Roebel&cables&from&REBCO&coated&conductors:&a&one5 century5old&concept&for&the&superconductivity&of&the& future&

Transcription

1 Roebel&cables&from&REBCO&coated&conductors:&a&one5 century5old&concept&for&the&superconductivity&of&the& future& Wilfried Goldacker 1, Francesco Grilli 1, Enric Pardo 2, Anna Kario 1, Sonja I. Schlachter 1,MichalVojenciak 2 1 Karlsruhe Institute of Technology, Institute for Technical Physics, HermannFvonF HelmholtzFPlatz1,76344EggensteinFLeopoldshafen,Germany 2 SlovakAcademyofSciences,InstituteofElectricalEngineering,DubravskaCesta9, 84104Bratislava,Slovakia Authortowhomcorrespondenceshouldbeaddressed:francesco.grilli@kit.edu 1

2 Abstract(( Energy applications employing highftemperature superconductors (HTS), such as motors/generators,transformers,transmissionlinesandfaultcurrentlimiters,are usually operated in the alternate current(ac) regime. In order to be efficient, the HTS devices need to have a sufficiently low value of AC loss, in addition to the necessary currentfcarrying capacity. Mostapplicationsareoperatedwithcurrents beyond the current capacity of single conductors and consequently require cabled conductor solutions with much higher current carrying capacity, from a few ka to upto20f30kaforlargehydrofgenerators. Acenturyago,in1914,LudwigRoebelinventedalowFlosscabledesignforcopper cables, which was successively named after him. The main idea behind Roebel cables is to separate the current in different strands and to provide a full transpositionofthe strandsalongthecabledirection. Nowadays, thesecables are commonlyusedinthestatoroflargegenerators.basedonthesamedesignconcept oftheirconventionalmaterialcounterparts,htsroebelcablesfromrebcocoated conductorswerefirstmanufacturedatthekarlsruheinstituteoftechnology(kit) andhavebeensuccessivelydevelopedinanumberofvarietiesthatprovideallthe requiredtechnicalfeaturessuchasfullytransposedstrands,hightransportcurrents andlowaclosses,yetretainingenoughflexibilityforaspecificcabledesign.inthe past few years a large number of scientific papers have been published on the concept, manufacturing and characterization of such cables. Times are therefore mature for a review of those results.thegoalis toprovidean overview and a succinctandeasyftofconsultguideforusers,developers,andmanufacturersofthis kindofhtscables. 1. Introduction( HighFtemperature superconductors(hts) in the form of REBCO(REBa2Cu3Ox with RE=Rare Earth elements) coated conductor (CC) tapes the second generation of HTS materials show great potential for use in many applications such as power 2

3 transmission cables, motors, generators, fault current limiters, transformers and magnets [1]K. Today the superconducting REBCO material is available as commercial product in long lengths with high currentfcarrying capacity from several providers [2 5]. Implementation of superconductors is particularly attractiveforlargefscaleapplications(suchasthosementionedabove)invirtueof the significantly reduced size and weight (typically a factor 2F3) and increased energy efficiency. The requested current capacity of many devices, however, is significantly beyond that of a single CC tape and demands for assembled highf currentcables.inmagnets,forexample,ahigherdrivecurrentallowsreductionof the winding number for a given field resulting in a lower inductance, which is mandatory for many applications. Most of the devices are operated in alternate current (AC) regime and keeping the occurring AC losses under an acceptable threshold is a quite general issue and a key point for the success of a superconductingsolution. The technological request for lowflosshighfcurrent conductors rose up already in veryearlytimeswhenconventionalelectricalmachinerywasbeingscaledtobigger size.atthebeginningofthe20 th centurythesizeofelectricalpowergenerators,for example, was limited by the occurring AC losses. The invention of a lowfloss assembled copper cable design with insulated strands and fulltranspositionby LudwigRoebelattheBBCcompanyinMannheim(Germany)(Germanpatent1914, seefigure1),wasthebreakthroughforaclossreduction.itpavedthewaytoanew power class of generators, and has established this new design of a highfcurrent lowfloss conductor as a standard until present[6]. Roebel was the first person to understand and identify the need of segmenting the conductor into strands (insulatedfromeachother)andoftransposingthestrandsalongthecabledirection toreduceinducededdycurrentsandcurrentloops.nowadaysroebelbarsarethe standard conductors in the stator windings of large conventional generators and motors[7,8] 3

4 Figure&1.&The&patent&for&a&low&loss&cable&for&generators&(1914,&BBC&Company&Mannheim,&Germany)&and&a& picture&of&ludwig&roebel&( ).& In the field of applied superconductivity, AC currents or ramped fields lead quite soontothesamerequesttoreducetheaclossesbymeansofasuitableconductor structure with the same features mentioned above a strand structure and transposition.inthelargecoiltask(lct)[9],investigatedintheyears1980f85,six large superconducting fusion magnets were designed, built and tested for the prospecteduseinatorusarrangementofatokamakfusionreactor.inoneunit,the EURATOM magnet, the first superconducting Roebel cable was made from transposed NbTi strands [9], see Figure 2. The ductility of NbTi allowed perfect shaping of the Roebel structure with a quite sharp stepfoverfbending edge and a quite short transposition length (280 mm). In contrast to the traditional Roebel geometrywithnarrowbuthighconductorstacks,thiscablewassmallinheightand broad, resembling a Rutherford cable. Cables of this type were used in the dipole magnetsoftheacceleratorfacilitiesatcern[10].duetotheplanartapegeometry of HTS coated conductors, the required tight bends for such cable designs are impossibleintheinfplanedirectionandnewsolutionswererequired. 4

5 Figure&2.&The&NbTi&Roebel&cable&of&the&EURATOM&toroidal&field&magnet&in&the&Large&Coil&Task&project&[9].& 2. Cable(design(and(preparation( InthissectionfirsttheevolutionofHTSRoebelcablesissummarized;thendetails about cable design and production methods are discussed; finally several possible modifications of the basic Roebel cable design and alternative concepts for highf currentcablesareexamined The(evolution(of(HTS(Roebel(cables( ThefirstHTSRoebelcablewasdemonstratedbytheSiemensCorporateTechnology groupusingbscco(2223)tapesasstrands[11].thiscableconsistedof13strands and showed a selfffield reduced DC transport current of about 400 A at 77 K. The quite long transposition length of typically 3 m in such cables was caused by the limited infplane bending ability of thematerial. The cable achieved the expected reducedaclossesincomparisonwithstackedtapesandservedasamotivationfor theapplicationinhtstransformers[12].theideaofaroebelstructurewithrebco coated conductor was proposed by Martin Wilson in 1997 [13] at the CEC/ICMC conference, but a way to manage the bending, the strand shape forming and the assemblingissuewasstillunknown.thesolutionwasfoundafewyearslaterthanks to the progress in homogeneity and robustness of CCs and to their commercial availability. The meanderflike shaping of the CC as shown in the CAD model of Figure 3 and presented by Wilfried Goldacker in 2005 [14] was first realized by means of precision punching technique at Forschungszentrum Karlsruhe (now KarlsruheInstituteofTechnology,KIT)andpublishedin2006[15].Thefirstcable wasmadefrom16punchedstrandsofdybcocoatedconductors(manufacturedby the THEVA company) and carried a selfffield transport current of 500 A at 77 K, 5

6 abouthalfofthesumofthecriticalcurrentsoftheindividualtapes.unfortunately thecablehadnocopperstabilizationandburnedthroughduetothelackofquench protection. The second presented Roebel cable from 12 mmfwide CuFstabilized SuperPowerMOCVDcoatedconductortapealreadyachievedaDCtransportcurrent of1.02kaat77kinselfffield.the0.36mlongsample(twotranspositionlengths) already showed the reliability of the strand punching process and excellent homogeneity, thanks to the use of coated conductorfrom SuperPower [16]. Small resistive contributions in the voltagefcurrent (V$I) characteristics above Ic/2 indicatedcurrentredistributionsbetweenthestrandsalongthecable.thedecrease of the measured transport current by 60% compared to the sum of the critical currents of the individual strands was ascribed to the generated selfffield, whose pattern was calculated by means of a numerical method based on a BiotFSavartF approach. A second group at Industrial Research Limited (IRL) adopted the topic of coated conductor Roebel cables as main subject of investigation, immediately focusing on the industrial production of such cables with machines specifically designed to producelonglengthsinanautomatedfabricationprocess[17]. Roebel cables from CCs offer a large variety of choices to increase the current, to optimize the cable design and to increase the thermal and mechanicalstabilityby modifying the structure of the composing strands. The potential for further increasedtransportcurrentswasshownbycabling3ffoldstacksofstrandsintoa45 Fstrandcableof1.1mlengthand18.8cmtranspositionlengthcarrying2.6kA(77K, selfffield)[18].increasingthetranspositionlengthtobeabletoaddmorestrandsis anotherpossibilitytoincreasethecurrentperformanceinasimpleway. 6

7 Figure& 3.& Schematic& illustration& of& a& Roebel& bar& made& from& coated& conductor& tapes.& Two& transversal& cross5sections&at&different&positions&are&also&shown.& 2.2. Design(parameters( The Roebel cable is made from meander shaped CC tapes. For the Roebel cable design we follow the nomenclature introduced by IRL [19]. The fundamental geometrical parameters are the original tape width WT,thetranspositionlength LTRANS.(whichisafullperiodofthemeander),thestrandwidthWR,thestrandFedge clearance WC (clearance in the cable centre), the crossover widthwx, the interf strandgaplisg,.thecrossoverangleϕ,thecutfofffilletradiusr,andtheinnerradius Ri.TheparametersareshownintheschematicsketchofFigure4. Figure& 4.& Nomenclature& to& specify& the& geometry& of& a& Roebel& cable& following& reference& [19].& The& inner& radius&ri&opposite&of&r&is&not&indicated&in&this&figure,&but&it&is&important&to&manage&the&stresses&at&this& point,&see&[20]&for&details.& 7

8 Figure&5.& Reel5to5reel& computer& controlled& pneumatic& punching&machine&utilized&at& KIT&for&producing& Roebel&strands.&The&mechanical&punching&tools&can&be&changed&for&obtaining&cable&widths&between&4&and& 12&mm.&At&present&the&transposition&length&for&4&mm5wide&tape&is&115.7&mm,&whereas&for&12&mm5wide& tape&it&is&126&mm.&& The transposition length is a suitable parameter to determine the number of applicable strands and needs for a specific application. The interfstrand gap is strongly correlated to the assembling procedure, being narrower for handfmade cables (KIT) and wider in the case of fully automatic process (IRL). Numerical calculations on the geometry with the best mechanical performance and current capacity[21]confirmedthesetofparametersusuallyusedatkit:aninnerradius Ri.=2mm(thestresshotspotinthetape),astrandFedgeclearanceof1F2mmforWT =10F12mmandnoclearanceforWT=4mm(whichneedsasufficientinterFstrand gap)andacrossoverangleof30degrees.accordingtothecalculationspresentedin [21],asharpouteredgeofthecrossoversectionandanincreaseoftheinnerradius leads to a reduction of the von Mises stresses under tensile loads. In the Roebel cables from IRL some parameters were chosen differently, in order to be better compatible with the assembling machinery, namely: a larger clearance width Wc betweenthetwosidesofthecableandasmallernumberofstrandspercablelength unit[17].whileproducingonesinglestrandfromacctape,thecrossoverwidthwx and the angle can be adjusted for best current performance. If several strands are cut in parallel from a wider CC material (e.g. 40 mm), WX is predetermined by geometrical reasons and the cross over section becomes the currentflimiting part [17]. 8

9 2.3. Production(methods(( SeveralmethodswereinvestigatedforthemeanderFlikeshapingprocessoftheCC tapes. Laser cutting with conventional equipment is a very flexible technique, but failed due to heating and melting defects. The newer picosecondsfinfrared laser technology avoids producing defects, but it not very economically attractive in termsofproductionspeed.mechanicalpunchingwasidentifiedbothbykitandirl asthebestmethodandcanachieveaprecisionof<50micronforthestrandwidth. Figure5showsthereelFtoFreelpunchingtoolinuseatKIT,whichallowsusingthe fulltapewidthandvaryingthetranspositionlengthinawiderange.advantagesof thistechniquearethepossibilityofadjustingthetooltothetapeconditionsandits high production speed, typically 50 meters of tape per hour. The loss in current carryingcapabilityfrompunchingcanbelimitedto<2f3%forhomogenouscctapes [16].Figure6shows10punchedstrandsbeforeandaftertheyareassembledinto cable. Figure&6.&Ten&strands&punched&from&12&mm5wide&coated&conductor,&before&(top)&and&after&(bottom)&they& are&assembled&into&cable.&& The assembling procedureoftheroebelcablesisaratherchallengingprocedure, which requires a complex bending of the tapes around each other, avoiding overf bending or plastic deformation of the material. IRL solved this problem inventing innovativemachineriesthatareabletoproducesuchcablesinlonglengths[19] 9

10 seefigure7.atkitsamplelengthsupto5marecurrentlystillmadebyhand.the advantagesarethepossibilitytoobtainadensepackingwithareducedcentralgap and the possibility to change cable designs, e.g. by multifstacking of strands or cabling with additional stabilisation. In that way the potential of the cable technologycanbeinvestigatedinawiderrange. Figure&7.&Device&for&assembling&15/5&(15&strands&with&5&mm&width)&Roebel&cables&(courtesy&IRL5General& Cable).& 2.4. Design(options(and(modifications( A couple of cable design options exist for the different requests coming from the specific applications or operation conditions, as for example temperature and backgroundfield Multi*stacking1 High transport currents at 77 K can be achieved by adjusting several design parameters.increasingthetranspositionlengthallowsincreasingproportionallythe numberofstrands,resultinginenhancedcriticalcurrent.thetranspositionlength, however, needs to meet the requirements and constraints of the prospected application(coilsize,lossreduction).thesecondwayofachievinghighcurrentsis interlacing stacks of strands instead of individual strands. The potential of this method was demonstrated for both, a 12 mmfwide (3Ffold stacking) [18] and a 4 mmfwidecable(3fand5ffoldstacking,seefigure8)[22].stackingmultiplestrands ishoweververychallengingtodoautomaticallyandsofarithasbeendemonstrated only on cables assembled by hand. Unfortunately multifstack cables are not very suitableforwindings,becausetheyhavethegeneralproblemofstacks:thetapesin thestacksarenotfullytransposedandthereforetheinnerccsneedtobeshorterto 10

11 match the meander pattern of the others. For applications where limited bending occurs, for example in busbarsorstraighthighfcurrent power lines, this method can be easily applied to enhance the current carrying capability of the cable. The consequences of a multifstacking arrangement for the cable s AC losses are discussedinsection4. Figure&8.&Multi5stacking&of&strands:&a&35fold&stack&of&punched&CC&tapes&and&3&different&Roebel&cables&with& 4&mm&width&are&shown.&The&upper&cable&consists&of&14&single&tapes,&whereas&the&middle&and&the&lower& cables&consist&of&13&35fold&stacks&and&10&55fold&stacks,&respectively.& Strand1coupling1 Usuallynoinsulationisappliedbetweenthestrandsandcouplingiscausedbythe natural contact between the strands. Coupling currents flow around the nonf punched edges of the tapes, since the buffer layers below the superconductor are insulators. Inhomogeneous current distributions in the CC and a controlled redistribution of currents betweenthestrands,whichis desirable in low field or selfffieldapplications,canbemanagedbyamoderatestrandcoupling.onewayof obtainingthiscouplingwasdemonstratedbyusingag/resinpaste,whichprovidesa moderate coupling with tolerable coupling AC losses [23]. Since the impregnated cable becomes quite stiff and is not suitable for strong bending, this option is however limited for application in situ wherenofurtherstrongbending of the sampleoccurs. 11

12 Recently, Majoros et. al. studied the effect of different kinds of interfstrand connections on interfstrand resistances, in order to increase the current sharing betweenthestrands[24].theyfoundthatbyjustapplyingapressureof8kpagives amaximuminterfstrandresistanceof105mω.usingatinfoilplacedontopofthe Roebel cable gives the maximum interfstrand resistance of 31.5 mω under a pressure of 8 kpa. The lowest maximum interfstrand resistance of 0.1 mω was achievedbysolderingcoppershunts.aclossmeasurementsrevealedthatevenan interfstrandresistanceaslowas0.1mωdoesnotcauseanysignificantcouplingloss increaseupto200hz,whileallowingcurrentsharing Internal1and1external1stabilization1 IndustrialCCs are usually plated with stabilizing copper for thermal stabilization. Thelayerthickness(typically20μm)hastobematchedwiththeoperationcurrent. This is particularly important when operation temperatures below 77 K are considered, where the transport currents can increase by one order of magnitude, and can lead to the necessity of using even thicker stabilization layers. Such a conductor is more difficult to be handled as Roebel strand in the cable fabrication process.inthiscasethesolutionistoapplyanalreadymeanderfshapedcoppertape on top of each strand, with limitations and difficulties similar to the multifstack option.asystematicinvestigationofthisoptionhasnotbeenperformedsofar. Classical copper Roebel cables have completely insulated strands. The insulation technology is an important issue and the subject of patents and company s knowf how.atcryogenictemperaturesandinordertomaintainthedensepackingofthe superconducting cable, impregnation techniques similar to those employed with lowftemperature superconductors are the first choice. IRL realized an epoxy acrylatecoatingoftypically20μmwithouteffectonthecurrentcapacity[25].the accuracy of the coating however is not perfect at the sharp edges of the CC. High voltage properties were not fully tested. Until now it is not clear if and where an insulationofthestrandsmakessense. 12

13 Current1and1voltage1contacts1 ThestandardtechniquetoinjectthetransportcurrentistosoldertheRoebelcable intoagroovedcufblocksurmountedbyanothercopperbar.mostoftheccsrequire useofspecificsoldermaterials[26]toavoidthermalstrainsinthecomposite,which canleadtocrackformationintherebcolayer.forshortersamplesuptoabout1m length,thecontactresistancedominatesanddeterminesthecurrentdistributionin the cable. A systematic experimental investigation and modelling of the current distributioninthecurrentleadsisstillmissing. Applying voltage contacts for the current measurements with the standard fourf point method is not trivial. Connecting all strands together leads to current redistributionatthecontacts,thereforemeasuringarepresentativestrandcangive misleadingresultsforthewholecable[18].thebestwayistomeasureallstrandsin parallel,whichgivesmoreinformationaboutthescatteringofthepropertiesofthe strands.thiscanbedonebyplacingvoltagetapsindifferentpositionsonthecable orbehindthecurrentleads[27].anindirectwayistomonitorthecurrentsharing with a parallel applied copper shunt that gives an image of the V(I) graph of the wholecable[18] Striations1of1the1strands1 StriationsweresuccessfullyappliedtoRoebelstrandsbylasergrooving(5filaments of1mmwidth,seefigure9)andaneffectontheaclossbehaviourwasobserved [28 31], although further systematic investigations are needed for a deeper understanding. The applied striations however already showed the importance of sufficient conductor homogeneity and the absence of defects. By means of Hall probescanssingledefectssignificantlylimitingthelocaltransportcurrentscouldbe identified [32]. Those results confirm the considerations in reference [33] on the homogeneitycriteriatoselectccforthepreparationofroebelstrands. 13

14 Figure& 9.& Filament& structure& in& Roebel& strands& made& by& laser& grooving& (KIT).& Image& reproduced& from& [31].&& 2.5. Alternative1Concepts1 For HTS AC cables other alternative concepts were developed and investigated. According to the assembling geometry of HTS power transmission cables, Danko vanderlaanpresentedtheconceptofthecableonroundcore(corc):theccsare helically arranged around a cylindrical former in one or several layers. See Figure 10. The concept provides the twisting of the strands, it is easy in fabrication (assembling method) and is flexible in terms of current capacity(number of tapes used)[34 36]. Until now this assembly has been done by hand. A disadvantage is that the engineering current density is significantly lower than in Roebel cables. Cables with selfffield critical currents of 2800 A and 7561 A at 77 K were demonstrated and first tests on smaller cables at 4.2 K and 20 T were performed [37].DuetothespecialarrangementofthetapesinCORCcablesselfFfieldeffectsdo not play a significant role and the measured critical currents of the cables are comparable to the sum of critical currents of the single tapes from which they are composed[35,36]. AnotherconceptmotivatedbyfusionmagnetresearchwaspresentedbyMIT[38]: theideaistosolder3stacksofccsintogroovedcopperrods,withtwist.thiscable designisknownastwistedstackedtapecable(tstc)andisshowninfigure10. Sofarthisconcepthassufferedfromthermalstrainsinthecomposite.Inaddition, the assembling procedure of thick stacks in long lengths has not been performed yet. In the frame of further activities to upgrade the Large Hadron Collider (LHC) at CERN, different cable concepts for MgB2 and HTS CCs are currently under investigation[39].inparticular,fortheccversiontwoconceptswereproposed:a 14

15 pairedfcc stack approach and a layered cylindrical arrangement similar to the CORC. Figure& 10.& Pictures& of& two& cable& designs& alternative& to& the& Roebel:& Top:& Cable& on& Round& Core& (CORC),& source:&[40].;&b)&&twisted&stacked&tape&cable&(tstc),&source:&[41].&the&thin&wire&around&the&corc&sample& is&for&mechanical&support&during&the&twisting&process.& 3. Physical(properties(of(Roebel(cables( InthissectionthephysicalpropertiesoftheRoebelcablearediscussedbyreporting the results of DC characterization at various temperatures, of current density distributions (calculated by numerical models and obtained by scan Hall probe scanning)andofmechanicalcharacterization DC(Transport(currents(at(77(K( Transport currents in Roebel cables are strongly influenced by the selfffield generated by the currents. A first field pattern for the cable cross section was calculated via a BiotFSavartFapproach and showed a complex field distribution reachingafewhundredmtattheouteredgesofthecable[18].thisquitesimple approachcouldexplaintheobservedsignificantcriticalcurrentreductioncausedby the selfffield. Each position of thestrands in the cable crossfsection experiences a different field, both in terms of magnitude and direction. A finitefelement method (FEM)modellingoftheselfFfieldpatternallowedamoredetailedanalysis,including thecurrentanisotropyoftheccandtheevaluationoftheindividualcriticalcurrents ofthestrands. ThehighesttransportcurrentinaRoebelcablemeasuredsofaris2.6kAat77Kin selfffield,acablewith15x3ffoldstackedstrandsandatranspositionlengthof188 15

16 mm, made from 12 mm wide SuperPower CC.Thatparticularcableshowed some degree of current percolation between the strands, resulting in unusual currentf voltage characteristics[16,18],probablytobeascribedtothefactthatthecopper contact was soldered on a relatively short length (abouthalfofthetransposition length). Usually, soldering the contact over one transposition length avoids the problemofthosepercolationcurrentsandthecurrentfvoltagecharacteristicsofthe differentstrandslookverysimilartoeachother,asshownintheexampleoffigure 11. Figure& 11.& Current5voltage& characteristics& for& the& Roebel& cable& used& in& [42,43],& measured& on& the& 10& different&composing&strands.&the&critical&current&corresponding&to&the&1&μv/cm&criterion&(450&μv&for&a& distance&between&the&voltage&taps&of&4.5&m)&is&about&1&ka.&the&value&of&936&a&used&in&the&references&and& in&the&table&of&section&3.6&refers&to&a&lower&critical&voltage.& Dependingonthewidthofthecable(10,12mmor4mm)wecandefinetwoclasses of current capacity. At 77 K the high current class can provide 1F2 ka transport current in selfffield, whereas the smaller cables can provide currents in the range ka (no strand stacking). MultiFstacking of the strands can increase the current capacity up to a factor of 2F3 with the restrictions in fabrication and applicationmentionedinsection2. 16

17 3.2. DC(Transport(currents(below(77(K( Roebelcablesareconsiderednotonly for applications at 77 K, but also for much lower temperatures. Cryocooler technology has made big progress during the last few years and offers the possibility of operating devices (motors, generators, transformers and magnets) at much lower temperatures than liquid nitrogen. Closed cooling cycles have already been tested with liquid hydrogen (20 K) and liquid neon (28 K). For busfbars in accelerator applications helium gas cooling is considered with T=10F15 K, whereasfor future fusion reactor scenarios (DEMO) HTS magnets operating at 50 K or below are being considered. CERN recently performedthefirstsuccessfulcurrentcapacitytestinthefrescatestfacilityat4.2 Kinbackgroundfieldsuptocloseto10T[44].Theresultwasaremarkableincrease ofthecurrentswithloweredtemperatureasshowninfigure12. Figure&12.&Field&dependence&of&the&critical&current&for&different&cable&samples&at&4.2&K.&Cable&A&is&from& GCS,&cables&B&and&C&from&KIT.&Source:&[44].& Conductors from KIT and General Cable Superconductors Ltd. (GCS) were successfullytested;theoccurringlorentzforceswerekeptundercontrolbyfixing thecablesonthesupportbymeansoflateralprefcompressing.acurrentofabout 14kAwasreachedfora12mmFwideRoebelcablefromKITwith10strandsof5.5 mm width at 4.2 K and a background(parallel) field of approximately 0.5 T. The fielddependencewasmeasuredforbothorientationsofthefield,perpendicularand parallel to thecable(see Figure12).Thedatashowabehaviorverysimilartothe 17

18 Ic(B,T) dependence of a single CC tape and the increase of the transport currents from77kto4.2kismorethanafactor10.theccmaterialfromsuperpowerwas significantlydifferentforbothkindofcables:bzodopedtapewasusedbykitand nonfdoped by GCS, respectively. Although GCS used 15 strands (width 5 mm) in comparison to 10 strands (width 5.5 mm) of KIT, the achieved transport current performancewascomparable,whichindicatestheicofthestartingmaterialsusedin thekitcablewassignificantlyhigheronaverage. Due to the smaller cable cross section, the engineering current density of the KIT cable was approximately 50% higher,abigadvantageformagnetapplications. Inanotheractivitypursued at KIT, the split coil magnet facility FBI was equipped withaheatingjacketsothatthesample stemperaturecanbeincreasedbeyond4.2 K[45].Thetechnologicalproblemoftheheatchamberinliquidheliumhasnotbeen completelysolvedyet,andtheachieveddatasufferfromthefactthatthesample s temperature is not precisely known [20]. The measured current values however indicate that scaling up the currents to other field and temperature conditions works quite similarly to single coated conductors. The measured results were compatiblewiththedataobtainedatcernwithintheerrormargin Current(distributions(and(selfGfield(pattern( Coatedconductorsshowstrongdependenceofthecriticalcurrentonthemagnetic field, and specifically a strongly anisotropic dependence on the orientation of the fieldwithrespecttothetape.thisbehaviourandalsothetemperaturedependence of the critical current are strongly correlated with the kind and orientation of artificialpinningcentres(apc)appliedbydopingthesuperconductor.themagnetic field distribution and associated local critical current density reduction inside the RoebelcablecrossFsectioncanbenottrivial.Afirstattempttogetaninsightintothe behaviourat77kwasperformedwithasimplemodelbasedonthebiotfsavartlaw [18,46]. Later, a more sophisticated analysis was carried out by means of a dedicated FEM model [47], which included the anisotropic dependence of the critical current density Jc on the local magnetic flux density see Figure& 13: with 18

19 thosecalculationsitwaspossibletoestimatethecriticalcurrentofthestrandsas theymovealongthecablelength. Figure 13. FEMFcalculated self field pattern in the cross section of a Roebel cable. Each tape represents the differentpositionsassumedbyatapealongonetranspositionlength.redrawnfrom[47]. Scanning Hall probe investigations were performed to reveal the magnetic field pattern alongthelength of Roebel cable samples, which reflects the geometrical arrangementofthecoatedconductorstrandsinthecablestructure[32].thewidth of the space between the strands can be observed in the field map. An example is giveninfigure14.undertheactionofamovingmagnet,highermagneticfieldsare foundinthemiddleofthetape,althoughtheirrelativesizedecreasesastheapplied field increases. Scan measurements before and after interfstrand coupling did not showsignificantdifferencesinthefieldmap. 19

20 Figure&14.&Exemplary&magnetic&field&map&obtained&by&Hall&probe&scanning&technique.&The&field&profiles& along& different& lines& in& the& x5& and& y5& direction& are& also& plotted.& The& applied& field& is& 230& mt.& Note& the& different&scales&adopted&for&the&width&and&the&length&of&the&cable&in&a),&which&make&the&aspect&ratio&of& the&cable&different&from&the&real&one.&reprinted&from&[32].& The Hall probe scanning technique was also used to investigate the magnetic field and,throughthesolutionofaninverseproblem,thecurrentdensitydistributionin individual strands used to assemble Roebel cables [48]. Field and current distributions in the straight part agree with the theory of thin films. A different behaviour for currents penetrating from the edges and currents penetrating from thetopandbottomsurfaceswasfound.thisresultsinanonfparallelcurrentflowin thecrossoverpartofasingleroebelstrand.thistechniqueallowsinvestigatingthe localpropertiesoftheconductorwithhighresolutionandisthereforeaveryuseful tooltofindproblems,especiallyassociatedwiththeuniformityoftheconductor,in the manufacturing process of Roebel cables. Two examples of current patterns in thepresenceofdefectsareshowninfigure15. 20

21 Figure&15.&Two&examples&of&current&flow&(reconstructed&from&Hall&probe&scan&measurements)&close&to& local&defects:&(a)&a&defect&at&the&inner&left&corner&leads&to&an&enhancement&of&the&current&density&close&to& the&opposite&edge&(yellow& &compare&with&the&right&corner,&which&does&not&present&such&defect);&(b)&due& to&a&reduction&of&the&cross&section,&the&current&density&is&increased&in&the&left&section.&reprinted&from& [48].& 3.4. Mechanical(properties(of(Roebel(cables( Mechanical induced effects from applied strain have been the subject of finitef element method investigations [21,25], which identified the inner radius of the crossoversectionasthecriticalpointwiththepeakvaluesofmechanicalstresses.it hasalsobeenfoundthatasharpouteredgeofthecrossoversection,asinthekit cables,reducesthepeakstrain[20]. ThefielddependencesofcriticalcurrentsofaKITandaGCScableweremeasuredat 4.2KinbothmagneticfielddirectionsbyFleiteretal.[44].Inordertowithstandthe Lorentzforcesthatarouseduringthemeasurements,thecableswerefixedbetween two stainless steel plates. Both cables withstood transverse stresses of 45 MPa. Since the cables are not flat, peak stress areas could be identified by means of Fujifilm papers. It was found that the effective section that experiences transverse stressisquitelimitedandcanbeestimatedtobeonlyabout36%and24%forthe 21

22 GCS and KIT cables, respectively. This means that a nominal loading up to an averagestressof40mpacorrespondstoalocalstressofatleast111mpa,forthe GCScable,and167MPa,fortheKITcables.Bydisassemblingthecablesandtesting thestrands,itwasconfirmedthatnodegradationofthesuperconductoroccurred. Inanotherstudy[49],Ugliettietal.investigatedtheeffectoftransversecompressive loadsonthecriticalcurrentofcoatedconductortapeof4mmwidth,ofapunched coated conductor strand 2 mm wide and of coated conductor Roebel cables (consistingof10punchedstrands).whilethetapescouldwithstandacompressive stress larger than 100 MPa without significant degradation of the critical current (less than 2%), the degradation of the critical current of some of the individual strands in the Roebel cables exceeded 30% at a transverse compressive stress as low as 10 MPa. Visual inspection of the extracted strands revealed some local damageofthestrandsurfacecorrespondingtothemeanderstructureofthestrand lying above or under the damaged strand. Subsequent measurements of the local criticalcurrentconfirmedthereductionofcriticalcurrentatthepositionsshowinga damagedsurface. Bumby et al. [50] performed a similar study (supported also by numerical simulations)ontensilestressesof12mmcoatedconductortape,5mmwideroebel strandsanda15/5htsroebelcable.theyfoundthatirreversibledegradationofic occurredat700,146and113mpa,respectively. The apparent conflict of those results indicates that there are still many open questions on the mechanical properties of Roebel cable, which need further investigation. ResinimpregnationcanhelpimprovetheresistanceofRoebelcablestomechanical stresses. However, the huge difference of the thermal expansion coefficients of YBCOandresins,ontopofthepeculiarlayeredstructureofcoatedconductorsand of the meander shape of the strands in a Roebel cable, makes the impregnation of Roebel cables a quite difficult task, compared for example to the impregnation of conventionalltscables.firstattemptstoimpregnatearoebelcablewitharaldite andsilicapowdermixturearepresentedin[51],althoughthedifferenceofthetest conditions used for the impregnated and nonfimpregnated cables do not allow 22

23 having a conclusive word on the efficacy of the impregnation technique presented there. In view of the application of Roebel cables in highffield magnets with strong mechanicalforces(hundredsofmpa),m.birdhasrecentlyproposedtheideaofa cablefinfconduitconfiguration,usingahastelloyjackettoprovidehighstrengthand stiffnesswhilealsoprovidingsimilarthermalcontractionastheybcotape[52] Cables(with(very(high(currents( VeryfewpossibleapplicationsofHTScables,asmagnetsinfusiondevices,bigwater powerorgasturbinegeneratorsrequireanoperationcurrentcapacityofthecable between20and30ka.infusionmagnetstheprojectedoperationtemperaturefor HTS cables is between 4.2 K and 50 K with approximately 13 T peak field at the conductor. Within a single Roebel cable such performance is hard to achieve, but with further improved CC performance this is not impossible in the future. This performance can be reached by using multifstacks of strands and a long transposition length, in the order of 0.5F1 m. KIT proposed a Rutherford cable designwithroebelstrandsaspotentialsolution[53].roebelcablesserveasstrands wound around a central former, which can be moderately flat or round and can providethechannelforthecoolant.thisstructureprovidesatranspositionofthe strands (Roebel cables), which are transposed aswell.efforts to realize a model cableof0.5mlengthpointedoutthebottlenecksofthisdesign[54].thebendingof theroebelstrandaroundtheedgeisacriticalissue:intheexperimentscarriedout in[54],threeroebelcableswerewoundontoa10mmthickstainlesssteelformer withawindingangleof20degrees.ofthethreecables,onewassuccessfullywound withacurrentdegradationaslowas12%;intheothertwosamples,thecurrentwas drasticallyreducedbecauseofthesolderflowinginbetweenthestrandsduringthe soldering of the current contacts and by the subsequent bending of the stiffened area.stillopenquestionsarethebehaviourofthebentsectionuponcoolingcycles, the need of avoiding delamination from stresses and how the cable assembling worksoverlonglengths.anadvantageistheflexibilityofthedesign,adisadvantage 23

24 the complex composite and the necessary thickness of the former(15f20 mm). In the future this concept has to compete with the potential of an upgraded single Roebel cable, already showing a selfffield critical current 14 ka at 4.2 K in a standard configuration[44]. Several parameters can multiply the current capacity, forexample:extendedtransposition,widertapes,improvedccperformance(being already shown in short samples by several producers) and finally the multifstack strands Examples(of(significant(cables( The following table summarizes the properties of six significant Roebel cable samples manufactured by KIT and GCS in recent years. These cables are reputed significant because of the high reached critical current (KITF2, GCSF2) and length (KITF3, GCSF3). Two cables manufactured with narrow 2 mmfwide strands(kitf1, GCSF1) are also listed. In the table the design critical current refers to the value obtained by simply summing the critical currents of the individual composing strands. KITF1 KITF2 KITF3 GCSF1 GCSF2 GCSF3 Numberof 10 3x15* strands OriginalCC s Ic.(A) Strandwidth 1.72F 5 5.4F (mm) 1.82 Strands Ic.(A) 54.3F 71** 149.5*** 140*** 123±1** 105.5, 125, Transposition length(mm) Cable slength (m) Cable scrossf section(mm 2 ) Cable sdesign Ic.(A) Cable s measuredic

25 (A) Ic.reduction fromselfffield (%) Engineering current density (A/mm 2 ) Reference [54] [18] [43,55] [25] [25] [56] Allcriticalcurrentsareat77KinselfFfield. *15stacksof3strandseach **measured ***estimated 4. AC(losses( RoebelcablesrepresentanattractivesolutionforhighFcurrentconductorswithlow AC loss. Not only can they carry large currents due to the numerous coated conductor strands assembled in the cable structure, but they can assure that the current is evenly distributed between the strands thanks to their transposition, whichmakeseachstrandexperiencethesameelectromagneticenvironment.thisis amuchmoreefficientsolutionwithrespecttoe.g.simplystackingtapestogether:in astackofparallelconductors,thecurrentwouldtendtoflowinthetapeslocatedon the top and the bottom, rapidly saturating them and causing a very high power dissipation [57]. A similar reasoning can be applied to the magnetization losses (causedbyanexternalvaryingmagneticfield):coatedconductorssufferfromvery highmagnetizationlossesinthepresenceofperpendicularmagneticfield;stacking coatedconductorsmaysolvetheproblemforlowappliedfields(belowpenetration) [58],althoughmostofthedissipationoccursonthetop/bottomregionofthestack [59].Thankstotheirperiodicallyrepeatingandtransposedstructure,Roebelcables represent a possible solution to reduce the magnetization losses and equally distributethembetweenthestrands. Inthefollowingsubsection,wereviewthemaintechniquesandresultsconcerning the measurement of transport and magnetization AC losses in Roebel cables. We also provide an overview of the main available tools to predict the loss values, includingnumericalmodelsandempiricalmethods. 25

26 4.1. Experimental(techniques(for(measuring(AC(losses(( The techniques to measure transport and magnetization loss are very different to eachother. The methods to measure the transport AC loss in Roebel cables essentially follow thesameprinciplesusedforsingletapes[60].transportaclossesaremeasuredby recording the voltage component in phase with the transport current, usually by meansofalockfinamplifier[61].duetotherelativelycomplexgeometryofroebel cables,however,thequestionofhowandwheretofixthevoltagetapsarises.the mostacceptedsolutionseemstobetosoldervoltagetapsonthetopofaparticular strandoveranintegermultipleofthetranspositionlength[22,62](figure16).this latteractionisnecessaryinordertoaveragethelosssignaloverallthepositions experienced by the strand inside the cable. Jiang et al. showed in [62] that the transportlossofaroebelcablewithnstrandscanbeestimatedbytakingthemean valueoftheinfphasevoltagesvk.measuredfromdifferentvoltageloopsattachedto thedifferentstrandsas: Q t = V mean I cable d f = 1 N N k=1 V k I cable d f whereicableisthetotalcurrentcarriedbythecable,disthelengthofthevoltageloop andfisthefrequency. Figure&16.VoltageloopssolderedonindividualstrandsformeasuringtransportAClosses.Reprintedfrom[62]. Placing many voltage loops can easily become very complicated; alternatively, the voltage taps can be positioned on the current leads. The drawback is that the (usuallylarge)resistivesignalofthecurrentleadsismeasuredaswellandneedsto be subtracted from the measured voltage in order to obtain the loss in the cable. Thiscanbequitetricky,especiallybecausethelosssignalcomingfromthecurrent 26

27 leadsisusuallylargerthanthesignalcomingfromthecable.agoodagreementwith the standard approach with the taps soldered on a strand has been reported in [22],althoughtheauthorsacknowledgethatitcouldbecoincidentalanddeserves further investigation. Another situation where the placement of voltage taps on a strand could be difficult is in the case of coils, especially if they are tightly wound [42,63]. Measurement of magnetization AC losses is typically performed by placing a short piece of Roebel cable (of length at least equal to the transposition length) in a uniform magnetic field usually generated by coils. Losses are then determined either by measuring the magnetization of the sample by means of pickfup coils [64,65]orbymeansofthecalibrationFfreemethod[66].Measuringashortsample of cable, however, presents the problem that the magnetic flux can enter from the ends of the cable; for this reason, experimental results evaluating the uncoupling betweenstrands(orfilaments)shouldbecarefullyevaluatedinthisperspective Modelling(of(AC(loss( EstimatingtheAClossesinaRoebelcableisnotaveryeasytask,mainlybecauseof the meanderflike shape of the strands and their braid arrangement in the cable structure. ThesimplestapproachtomodelaRoebelcable(bothinthecaseofusinganalytical expressionsorbuildinganumericalmodel)istoconsideronlythetransversal(2fd) crossfsection of it. This simplified approach is based on the fact that the transposition length is much longer than the strands width, and the currents crossing the cable s whole width are expected to have negligible effects see schematicrepresentationinfigure&17. 27

28 Figure 17. Qualitative representation of the current paths in a Roebel strand in a multiplefstrand cable submittedtoanappliedmagneticfield(top)oratransportcurrent(bottom).thelongitudinalcurrentdensity changesalongthestrandlengthbymeansofacurrentdensitycomponentinthewidthdirection.ingeneral,the component of the current density in the tape width is much smaller than the longitudinal one because the transpositionlengthismuchlargerthanthestrandwidth.reprintedfrom[67].& With this geometrical simplification, analytical expressions can be used for having an approximate estimate of the loss. In particular, for applied fields much larger thanthecableselfffield,onecanusebean sslabmodel[68]payingattentiontouse thepropervaluefortheslabwidth w used in the model, i.e. the strand or cable widthfortheuncoupledandcoupledcases,respectively. This model also assumes constant critical current density Jc and the sharp E(J) relation of the critical state model[69].theaclosspercycleandcablelengthinthiscaseisq = µ 0 dw 2 c J c,coupled H m andq = 2µ 0 dw 2 s J c,uncoupled H m forthecoupledanduncoupledcases,respectively,where wcandwsarethecableandstrandwidth,respectively,disthetotalcablethickness, Jc,coupledistheengineeringJcofthewholecableandJc,uncoupledistheengineeringJcof onecolumnofstrandsinthecrossfsection(seefigure& 13).Thisequationsuggests thattheroebelcabletranspositionreducestheaclossbyafactoraround2,since the strand width is around half of that of the whole cable and the horizontal gap between strands in Figure& 13 is small. However, the equation above is not applicableformagneticffielddependentcriticalcurrentdensities,unlessthecableis submittedtoadcmagneticfieldmuchlargerthantheamplitudeoftheacmagnetic field. 28

29 The Norris strip and ellipse formulas [70] provide a rough estimation for the transportloss,assumingaconstantjc. Q E = µ I 2 0 c π " ( 1 i)ln 1 i # $ Q S = µ 2 0I c " #( 1 i)ln 1 i π ( ) + ( 2 i) i 2 ( ) + 1+ i ( )ln 1+ i % & ' (ellipse) (1) ( ) i 2 $ % (strip) (2) wherei=ia/icisthenormalizedamplitudeoftheappliedcurrentia. Theanalyticalmodelsdescribedaboveprovidehoweveraveryroughdescriptionof thephysicsandgeometryofthecable.morerealisticdescriptionsofroebelcables canbeobtainedbymeansofnumericalmodels.mostmodelsstilldescribethecable as two stacks of rectangular tapes, but they have the possibility of including the variouspartscomposingacoatedconductor(e.g.substrate,stabilizer)and more importantly ofcontrollingthecurrentdistributionbetweenthestrands.typically, two extreme situations can be considered: one can leave the current free to distribute between the strands(asiftheywere electrically in parallel) or force an evencurrentdistributionbetweenthem.thissecondconditioncorrespondstowhat is expected to happen in reality thanks to the transposition of the strands and results in lower losses [22]. When only an external AC magnetic field is applied, thesetwosituationscorrespondtocompletecouplingoruncouplingofthestrands. Which of these two situations is most beneficial from the point of view of losses dependsonthemagnitudeoftheappliedfield[22],thegeometryofthecable(e.g. cable thickness, gap), and the direction of the applied field. For all cases, at high appliedfieldstheuncoupledcasepresentsthelowestloss (see Figure& 18). The behaviour at low applied fields depends on its orientation. For parallel applied fields,theuncoupledcaseisstillfavourable[71],whileforperpendicularonesthe coupledcasepresentslowerlosses[59].forthelattersituation,thegeometryplays animportantrole.thenarrowerthehorizontalgap,thewiderthepeakintheloss factor for the uncoupled case (and the higher the loss at low applied fields) [72]. Withdecreasingthecablethickness,thiseffectbecomesmorepronounced. 29

30 loss factor Q/B 2 (J/cycle/m/T 2 ) MMEV uncoupled MMEV coupled FEM uncoupled FEM coupled FEM uncoupled n=101 FEM coupled n= applied field amplitude (mt) Figure18.Comparisonofthemagnetizationlossina14FstrandRoebelcableforthecasesoffullcouplingandfull uncoupling between the strands, calculated with the powerflaw and critical state models, solved with finite element(fem)andminimummagneticenergyvariationmethods(mmev).reprintedfrom[67].& The simulation of Roebel cables as two stacks of coated conductor was first proposed in [22], and further refined by Pardo and Grilli in [67] and [73]. Those publications confirmed the results discussed above and in particular [73] showed the importance of the parallel component of the magnetic field. More specifically, theaclossdependsontheparallelcomponentoftheappliedfieldfortworeasons. First,atlowappliedfieldsandlowangles,theAClossduetothepenetrationacross the thickness is important; second, because for YBCO the field anisotropy injc is relativelyweak.then,jcreducessignificantlywithincreasingparallelcomponentof theappliedfieldforthesameperpendicularcomponentoftheappliedfield.thisis verypromisingforsolenoids,wheretheaclossduetotheparallelcomponentofthe applied field is important. Thetransposition of the strands has only a moderate effects in reducing thetransport losses, as confirmed by simulations and experiments seefigure20andsection4.3.1,respectively. Numericalmodelshavebeenextendedtocalculatethelossesincoilgeometries,by meansofaxisfsymmetricmodels[42,71].in[43]theauthorsaddedadedicated3fd modelforestimatingthelossesinthecoppercontactsaswell.2fdsimulationshave alsobeenusedtocalculatethefieldprofilesincablemadefromtapeswithmagnetic substrate[74]. 30

31 Thefirst3FDmodelforaRoebelcablewasproposedbyNiietal.[75].Themodelis for example able to calculate the current density distribution and the local dissipation in the crossing points (see Figure& 19). That work has been recently extendedin[76],wheretheauthorscometotheconclusionthatwhilethecurrent lines on the strand of the Roebel cable and the mode of magnetic flux penetration are influenced by the threefdimensional transposed structure of the Roebel cable, giving rise to regionsof high loss concentration, the AC loss of the Roebel cable averagedalongitstranspositionlengthisalmostthesameasthoseofthestacksof coated conductors, which simulate bundled conductors with uniform current distribution.forsakeofprecision,ithastobementionedthatthemodelpresented in[75,76]considersthesuperconductorstobeinfinitelythin,andassuchitcannot take into account the magnetic flux penetration from the wide faces of the superconductor.thislimitationhasbeenrecentlyovercomebyzermenoetal.[77], whohaveproposedafully3fdmodelforaroebelcable:whilethemodelisableto solveafully3fdproblem,itsroutineusemaysufferfromtheintensecomputational effortandissuesrelatedtomeshgenerationandoptimization. Figure 19. Current density (a) and AC loss density (b) distributions in a sixfstrand Roebel cable carrying AC currentandsubjectedtoanacperpendicularmagneticfield.reprintedfrom[75] Observed(AC(loss(behaviour(( In this section we report the main experimental results on transport and magnetization loss measurements on Roebel cables. In the following, we focus on cables made from coated conductors with nonfmagnetic substrate because of the 31

32 dwindling use of magnetic substrates in applications, especially in view of recent findings which indicate the possibility of utilizing substrates with virtually nonf magnetic behaviour for manufacturing coated conductors with RABiTS technique [78].Attheendofthissection,wepresentabriefsummaryoftheAClossbehaviour of Roebel cables made of tapes with magnetic substrate and we list the relevant references Transport1loss1 Jiangetal.measuredthetransportlossofaRoebelcablecomposedoffivestrands withnonfuniform current distribution in a range of frequency from 59 to 354 Hz [62].Itwasfoundthatthelossesaremostlyhystereticandthattheaveragevoltage method described above is a valid estimation of the losses of the cable. A mostly hysteretic loss contribution was also reported in[22], where the transport loss of cables composed of individual strands and stacks of strands was measured. Numericalsimulationsbasedonanequallydistributedcurrentbetweenthestrands agreewellwithexperimentalvalues. The spacing between the strands (Wc parameter in Figure 4) influences the magneticfieldexperiencedbythesuperconductor,andthereforetheaclossofthe cable.inparticular,alargerspacingincreasesthecriticalcurrentanddecreasesthe transportlosses,sospacingthestrandsmaybeusefulforreducingthecablelossin applications where transport loss is dominant, although this reduces the cable s engineeringcurrentdensity[79]. EvaluatingtheimpactoftheRoebelgeometryontransportlosscharacteristicsisnot straightforward, because different objects can be used for comparison. For this purpose,norris sformulascanbeofhelp. OnecancomparethelossofaRoebelcablecomposedofNstrandswiththelossofN conductorsbundledtogether,asdonein[62].inthatcase,thelossofaconductorin abundleshouldbentimeshigherthanthelossofanisolatedconductor.however, experimental findings in[62] indicate a smaller loss increase. In a later work[80] theauthorscomparethetransportlossofaroebelcablecomposedofeight2mm widestrandswithastackcomposedoffour4mmwidetapesconnectedinseriesto 32

33 impose the same current in each tape: at low currents the loss is similar, but at mediumfhigh currents the Roebel cable has lower losses; in particular, atit=0.99ic the loss of the Roebel cable is about 30% lower than that of the stack. However, morethanasapositiveeffectofthetransposition,thiscanbeseenasasimpleeffect of the central gap inside Roebel cable: the strands in the Roebel cable are more looselyarrangedthaninthestack(wherethereisnogap),theselfffieldislowerand thelossesareconsequentlyloweraswell.thiskindofaclossreductionhasbeen discussedfortwotapesin[81](seefigures4and5ofthatarticle) ac loss (J//cycle/m) normalized current amplitude I a /I c MMEV transposed MMEV untransposed MMEV monoblock FEM transposed FEM untransposed FEM monoblock strip ellipse 1 Figure& 20.& Transport& AC& loss& for& transposed& and& untransposed& strands& with& a& cross5section& representative&of&that&of&a&roebel&cable&(two&stacks&of&tapes),&calculated&using&two&different&models&(fem& and& MMEV,& refer& also& to& Figure 18)& and& compared& to& the& loss& of& a& rectangular& monoblock.& Figure& reprinted&from&[67].&& Alternatively, one can compare the loss of a Roebel cable to those of conductors (with elliptical or rectangular crossfsection) with the same critical current of the Roebel cable. In[22] it was found that the measured loss falls between that of an elliptical and thin rectangular conductor. Numerical calculations for two stacks of tapeswithuniformcurrentdistributionamongthemagreewellwithexperiments. For the same Roebel cable geometry, in[67] the authors compared the calculated transport loss for the transposed and untransposed case, finding that the transpositionreducesthelossbyabout20%(figure20).thisisduetothefactthat theroebelcablesunderstudyarethinobjects,andforsuchgeometrythecurrentis 33

34 already approximately balanced between the strands even without transposition; therefore,thetranspositioncanreducethelossonlymoderately Magnetization1loss1 The first measurements of magnetization loss were reported in [82,83]: a weak frequencydependencewasobserved,whichindicatesthatthemostimportantloss contribution comes from the superconductor losses. An even weaker frequency dependencewasobservedonthesampleswithdifferentarchitecturepresentedin [22].Inthatpapernospecialresistivematerialwasusedforreducingthecoupling loss;thismeansthatthecontactresistancebetweenstrandsissufficientlyhighfor suppressing the coupling loss. In [84] Lakshmi et al. ascribe the observed slight frequencydependenceofthelosstotheintrinsicfrequencydependenceoftheloss of the superconductor, and they use finitefelement method (FEM) calculations to supportthisconclusion seealso[85],[86]. In order to increase the current carrying capability, Terzieva et al. [22] prepared cableswithstacksof3and5strands.thisleadstoabetter(partial)shieldingofthe applied magnetic field, to the shift of the field of full penetration to higher amplitudes,andtothereductionofthelossatlowappliedfields. In[87]theauthorscomparedthemagnetizationlossofa5FstrandRoebelcablewith insulatedstrandstothatofanindividualstrand,showingareductionofthelossat low and intermediate fields and a convergence of the two loss curves at higher fields, when the penetration of the cable is complete. They also show that the angulardependenceoflossobeysasimplescalinglaw,accordingtowhichonlythe perpendicularcomponentofthemagneticfieldmatters[87].ithastoberemarked, however,thatthelossresultspresentedtherespanoversixordersofmagnitude,so variations in the order of 20F30% are scarcely visible. In fact, calculations carried out by Pardo and Grilli [73] showed a more complex behaviour caused by the complexangulardependenceofjconthemagneticfield.theyfoundoutthat,while thedependenceoflossonlyontheperpendicularcomponentofthemagneticfieldis a reasonable approximation for angles higher than 15F30 degrees (perpendicular 34

35 field corresponding to 90 degrees), this is no longer the case in general, as can be seenfromtheplotofthelossfunctionq/hm 2. In [87] the authors manufactured a coupled cable (which is more stable against defects)bycouplingthestrandsbymeansofcufbridges:thecoupledcableshowed the dominance of coupling currents at low frequencies and a saturation of loss at high field, a situation where the cable behaves as a monolithic conductor with higherlossthanthatofanuncoupledcable. In[87]Lakshmietal.analysethefrequencydependenceofthemagnetizationloss for two types of Roebel cables: an uncoupled cable (where the strands are electricallyinsulatedfromeachother)anda coupledcable (wherethestrandsare not individually insulated and some degree of coupling is present). A very weak frequency dependence of the magnetization loss is reported for the uncoupled cable: losses decrease with frequency at low fields and increase with frequency at highfields,thecrossfoverbetweenthetwobehavioursoccurringapproximatelyat thepeakofthelossfunction.thisisduetotheintrinsicfrequencydependenceof the superconductor material due to the flux creep, as confirmed by analytical[88] andnumerical[86,89]calculations.thesamedependenceisalsodescribedin[90], wherethetwofrequencyregimesandtheircrossfoverismorevisible,andwherean additional loss contribution is reported. Overall, for the uncoupled cable, the frequencydependenceisintherangeof10%inonedecadeoffrequency,andhence negligible for practical applications. A much stronger dependence is observed for thecoupledcable,especiallyatlowfields,andascribedtothecouplingbetweenthe strands; at higher fields the coupling contribution is less important and the loss curvesfordifferentfrequenciesconverge Roebel cables with striated strands have been assembled. The strand striation furtherreducestheloss[28,30,31,91]seefigure& 21;however,theeffectivenessof this method for reducing the loss in practical application has still to be proven, becauseintheexperimentalsetfup:thefilamentsareelectricallyisolatedfromeach other at the ends, and hence there are no coupling currents, whereas in real situations the filaments will be coupled at the ends. The concept of additional transposition by means of the more complex structure of a Rutherford cable with 35

36 Roebelcablesusedasstrandswasproposedin[53]andtestedwithappliedRoebel strandsrecently[54].however,striatedstrandswerenotinvestigatedinthatwork. Figure 21. Reduction of magnetization loss due to Roebel cabling (S0_N10) and successive filamentarization (S5_N10)withrespecttothelossintheoriginalcoatedconductor(S0_N1).Theanglesrepresenttheorientation ofthemagneticfieldwithrespecttotheflatfaceofthecable.reprintedfrom[30] Combination1of1transport1and1magnetization1loss1 TheonlyreportonAClossesforthecaseofcombinedtransportandmagnetization is a recent paper from Jiang et al.[92]: the author measured the AC loss resulting from the combination of transport current and magnetic field with varying orientation with respect to a tape made of six 2Fmm wide strands. The AC loss characteristics are quite complicated, due to the interaction of transport and magnetizationlosses,andthedifferentpossibleorientationoftheexternalfields.in brief, the results can be summarized as follows. When the field is almost perpendicular to the flat face of the cable, the losses scale with the perpendicular componentofthefieldandincreasewiththetransportcurrent.asthefieldbecomes more parallel, the relative weight of the magnetization losses decreases, and the lossesaremostlyduetothetransportcurrent.inthatpaper,theauthorsprovidea useful maximum entropy model that fits the losses in the presence of transport currentandperpendicularmagneticfield,andlaterquicklyevaluatethem Cables1with1magnetic1substrate1 For the convenience of the reader, we list here the main results of AC loss measurements on Roebel cables assembled from tapes with magnetic substrates: 36