Description

The currentinvention solves the problem ofthe winding ofHigh Temperature Superconductors(HTS)in theform ofatape,in magnetsoftheCanted CosineTheta (CCT)type.

The state-of-the-artforthe winding ofCCT magnets today does not allow the windingofHTStapes.Thepresentinventionmodifiesthewaythewindin gsaredefined and allowstheuseofHTS tapes.Itisbased on a modification ofthedefinition ofthe CCT windingshapeintheplaneperpendiculartothelengthofthemagnet,fr om acircle toa "RaceTrack”patternmadeupofstraightandcurvedsegments.

PriorArt

CCT electromagnets,alsoknownas "double-helix"magnets,arebasedonadesign wherea groove iscutin a mechanicalsupportstructure,the "magnetformer",which precisely determinesthe position ofthe cable-conductorand the currentflow,which determinethe characteristicsofthe magnet. The magnetic field iscreated inside the magnetformer,which ishollow. The equations defining the position ofthe groove (and,therefore,oftheconductor)are given below. Thefirstmention ofCCT magnet designcanbefound inthe70s.CCT magnetsstartedbecoming popularamong magnet designersduringthecurrentdecades(2010-2020),dueto theadventofautomated lathe techniques (CNC machines) and 3D printers,as well as due to their simplicity, excellentmagneticquality,low-costandspeedofconstruction.

PriorArtandinitialDescription

The current invention introduces a new winding array that allows High TemperatureSuperconductor(HTS)Tapestobeused inaCanted CosineTheta(CCT) magnetformer.Furthermore,a new design ofthe CCT magnetformerin away that allowsforsuch a specific winding becomespossible.Withoutit,itisimpracticalto buildaCCT magnetwithHTSconductors.

HTS materials offer high efficiency compared to traditional low temperature superconductormaterialsand arenow increasingly used. However,theusualform of HTS superconductorsisHTS Tapesand notthetraditionalconductorsofcylindrical cross-section(cables).Thesetapesareusually4-12mm wide,50-100micronsthickand canhavealengthofuptomanykilometers.

Tapesdifferfrom thetraditionalconductorsofcylindricalcross-sectionbythefact thattheyareflexibleinthedirectionparalleltotheirwidth,butver yrigidandfragilein thedirectionparalleltotheirthickness. In orderto achieve highermagnetic fieldsand given the factthatHTS tapesare very thin,a stack oftapescan be used.The invention refersto stacksofHTS tapes, includingthestackofone(singlestrip).

Themagneticfield ofamagnet,in aplaneperpendicularto itslong dimension,is characterized by amixtureofskew and normalmultipolecomponents.Multipolesare dipoles, quadruples, hexapoles, and so on.Most magnets have a main multipole componentwith allothersbeing a lotweaker(ofthe orderofonethousandth ofthe strengthofthemainmultipole,orless),whichrepresentmagneticdef ects.

CCT magnetshave agroove in ahollow-shaped formerin the shape ofa hollow cylinder,thecentreofwhichatthelowestpointisgivenbytheequatio n

WhereR istheradiusofthecoiland nAandnBaretheskew andnormalmultipole orders.The order number 1 represents a dipole magnetic field, 2 quadrupole, 3 sextupole,and so on.The anglesa _nA anda _nB arethe minimum anglesofthe groove withrespecttotheverticalplane(x,y)perdesired multipole,(calledtheskew angles). They are inversely proportionalto the strength ofthatcomponent.An angle of 90 degreeswould ensure no relevantmultipole component,whereastheminimum angle, (thatgivesthe maximum multipole field),is limited by practicalconsiderations,(the groove cannotrun onto itself),to about25 degrees.0 isthewinding angle and runs from 0 to 2π _nt wheren _t isthenumberofturns,m istheconductorpitch (thedistance betweensuccessivewindings).

In thelimitwhere conductorsizeisvery smallcompared toR (i.e.thegrovehas zero width and depth and the conductoris simply a line),the resulting field ofan infinitely long magnet away from the edges is a perfect reflection of the mix of multipolesofequation [1]withnomultipoleerrors.

The mostcommon magnetsare dipoles,(allanglesa arerr/2exceptforn _B = 1), quadrupoles(allanglesa α are exceptforn _B = 2)and sextupoles(allanglesa are n/2 exceptforn _B = 3).A CCT magnet,in addition to the main multipole,can be designedtocontainalsosmallamountsofothermultipoles.

Since thisarrangementproducesalso a field along the longitudinal(z)direction, which isunwanted in mostcases,a second CCT layerwith a slightly increased R, depending onthethicknessoftheformer,oppositewinding direction and askew angle ofopposite sign isincorporated.The startofthe outerlayerand the end oftheinner layerarelocatedontopofoneanother.Thissecond layerhasthesamecurrentflowing intheoppositedirectionthanthefirstlayer.Theresultisthatthelo ngitudinalfieldsof the two layerscancel,and the intended multipole contributionshave the same sign. SometimestheCCT designisreferredtoas “doublehelix”duetothetwolayers.Inany case,thetwolayersareidenticalinconceptsowewillonlyrefertoone layerhere.The exactsamemethodcanbeincorporatedintheotherlayer.

According to equation [1],inthe(x,y)plane,thegroovedescribesacircleand in three dimensions itis located on the surface ofa cylinder.Inz0 space,the groove describesasinecurveforaspecificmultipole.

Recently,someCCT magnetsfollow acurvedpath,wherethecentreofthemagnet (which in equation [1]liesat(x,y)= (0,0))describesacircleinthe(x,z)planewith radiusRcurved,whereRcurved »

CCT magnetwindingforUTS tapes:thepresentinvention

One preferredembodimentoftheinventioncomprizesthefollowingpartsa nd features:

1.HighTemperatureSuperconductor(HTS)tape(1)

2.Magnetformer(2)

3.Tapetrace(3)

4.StraightSegments(4)

5.Curvedsegments(5)

6.Enclosedradiusofcurvature(6)

7.Windingangle0(7)

ThefollowingFiguresareattachedtothecurrentDescription:

Figure 1A:a stack ofHTS tapes (1)(dark colour,left) following the groove in a Magnetformer(2)ofaquadrupoleCCT magnet(right).Halfaturn isshown,and the stackoftapesisshownseparatelyfrom themagnetformer.

Figure IB:transparentsketch ofa stack oftapes(halfturn)andthetapetrace(3)(the blackline)followinga “RaceTrack"CCT path.

Figure2A:thegeometricsiteoftheHTStapetrace(3)inthe(x,y)pl aneformsa "Race Track"shape(solid line),comparedtotheconventionaltypeofCCT designwhich isa circle(dashed line). This "RaceTrack” consistsofanumberofstraightsegments(4) andcurved segments(5).Thisexampleisforaquadrupolemagnetandthedimension s are exaggerated for illustration purposes. The "Race Track" for a dipole has two straightsegments,foraquadrupolefour,forasextupolesix,etc.

Figure 2B.alternative design (one ofmany)wherethe centresofthe arcsare atthe samepoint,at(0,0). Figure 3A and 3B:the currentinvention uses a "Race Track" profile instead ofa circularshapeasatapetrace(3)inthe(x,y)plane,projectioninthe( x,y)planein3A, isometricview in3B.HalfaturnoftheHTStapestackisvisible.(A typicalmagnethas manyturns).

Figure 3C:sameas3A,transparentsketch.Thetapetrace(3)can be seen.Ithasthe shapeofa "RaceTrack"withcurvedsegmentsconnectedbystraightsegments.

Figure4:Thestraightnessrequirementofthestraightsegments(4 )ofthe "RaceTrack" inthisinvention,withaspecificexampleforeasierunderstanding. The “RaceTrack” CCT designofaquadrupoleisshowninthexy planeprojection(solid line).Thisisthe projectionofthetapetrace(3)inthe(x,y)plane.Thestraightsegmen tshavelengthsof 20mm,andtheconvex segmentsareformedby circleswith adiameterof20mm. The totalwidth ofthe "Track"is40mm,and the circumference isindicated by the dotted line. This leads to an average diameter of 45.46mm and the average radius Rmean=22.73mm.A curveappearsforthestraight-linesegmentatthetop (dashed line), wherethecurvaturediameteris90.93mm.

Detailed Description

Formula[1]intheprevioussectionworksperfectlyforaflexiblec onductorsuchas a thin wire ofcylindricalcross-section.However,theHTS conductors,asmentioned above,comewiththeform factorofatapeofafew millimetreswide,(4to 12mm),and athicknessofafew tensofmicrometers(50-lOOpm).Duetothelargedifferencesize in thetwo directions,atapeexhibitsgreatdirectionality asitcan bend with very little effortaroundthedirection parallelto itswidth,butitcannotbend,(exhibitsvery high stiffness),around thedirection parallelto itsthickness.The same appliesto stacksof tapes.Forcingatapetobendintheplaneofhighstiffnessbeyondtheel asticlimitmight resultindamagingthetapeandpossiblytoalossofsuperconductingpe rformance.

TheCCT formuladescribed in [1]appliesto alineandnotasolid object.A round conductorwhose diameteris much smallerthan the radiusR ofthe magnetcan be approximated verywellby a line.A tape,however,in general,cannot.Thetapetrace (3)isdefinedasthecentreofoneedge,orofthemiddleofthestackofta pes.Thisedge is taken to be the one closestto the centre ofthe magnet,(defined along the line (x,y)= (0,0)((3)inFigureIB),however,theexactsameargumentsapply iftheedge istheonefurthestaway from thecentreofthe magnet,orthemiddleofthetape.The tapetrace(3)istheonethatfollowsequation[1],

When a tape,orstack oftapes,triesto follow a curved path on the surface ofa cylinder,itbuckles,andthetapeisnolongerperpendiculartothesur faceofthecylinder atalltimes.Successivebends,asin thecaseoftheCCT,requirethe stack oftapesto change from a positive bending radius (concave) to a negative radius (convex),as shown in Figure 1A. Between two successive turnsthe tape musttwist.However, twistingwhilefollowingacurvedsurfaceisgenerallynotpossibleas itrequiresbending alongthenon-bendingaxisofthetape. Thepresentinventionusesa "RaceTrack"shapeforthegeometricsiteofthetape trace (3) in the (x,y)plane, (which in the case of equation [1] is a circle for a conventionalCCT magnet),asshown inFigure2.StraightSegments(4)arejoinedby curved segments (5),forexample,circle arcs. The centresofthese circlesmay be differentfrom thecentreofthemagnet,asinFigure2A,orcoincideasinFigure2B,or haveany othershape. Thestraightsegmentsenablethetapetotwistbetweenconcave and convexbends,which isnotpossibleifthereisonly onecircularsegmentasinthe conventionalCCT magnet.

Thenumberofstraightsegments(4)isequaltotwicetheorderserie softhebasic multipoleofthemagnet:(two straightsegmentsforadipole,fourforaquadrupole,six fora sextupole,etc.).Straightsegmentsgivethe opportunity to the stack oftapesto twist,ready forthenextbend.Thesestraightsegments(4)arelocated aroundthetape twisting points of the design around the areas where sin(n _B 6)= 0 for normal multipolesand cos(n _A 0)= 0 forskew multipoles,whereG isthewinding angleand n _A andn _BA istheordernumberoftheskew andnormalmultipoles(n _A ,n _B = 1,2,3,...).

Figure 3 showsthe design ofthe "RaceTrack"ofthisinvention in the case ofa quadrupole;the projection on the (x,y) plane, as well as the isometric view are displayed;a smallpartofthe stack ofFITS tapes,(halfa turn),isdisplayed,butthe principledescribedhereapplieseverywherealongtheconductor.

A circleisfittedto theplanethatenclosesexactly theprojection,and atthesame timetouchesthecurvedsegments(5),beforeandafterthestraightpar t anditsradiusis noted. Thisisthe enclosed radius ofcurvature (6)ofthe projection ofthe straight segments(4)intheplaneperpendiculartothelengthofthemagnet.