can be reduced by canceling it withthe coupling current of the same tape on another turn. To makethe canceling current in the opposite direction the cable needsto be twisted properly.A fabrication method of a TF coil is shown in Fig. 7(a),where two turns of a twisted stacked-tape cable using the STTWmethod are wound, but the tapes at the straight parallel-tapessection (S-section) are not twisted. In the S-section at the first(left) turn in Fig. 7(a), Tape A is at the outermost edge. Thenthe cable is twisted with an odd number (2n 1) of half-twistsover the other sections, M-sections and O-section, so that TapeA of the cable will be at the innermost edge of the stack at theS-section of the second-turn (Tape B is now at the outermostedge) as shown in Fig. 7(a). The TF coil is wound in this wayto change the tape locations from the inner most to the outermost locations alternatively at the S-sections. In this way, thedirections of the induced current in each tape in the cable arechanged at the first and the next turns, and the coupling currentscancel out and the losses are minimized.

S-section is in the opposite direction of that in the O-section.That is, the induced tape current of each tape cancels out between the two sections.If the flux crossing-areas of the parallel-tape cable are Asand Ao at the S-section and the O-section of the conductor,respectively, the condition to cancel the induced tape currentsin the S- and O-sections is given byA s Hs A 0 H0Fig. 7. (a) A conceptual illustration of two-turn coil method to cancel out fieldinduced coupling currents. The cable of M-sections and O-section is twisted(2n 1 half-twists). (b) Winding cross-section of an inner leg of a TF magnet,showing coupling flux compensation arrangements from the symmetry of thewinding.(1)where Hs and Ho are the magnetic fields at the S-section andO-section, respectively.Using a rough estimation, the toroidal magnetic fields Hs andHo at the S-section and O-section in the inner most turn (highestfield) follow (2) from Ampère’s law,Hs Rs R0 H0(2)From (1) and (2), one can obtainWo LoRo Ws LsRsFig. 8. Single-coil cancelation method to mitigate the field induced current.The cable is twisted between the S-section and the O-section of a coil whosecable is not twisted. Each transition of the stack of tapes in the cable betweenthose sections is twisted by an odd number (2n 1) of half-twists.Fig. 7(b) illustrates a cross-section of a TF magnet in a layerwinding at the midplane of the S-section. Each square shows acable cross-section where the tapes are parallel to the windingaxis. To achieve a good cancelation of the coupling currents,each layer of a TF coil should be made with an even numberof turns as shown in Fig. 7(b), so that the coupling current ofthe coil turn 1a, for example, is canceled with 1h, located in thesymmetric location to 1a. In the same way 1b and 1g, 2a and2h, 3a and 3f, 3c and 3d, 8a and 8d in Fig. 7(b) make good pairsfor current cancelations. In the case of a pancake winding, thepaired winding turns should be arranged in the same pancakebecause the coil turns do not have exactly the same magneticflux distributions. Therefore, the cancelation requires proper coildesign considering the magnetic field intensity and the cablelength.C. Single-Turn Mitigation MethodA method for canceling the coupling currents in one TF coilis illustrated in Fig. 8. A conductor is twisted between theS-section and the O-section of a coil. In the S- and O-sections ofthe cable, the tapes are not twisted. However, in each transitionof the cable between those sections, the stack of tapes is twistedby an odd number (2n 1) of half-twists. Therefore, Tape Alocated at the outer in the S-section becomes an inner tape inthe O-section. In this way, the induced current of Tape A in the(3)here, Ws and Wo are the widths of the S-section and O-sectionfacing the magnetic flux, and Ls and Lo are the lengths of thesesections.To satisfy the condition given by (3), the width Wo timesthe length Lo (Wo · Lo ) for the O-section needs to be designedlarger than Ws · Ls , since the ratio of Ro /Rs is larger than 1.If the cable has a uniform cable width (Wo Ws ), it will bedifficult to satisfy the condition in (3) only adjusting the lengthsof Lo and Ls . However, if the width Wo can be varied and madelarger than Ws , it will be possible to satisfy (3). This can be doneby selecting the proper thickness spacers between tapes in theparallel-tape segment at the O-section. This single-turn methodmay be a useful method for a short coil such as a segmented coilor a demountable coil [14].IV. CONCLUSIONThe critical currents of a twisted single-tape sample with thetwist-pitch of 100 mm were measured at 4.2 K in fields upto 17 T, and it was compared with the critical currents of aflat tape in c-axis fields. Both samples (SuperPower REBCOtapes SCS4050-AP) showed very similar critical current behavior within 3% deviation at 4.2 K over a wide field range between2 T and 17 T, although those critical currents at 77 K differedby more than 12%.We have successfully achieved 6.0 kA (for a 100 μV/m criterion) at 17 T and 4.2 K with a 40-tape (4 mm width) TSTCconductor made from SuperPower REBCO tapes. The n-indexvalue was as high as 35. This indicates that the cable terminationswere well fabricated with reasonably uniform joint-resistances.The cable performance was compared with the critical currents of the single tape samples. From a simple comparison, thecable was degraded 16% from the expected single tape criticalcurrents in fields between 10 T and 17 T. However, no degradation of the critical currents with cyclic loading was observed inthis field range. Those results indicate that the degradation dueto the Lorentz load up to 102 kN/m (17 T 6.0 kA) was notsignificant. Origins of the cable degradation of 16% are still

not clear. Further investigation will be required to understandthe critical current discrepancy between the cable and the singletape performance. For high-field magnet applications, it is veryimportant to evaluate the conductor performance in a Lorentzload environment representative of the conditions experiencedin real operations (high fields and high currents) and the performance achieved so far is very promising for the future uses ofthe TSTC conductor in high-field high-current magnet applications. Nevertheless, more experiments in high-field conditionsare necessary to reach even higher Lorentz loads.A method to mitigate the flux coupling AC loss, if a paralleltapes superconducting cable conductor is used in a ToroidalField (TF) tokamak magnet, was discussed using a variationof the TSTC conductor and the STTW method. The methoddiscussed allows a parallel-HTS-tape flat cable at the inner legsof a D-shape TF coil to make the conductor rigid against thetransverse Lorentz load and to mitigate the coupling currentsissue. Applicability and modifications of this method should beconsidered depending on the winding methods (layer or pancakewindings) and the size of the magnet to be built together with itsoperational conditions such as intensities and ramp rate speedsof the magnetic field.ACKNOWLEDGMENTThe authors would like to thank P. Grondstra from MevionMedical System for the high-field test at NHMFL, E. Fitzgerald,M. Iverson, B. Forbes, R. Viera, and B. Beck for pentagon sample holder fabrication and A. Radovinsky and F. J. Mangiarottifor useful discussions at MIT, PSFC.REFERENCES[1] D. C. van der Laan, P. D. Noyes, G. E. Miller, H. W. Weijers, andG. P. Willering, “Characterization of a high-temperature superconductingconductor on round core cables in magnetic fields up to 20 T,” Supercond.Sci. Technol., vol. 26, no. 4, 2013, Art. no. 045005.[2] D. C. van der Laan et al., “Engineering current density in excess of200Amm-2 at 20T in CORC magnet cables,” containing RE-Ba2Cu3O7-δtapes with 38μm thick substrates,” Supercond. Sci. Technol., vol. 28, 2015,Art. no. 124001.[3] A. Kario et al., “Investigation of a Rutherford cable using coated conductor Roebel cables as strands,” Supercond. Sci. Technol., vol. 26, no. 8,Aug. 2013, Art. no. 085019.[4] G. Celentano et al., “Design of an industrially feasible twistedstack HTS cable-in-conduit conductor for fusion application,” IEEETrans. Appl. Supercond., vol. 24, no. 3, 2014, Art. no. 4601805.doi: 10.1109/TASC.2013.2287910.[5] G. De Marzi, G. Celentano, A. Augieri, L. Muzzi, G. Tomassetti, andA. della Corte, “Characterization of the Critical Current Capabilities ofCommercial REBCO Coated Conductorsfor an HTS Cable-in-ConduitConductor,” IEEE Trans. Appl. Supercond., vol. 25, no. 3, Jun. 2015, Art.no. 6602804.[6] D. Uglietti, R. Wesche, and P. Bruzzone, “Design and strand tests of afusion cable composed of coated conductor tapes,” IEEE Trans. Appl.Supercond., vol. 24, no. 3, Jun. 2014, Art. no. 4800704.[7] D. Uglietti, N. Bykovsky, K. Sedlak, B. Stepanov, R. Wesche, and P.Bruzzone, “Test of 60 kA coated conductor cable prototypes for fusionmagnets,” Supercond. Sci. Technol., vol. 28, 2015, Art. no. 124005.[8] N. Yanagi1 et al., “Design and development of high-temperature superconducting magnet system with joint-winding for the helical fusion reactor,”Nucl. Fusion, vol. 55, no. 5, 2015, Art. no. 053021.[9] M. Takayasu, L. Chiesa, L. Bromberg, and J. V. Minervini, “HTS twistedstacked-tape cable conductor,” Supercond. Sci. Technol., vol. 25, no. 1,2012, Art. no. 014011.[10] M. Takayasu, L. Chiesa, N. Allen, and J. V. Minervini, “Present status andrecent developments of the twisted stacked-tape cable conductor,” IEEETrans. Appl.Supercond., vol. 26, no. 2, Mar. 2016, Art. no. 6400210.[11] M. Takayasu, J. V. 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PSFC/JA-17-89 Investigation of HTS Twisted Stacked-Tape Cable (TSTC) Conductor for High-Field, High-Current Makoto Takayasu 1, Luisa Chiesa2, Patrick D. Noyes3, and Joseph V. Minervini September 3, 2016 1MIT Plasma Science and Fusion Center, Cambridge, MA 02139, U.S.A. 2Mechanical Engineering Department, Tuft