FILAMENTARY SUPERCONDUCTORS FOR PULSED MAGNETS

D B Thoma s an d M N Wi 1son

Rutherford High Energy LaboratoryChilton, Didcot, Berks., England

Abstract

I I I. Matrix losses

I I. Losses in filaments

The hysteresis loss in a cylindrical sampleof superconductor of unit volume may be calcul­ated from the formula: 2

(I)4dJ B

Qf = ------30

0 In [(B + B )/B ]1T 0 0

where Qf is the loss per cycle during a fieldpulse which rises to B and then falls again tozero. The diameter of the sample is d, Jo is thecritical current density at zero field and Bo isthe field in the well known Kim-Anderson formulaJc = JoBol (B + Bo)' I t wi 11 be noted tha t thedissipation is not dependent on the rate of fieldrise. To put this relationship into perspective,a practical example is quoted. Suppose unitvolume of niobium-titanium, subdivided into 5 ~

diameter filaments, is cycled from zero field to5 T and returned to zero, then the loss per cycleis given by:

provided for each superconducting filament andelectrically insulated from all other filaments,a problem which has yet to be solved in practice,some electrical coupling between filaments mustbe accepted and with it increased losses underpulsed field conditions. The inevitable comprom­ises involved in developing a satisfactory geo­metry of superconductor for pulsed field applica­tions are described in the following sectionswith particular reference to the latest prototypefilamentary conductors and cables under develop­ment.

The value of Bo has been assumed to be 1 T andthat of J o 9 x 109 Am-2 .Design considerations forpulsed magnets for superconducting synchrotrons,which have provided the main motivation for thedevelopment of pulsed superconductors, indicatethat dissipation rates of this order, or perhapsa I ittle more, are tolerable. Thus it is gener­ally accepted that subdivision of the supercon­ductor to the 5 to 10 ~ level is necessary anda greater degree of subdivision is desirable ifthis can be achieved.

The practical multifilament superconductorsproduced to date have all been manufactured byco-processing niobium-titanium in a metallic \matrix, usually copper or copper/cupro-nickel.

I. Introduct ion

The present stage in the development ofsuperconducting composites and cables intendedfor use in pulsed magnets and based on niobium­titanium is described. The principal formulaefor calculating ac losses are quoted and somenumerical examples are given.

In contrast with their loss-less conductionof dc current, the high field Type I I supercon­ductors do exhibit losses under conditions ofchanging current or changing external magneticfield. The mechanism of this loss is well under­stood as being due to the penetration of magneticfield into the bulk superconductor when thelatter is in a flux flow resistive state. l Itfollows that the rate of dissipation of heat canbe obtained by multiplying the critical currentdensity of the superconductor by the voltagegradient associated with the changing flux, andintegrating this product over the volume of thesuperconducting material. One salient pointarising from the analyses performed along theselines is the need for fine subdividion of thesuperconductor into numerous individual filamentsif acceptable losses are to arise in practicalpulsed superconducting devices. Numericalexamples given later in this paper illustrate themagnitude of the losses and indicate that forcoils with field rise times of the order of 1 secit is necessary to subdivide the superconductorinto fi laments of the order of 5 ~ diameter. Nowa 5 ~ diameter filament, adopting niobium­titanium superconductor by way of example, willcarry a current of about 30 mA at 5T. A conduc­tor rated at 3000 A for a pulsed magnet wouldthus have to be subdivided into about 105 suchfilaments. It is this type of reasoning thatsets the real problem for the designer of theconductors to be used in pulsed superconductingdevices. How can an assembly of, typically, 105

superconducting filaments be made into a prac­tical conductor bearing in mind that any directelectrical contact between individual filamentswi!! tend to make them behave cooperatively withhigher overall dissipation under pulsed condi­tions? Furthermore coil protection precautionsmust not be overlooked for following a 'quench'transition of the superconductor to its normalconducting state the current which each individ­ual filament is carrying must transfer safelyto a low resistance shunt path. This is necess­ary since the resistivity of a superconductor onreversion to its normal state is high, and indeedtoo high in most practi~al cases to avoid coilburn-out unless precautions of the type describedare taken. Unless an individual shunt path is

493

Electrical problems then arise from the fact thatthe filaments are now connected together by thenormally conducting material of the matrix andthis causes them to be coupled together in achanging magnetic field. The hysteresis of thecomposite is greater than the hysteresis of thesum of the separate filaments, losses are in­creased, and stabil ity against flux jumping isreduced. Twisting of the composite about itslongitudinal axis is the first remedy to be adop­ted to minimise coupl ing. 2 As the number of fila­ments is increased and with it the overall wirediameter it becomes increasingly difficult totwist the composite tightly enough to decouplefilaments sufficiently for pulsed operation atfield rise times of the order of 1 sec.

superconductor ratio of about 1.5:1. In practiceit proves impossible to twist such a compositewire with a twist pitch much tighter than aboutfive times the wire diameter. (Even if this werepossible the current carrying capacity of thehelical filaments in the forward direction wouldbecome seriously reduced.) If a value of t of0.3 mm (4£ = 5 x wire diameter) is substitutedinto the second term in Equation (6) togetherwith a value for Pe of 4 x la- 11 0m then thematrix loss associated with a single triangular.shaped pulse in which the field varies at rate Bfrom zero to 5 T and back is given by:

(])

(5)

Q = 4A J dB 1n [( B + B ) / B ]3n 0 0 0 0

It has been shown that the magnetisation ofa twisted filament composite exposed to achanging external field may be written: 3

A comparison of the matrix loss in the model com­posite conductor taken in this example with thelosses in the superconducting filaments, canreadily be performed by calculating the value ofBat which these two losses become equal. EquatingQM from Equation (7) with A Qf where A the fillingfactor for this conductor has the value 0.4 and~f is given by Equation (2) yields the valueB = 2.8 T sec- l at which the total losses aredouble the filament loss. That the charging rateat which losses double is inversely proportionalto the number of filaments in composites of thesame type can readily be shown since the maximumpermissible twist pitch is proportional to thediameter of the composite. Thus if a 10,000filament conductor is conyidered, losses willdouble at B = 0.28 T sec-. Since the tendencyin high current pulsed magnets now appears to betowards even higher numbers of filaments perstrand, composite conductor with resistive barr­iers of cupro-nickel between filaments are be­coming increasingly accepted to minimise matrixlosses at fast rates of field rise. Now the effec­tive resistivity of cupro-nickel matrix is about7 x 10- nm ie. some 2000 times that of purecopper matrix. Unfortunately fine filament comp­osites with cupro-nickel matrices have been shownnot to perform well in magnets and some coppermust always be included in the matrix to improvethermal conductivity and provide magnetic dampingif satisfactory operation is to be obtained.Furthermore the copper provides coil protectionas a low resistance shunt path. Composites withboth copper and cupro-nickel in the matrix, theso-cal led three component composites, are there­fore frequently employed for pulsed magnetappl ications.(6)

(4)

B£2 1M (l + 'J d - + ..... )

o 1\ c Pe

where w is the thickness of normal metal betweeneach filament and Pw is its resistivity.

The loss per cycle is given by integratingMdH over the complete cycle. Substituting forM from Equat ion (4) into Equat ion (3) andi~tegrating over a cycle consisting of a 1inearfield rise fol lowed by a linear field fall gives:

M

is the magnetisation of the individual filaments,Bthe rate of change of field, 4£ the twist pitch,A the fill ing factor (superconductor to totalvolume), Jc the critical current density and dthe filament diameter. For a simple compositewith only one metal in the matrix and a uniformarrangement of filaments, Pe is given by:

where Mo

The first term is the simple filament loss term,Qf' already given by Equation (1) but differingin this case by the factor A since the loss isnow expressed in terms of unit volume of compositerather than unit volume of superconductor. Thesecond term defines the matrix losses QM'

As an example consider a composite in which1000 5 ~ filaments are embedded in a coppermatrix, uniformly distributed to give an overallcomposite diameter of 0.25 mm with a matrix:

A three component composite with 14,701individual 5 ~ filaments is shown in Figure 1.Photographs of other less sophisticated three­component filamentary conductors are givenelsewhere. 3 The composite illustrated inFigure 1 is the most advanced that has yet beenproduced and is available at present only insample form. It is intended for use in multi­thousand ampere cables or tapes in applicationswhere field rise times of order 1 sec are required.

4lJ4

\ .--~~.

"c? ~

y

..,-'

;. .r"V- ) ... ....

'y " ...-';... ~.

"'y

,.l...."y'

.'

~'('~

"f .......

...~

..r

,r.'. '--',. ( \ .

I!

,'"1

~.'

I.. J

~L-.-\-

(a)

(b)

Fig. la.A cross-section of a 14,701 filamentniobium-titanium composite conductor.

b.An enlargement of a region of the cross-section.

1.06 mm diaj 5.3 p fjlaments;~430A at 5T and 10- 14 nm measuringsensitivity; effective resistivity (p )~ 8 x lO-tl nm. e

Each filament is surrounded by copperand then cupro-nickel. Groups of 241fi laments are assembled into a "spidercan" of cupro-nickel with cupro-nickelradial spokes separating copper regions.61 groups of 241 filaments are thenassembled into a simi lar "spider-can".

[Manufacturer:Imperial Metal Industries(Kynoch)Ltd.]

4'J5

IV. Self Field Losses

A transport current flowing in a circularcomposite wire produces self field 1ines in theform of concentric circles centred on the centreof the wire. There is always a self field fluxenclosed between the outer filaments of the wireand those near the centre. This flux tends tocouple the filaments together and thus increasethe hysteresis loss. It is not possible toreduce the coupling by twisting and, to a firstapproximation the self field behaviour of atwisted filamentary composite is the same as thatof a solid wire. The effect could be removed ifit were possible to transpose fully the filamentsso that outer and inner filaments change placesalong the length of the wire but this seems un­likely in any practical composite.

If the current in a wire is increased fromzero to critical and then reduced to zero again,the self field loss is given by:3

(8)

where a is the wire radius and ~ is a numericalfactor depending on the past history of the wire.The usual case of repetitive pulsing of currentin the same direction gives:

~= 3/2 - 2 In 2 = 0.114

Thus the 0.25mm diameter wire used in the previousexample will have a self field loss:

Q = 200 Jm-3s

which is negligible in comparison with Equation 2.If the composite radius were to be increased bya factor of ~8 however (i .e. 60,000 filaments)the self field and filament losses would be com­parable.

Self field losses are thus not important inany of the composites presently in use. Thereare also theoretical grounds for believing thatEquation 8 is pessimistic and that the losseswill in practice be reduced by spiral fieldeffects and the displacement of the electriccentres within the filaments. 3 It thereforeseems not unreasonable to contemplate much largercomposites containing ~105 filaments and workalong these lines is planned at RutherfordLaboratory.

V. Cables

It has already been pointed out that theneed for a high magnet operatIng current, combinedwith the requirement for fine filament diameters,means that a typical magnet conductor must con­tain ~105 filaments.

With presently available composites thismeans that between 10 and 1000 wires must be

connected in parallel as a cable. The wires mustbe twisted to minimize magnetisation currentsflowing between wires - either directly acrossthe cable or through the end terminations. Be­cause self field effects are expected to becometroublesome in conductors of this size, it isalso desirable that the wires are fully trans­posed.

So far, magnets have been made from twobasic types of cable: woven braids and compoundtwisted ropes. Both types are fully transposedand have been shown to carry pulsed currentswith good current sharing between wires and lowhysteresis losses. Their principal disadvantageis a rather low filling factor. In an attemptto improve this the cables have been compactedusing rollers but it has proved difficult toattain filling factors of better than ~ 60%without damaging or even breaking the compositewires. The reason for this problem appears to bethe closely interwoven structure of a transposedcable which gives rise to many cross-over pointsand kinks in the wires.

If the wires in the cable are in electricalcontact, a changing magnetic field can inducerate dependent magnetisation currents to flowacross the cable. The process is very similar tothe induction of magnetisation currents withinthe matrix of an individual composite wire andthe increase in total magnetisation is given bya formula simi lar to Equation 3. If the ratedependent magnetisation is well below saturation,the two effects may simply be added together.

A recent development at RutherfordLaboratory has been the flat tape shown inFigure 2. This cable consists essentially of ahollow tube of helically twisted wires which hasbeen rolled flat. Because the paths of the indi­vidual wires are now much less tortuous than inthe interwoven cables, it has been possible tocompact these tapes to filling factors of >85%with a ne~ligible reduction in current carryingcapacity. AI I cables of this type are approxi­mately two wire diameters thick and the widthdepends on the total number of wires. A practi­cal limit seems to be about 20 wires, giving amaximum aspect ratio of 5:1. It is thereforenecessary to make these cables from rather largecomposites containing up to 10,000 filaments ifcurrents of 5000A or so are required. The con­ductor shown in Figure 2 is a model of the cableplanned for the AC5 magnet which will contain 15strands of '.05 mm diameter, 8917 filament com­posite (7~ filament diameter).

( 11 )

Fig. 2. A flat twisted cable: copper model of theconductor planned for the AC5 magnet.The superconducting version will be madefrom 15 strands of 1.05 mm dia. threecomponent composite, each strandcontaining 8917 filaments 7~ in diameter.

where f is the geometry factor~ l,a is the aspectratio of the tape and Pa is the average resis­tivity across the tape. 5

For round or square cables the effectiveresistivity is given simply by the averageresistivity across the cable multipl ied by ageometrical factor of order unity. For flattapes the magnetisation occurs with the appliedfield at right angles to the broad face of thetape. In this case we find:

It has been found that filling the cablewith solder can reduce its susceptibility to wiremovement effects - presumably by improving mech­anical rigidity and increasing heat capacity.Unfortunately this also increases magnetisationloss by reducing the average resistivity acrossthe cable. For example, a solder-filled flattape will have an average resistivity of ~10-8 nm.An as~ect ratio of 3:1 will reduce Pec to~ 10-~ nm so that, for a 10 cm twist pitch and5~ filaments, the magnetisation (and hence theloss will dou~!e at a_rate of change of field ofonly ~ 5 x 10 T sec . A successful attemptat increasing Pec by a factor of 10 or more hasbeen reported. 6 It is also of course possible

(10)

cable twist pitch

effective resistivity across the cable

M= Mo

",he re 4L

496

in principle to reduce the twist pitch. Never­theless it seems reasonable to conclude that thelosses in soldered braids will always be toohigh for the usual synchrotron rise times of afew seconds.

If each strand in the cable is organicallyinsulated, ego with PVA enamel, the effectiveresistivity is essentially infinite, the last termin Equation 10 is zero and there will be no addi­tional losses due to the cable. Unfortunately,this approach results in the following practicalproblem. After rolling the flat tape it is desir­able to heat treat in order to anneal the copperin the matrix (to increase conductivity andimprove handling) and also to increase the currentdensity in the superconductor. Typical heattreatments are 1 hour at 350°C - 400°C and thiswill burn most organic insulations. Work is inhand on heat resistant enamels.

The approach which has been adopted so farat Rutherford Laboratory 1ies between solderfilling and total insulation. It has been foundthat the naturally occurring oxide layer on thecopper produces a contact resistance between thewires which gives ~n average resistivity acrossthe cable of ~10- nm. For a 3:1 aspect ratiowe have Pec ~ 10-5 nm so that the magnetisationloss wil I now double at 5 T sec-I (5~ filaments,10 cm twist pitch). A simple cable made frombare wires is therefore quite adequate for mostpurposes and if necessary the resistance of theoxide layer can be increased by electrolytictreatment. The layer is not destroyed by heating.The cables used for both the AC3 and Ac4 pulsedmagnets use oxide insulation.

composites allow multi-thousand ampere cables tobe produced using as few as 5 to 10 such wires.Packing factors in the resultant simple cablesand tapes of more than 80% are then possible.If conductors with ~ 105 filaments can be pro­duced successfully,solid multi-thousand ampereconductors could perhaps then be used to advan­tage in pulsed magnet construction, but therestill remain theoretical doubts about the 'self­field' stabi 1ity of such large composites. In­sufficient measurements have yet been performedon large composites to resolve this point.

VI I. Acknowledgements

The authors wish to acknowledge the helpof their colleagues, notably P F Smith,C R Walters and G Gallagher-Oaggitt, for manyhelpful discussions on the subject matter reportedin this paper. Collaboration between theRutherford Laboratory and Imperial MetalIndustries Ltd has resulted in the fabricationof a variety of filamentary superconductors in­cluding the advanced type described. Notablecontributions to the work by 0 J Sambrooke andR A Popley of IMI Research Oepartment areacknowledged.

VI I I. References

1. H London, Phys. Lett. §., 162 (1963)

2. Superconducting Appl ications Group,Brit. J. Phys. D 1, 1517 (1970)

3. M N Wilson, Proc. Appl. SuperconductivityConf.,Annapolis, 1972

VI. Conclusions

The present trend in the development ofniobium-titanium composites for pulsed magnetsis towards wires with larger numbers of 5 to 10~

filaments. Conductors with 14,000 fi laments havealready been produced in sample form and largernumbers of filaments are being attempted. Such

4Y7

4.

5.

6.

G Gallagher-Oaggitt, Rutherford LaboratoryReport RHEL/M/A25 (1972)

M N Wilson, Rutherford Laboratory ReportRHEL/M/A26 (1972)

A 0 Mcinturff, Proc. Appl. SuperconductivityConf., Annapolis, 1972