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1. Introduction to Superconductors where to find more information

1. Introduction to Superconductors where to find more information properties of superconductors, critical field, critical temperature & critical current density screening currents and the critical state model 2. Magnetization, AC Losses & Filamentary Wires

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1. Introduction to Superconductors where to find more information

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  1. 1. Introduction to Superconductors where to find more information properties of superconductors, critical field, critical temperature & critical current density screening currents and the critical state model 2. Magnetization, AC Losses & Filamentary Wires irreversible magnetization and hysteresis loops field errors and flux jumping ac losses in terms of magnetization fine filaments & composite wires, coupling & twisting 3. Cables and Materials Manufacture why accelerators need cables coupling currents in cables: anisotropy interstrand resistance manufacture of wire and cable 4. AC Losses in Magnets - and Training summation of ac loss and refrigeration load temperature rise and temperature margin measurement of ac loss training - energy releases in the magnet conductor design for stability 5. Quenching and some other Accelerators the quench process decay times and temperature rise propagation of the resistive zone quench protection schemes case study: LHC protection pictures of superconducting accelerators Pulsed Superconducting Magnets (for accelerators)Plan of the LecturesMartin N Wilson (Rutherford Lab  Oxford Instruments  consultant) 'Pulsed Superconducting Magnets' CERN Academic Training May 2006

  2. Pulsed Superconducting Magnets- why bother? Superconductivity Abolishes Ohm’s Law ! • no Ohm's law • no power consumption (except refrigeration) • lower power bills • ampere turns are cheap, so don’t need iron (except shielding) • higher magnetic fields •  higher energies and /or smaller rings • reduced capital cost • high current density •  compact windings •  high gradients •  higher luminosity • but • superconductors suffer losses when the field changes • rise in temperature (and there's not much margin) •  increase in refrigeration load 'Pulsed Superconducting Magnets' CERN Academic Training May 2006

  3. Superconducting Magnets Superconducting Accelerator Magnets: KH Mess, P Schmuser, S Wolf., pub World Scientific, (1996) ISBN 981-02-2790-6 High Field Superconducting Magnets: FM Asner, pub Oxford University Press (1999) ISBN 0 19 851764 5 Case Studies in Superconducting Magnets: Y Iwasa, pub Plenum Press, New York (1994), ISBN 0-306-44881-5. Superconducting Magnets: MN Wilson, pub Oxford University Press (1983) ISBN 0-019-854805-2 Proc Applied Superconductivity Conference: pub as IEEE Trans Applied Superconductivity, Mar 93 to 99, and as IEEE Trans Magnetics Mar 75 to 91 Handbook of Applied Superconductivity ed B Seeber, pub UK Institute Physics 1998 Cryogenics Helium Cryogenics Van Sciver SW, pub Plenum 86 ISBN 0-0306-42335-9 Cryogenic Engineering, Hands BA, pub Academic Press 86 ISBN 0-012-322991-X Cryogenics: published monthly by Butterworths Cryogenie: Ses Applications en Supraconductivite, pub IIR 177 Boulevard Malesherbes F5017 Paris France Materials Mechanical Materials at Low Temperature: Ed RP Reed & AF Clark, pub Am. Soc. Metals 1983. ISBN 0-87170-146-4 Handbook on Materials for Superconducting Machinery pub Batelle Columbus Laboratories 1977. Nonmetallic materials and composites at low temperatures: Ed AF Clark, RP Reed, G Hartwig pub Plenum Nonmetallic materials and composites at low temperatures 2, Ed G Hartwig, D Evans, pub Plenum 1982 Austenitic Steels at low temperatures Editors R.P.Reed and T.Horiuchi, pub Plenum1983 Superconducting Materials Superconductor Science and Technology, published monthly by Institute of Physics (UK). Superconductivity of metals and Cuprates, JR Waldram, Institute of Physics Publishing (1996) ISBN 0 85274 337 8 High Temperature Superconductors: Processing and Science, A Bourdillon and NX Tan Bourdillon, Academic Press, ISBN 0 12 117680 0 Some useful references 'Pulsed Superconducting Magnets' CERN Academic Training May 2006

  4. Cryodata Software Products GASPAK properties of pure fluids from the triple point to high temperatures. HEPAK properties of helium including superfluid above 0.8 K, up to 1500 K. STEAMPAK properties of water from the triple point to 2000 K and 200 MPa. METALPAK, CPPACK, EXPAK reference properties of metals and other solids, 1 - 300 K. CRYOCOMP properties and thermal design calculations for solid materials, 1 - 300 K. SUPERMAGNET four unique engineering design codes for superconducting magnet systems. KRYOM numerical modelling calculations on radiation-shielded cryogenic enclosures. Cryogenic properties (1-300 K) of many solids, including thermal conductivity, specific heat, and thermal expansion, have been empirically fitted and the equation parameters are available free on the web at www.cryogenics.nist.gov. Plots and automated data-look-up using the NIST equations are available on the web for a fee from www.cpia.jhu.edu. Other fee web sites that use their own fitting equations for a number of cryogenic material properties include: www.cryodata.com (cryogenic properties of about 100 materials), and www.jahm.com (temperature dependent properties of about 1000 materials, many at cryogenic temperatures). Commercially supplied room-temperature data are available free online for about 10 to 20 properties of about 24,000 materials at www.matweb.com. thanks to Jack Ekin of NIST for this information Materials data web sites 'Pulsed Superconducting Magnets' CERN Academic Training May 2006

  5. Niobium titanium NbTi is the standard ‘work horse’ of the superconducting magnet business it is a ductile alloy picture shows the critical surface, which is the boundary between superconductivity and normal resistivity in 3 dimensional space superconductivity prevails everywhere below the surface, resistance everywhere above it we define an upper critical fieldBc2(at zero temperature and current)and critical temperature qc (at zero field and current) which are characteristic of the alloy composition critical current density Jc(B,q) depends on processing The critical surface of niobium titanium Temperature (K) Field (Tesla) Jc Current density (kA.mm-2) qc Bc2 'Pulsed Superconducting Magnets' CERN Academic Training May 2006

  6. because magnets usually work in boiling liquid helium, the critical surface is often represented by a curve of current versus field at 4.2K niobium tin Nb3Sn has a much higher performance in terms of critical current field and temperature than NbTi but it is brittle intermetallic compound with poor mechanical properties note that both the field and current density of both superconductors are way above the capability of conventional electromagnets The critical line at 4.2K 104 Nb3Sn Critical current density A.mm-2 103 NbTi 102 Conventional iron yoke electromagnets 10 Magnetic field (Tesla) 'Pulsed Superconducting Magnets' CERN Academic Training May 2006

  7. for reasons that will be described later, superconducting materials are always used in combination with a good normal conductor such as copper to ensure intimate mixing between the two, the superconductor is made in the form of fine filaments embedded in a matrix of copper typical dimensions are: wire diameter = 0.3 - 1.0mm filament diameter = 10 - 60mm for electromagnetic reasons, the composite wires are twisted so that the filaments look like a rope (see Lecture 3 on filamentary conductors and cables) Filamentary composite wires 'Pulsed Superconducting Magnets' CERN Academic Training May 2006

  8. Critical properties: temperature and field 1 Critical Temperatureqc It costs energy to keep the field out. Critical field happens when the condensation energy of the superconducting state is just equal to the energy penalty of keeping the field out. where kB is Boltzmann's constant and D(0) is the energy gap (binding energy of Cooper pairs) of at q = 0 where G is the Gibbs Free Energy of the normal/superconducting state. BCS theory says Critical FieldBc: Type 1 superconductors show the Meissner effect. Field is expelled when sample becomes superconducting where NFis the density of states at the Fermi surface of metal in normal state - calculate it from: where g is Sommerfeld coefficient of electronic specific heat 'Pulsed Superconducting Magnets' CERN Academic Training May 2006

  9. Critical properties: temperature and field 2 combining the previous equations: 'thermodynamic critical field'Bc so like the critical temperature, Bc is defined by the 'chemistry' typically for NbTi g~ 103 J m-3 K-1 so if q = 10 K Bc = 0.24T Conclusion: Type 1 superconductors are useless for magnets! Note however: Meissner effect is not total, the magnetic field actually penetrates a small distance l the London Penetration Depth. Another characteristic distance is the coherence length z - the minimum distance over which the electronic state can change from superconducting to normal 'Pulsed Superconducting Magnets' CERN Academic Training May 2006

  10. Critical properties: type 2 superconductors I f = h/2e Theory of Ginsburg, Landau, Abrikosov and Gorkov GLAG defines the ratio k = l / x If k > 1/2 the magnetic field can penetrate in the form of discrete fluxoids - Type 2 a single fluxoid encloses flux where h = Planck's constant, e = electronic charge where rn is the normal state resistivity - best superconductors are best resistors! in the ‘dirty limit' upper critical field thus the upper critical field for NbTi: g ~ 900 J m -3 K-2rn ~ 65 x10 -8 W m qc = 9. K hence Bc2 = 18.5 T 'Pulsed Superconducting Magnets' CERN Academic Training May 2006

  11. Critical properties: current density Fluxoids consist of resistive cores with super-currents circulating round them. precipitates of a Ti in Nb Ti spacing between the fluxoids a uniform distribution of fluxoids gives no net current, so Jc= 0, but a gradientproduces a net current density • gradients must be produced by inhomogeneities in the material, eg dislocations or precipitates • process is known as flux pinning • flux pinning is an irreversible lossy process fluxoid lattice at 5T on the same scale 'Pulsed Superconducting Magnets' CERN Academic Training May 2006

  12. Critical properties: a summary • Critical temperature: choose the right material to have a large energy gap or 'depairing energy' • Critical field: choose a Type 2 superconductor with a high critical temperature and a high normal state resistivity • Critical current density: mess up the microstructure by cold working and precipitation heat treatments • - this is the only one where we have any control Similar effects in high temperature superconducting materials : fluxoid lattice in BSCCO 'Pulsed Superconducting Magnets' CERN Academic Training May 2006

  13. Upper critical fields of metallic superconductors MgB2 Note: of all the metallic superconductors, only NbTi is ductile. All the rest are brittle intermetallic compounds 'Pulsed Superconducting Magnets' CERN Academic Training May 2006

  14. High temperature superconductors • many superconductors with critical temperature above 90K - BSCCO and YBCO • operate in liquid nitrogen? YBa2Cu3O7 'YBCO' 'Pulsed Superconducting Magnets' CERN Academic Training May 2006

  15. High temperature superconductors YBCO structure Conduction layers consist of two CuO2 layers separated by yttrium atoms. The charge layer consists of copper, barium and oxygen atoms Note: this structure makes the properties highly anisotropic 'Pulsed Superconducting Magnets' CERN Academic Training May 2006

  16. Irreversibility line - a big disappointment r r q q metallic Oxide HTS Unlike the metallic superconductors, HTS do not have a sharply defined critical current. At higher temperatures and fields, there is an 'flux flow' region, where the material is resistive - although still superconducting The boundary between flux pinning and flux flow is called the irreversibility line 'Pulsed Superconducting Magnets' CERN Academic Training May 2006

  17. Engineering current density In designing a magnet, what really matters is the overall 'engineering' current density Jeng fill factor in the wire insulation where mat = matrix : superconductor ratio typically: for NbTi mat = 1.5 to 3.0 ie lmetal = 0.4 to 0.25 for Nb3Sn mat ~ 3.0 ie lmetal ~ 0.25 for B2212 mat = 3.0 to 4.0 ie lmetal = 0.25 to 0.2 lwinding takes account of space occupied by insulation, cooling channels, mechanical reinforcement etc and is typically 0.7 to 0.8 NbTi Cu So typically Jeng is only 15% to 30% of Jsupercon 'Pulsed Superconducting Magnets' CERN Academic Training May 2006

  18. the field produced by an infinitely long solenoid is Importance of (engineering) current density: (1) solenoids • in solenoids of finite length the central field is • where f is a factor less than 1, typically ~ 0.8 • so the thickness (volume, cost) of a solenoid to produce a given field is inversely proportional to the engineering current density Je 'Pulsed Superconducting Magnets' CERN Academic Training May 2006

  19. Importance of (engineering) current density: (2) dipoles I I B I field produced by a perfect dipole is Je = 37.5 Amm-2 LHC dipole Je = 375 Amm-2 120mm 660mm 9.5x105 Amp turns =1.9x106 A.m per m 9.5x106 Amp turns =1.9x107 A.m per m 'Pulsed Superconducting Magnets' CERN Academic Training May 2006

  20. Some engineering current densities 'Pulsed Superconducting Magnets' CERN Academic Training May 2006

  21. Measurement of critical current • this sample holder is placed in the bore of a superconducting solenoid, usually in liquid helium boiling at 4.2K • at each field level the current is slowly increased and voltage across the test section is measured 'Pulsed Superconducting Magnets' CERN Academic Training May 2006

  22. Resistive transition 1 Overall Current density 10 8A.m-2 When measured sensitively, the boundary between superconducting and resistive states is not sharp, but slightly blurred. If we measure Jc with voltage taps across the sample, we see that the voltage rises gradually. To define Jc, we must therefore define a measurement sensitivity in terms of electric field or effective resistivity. Commonly used definitions arer = 10-14 Wm or E = 1mV.m-1 Critical current defined at this level is about what you would expect the conductor in a resin impregnated solenoid to achieve. At higher resistivity, self heating starts to raise the internal temperature and reduce the critical current 'Pulsed Superconducting Magnets' CERN Academic Training May 2006

  23. Resistive transition 2 It has been found empirically that the resistive transition may be represented by a power law a) perfect filament b) mid sausaging c) bad sausaging where n is called the resistive transition index. The effect is partly intrinsic and partly geometrical. 'Sausaging of the filaments, forces current to cross the copper matrix as critical current is approached. resistive transition can be the main source of decay in persistent magnets 'n' is often taken as a measure of quality - look for n > 50 HTS conductors so far have low n ~ 5 - 10 'Pulsed Superconducting Magnets' CERN Academic Training May 2006

  24. Screening currents and the critical state model J J B x • when a superconductor is subjected to a changing magnetic field, screening currents are induced to flow • screening currents are in addition to the transport current, which comes from the power supply • they are like eddy currents but, because there is no resistance, they don't decay • usual model is a superconducting slab in a changing magnetic field By • assume it's infinitely long in the zand y directions - simplifies to a 1 dim problem • dB/dt induces an electric field E which causes screening currents to flow at critical current density Jc • known as the critical state model orBean model • in the 1 dim infinite slab geometry, Maxwell's equation says • so uniform Jc means a constant field gradient inside the superconductor • everywhere in the superconductor the current density is either Jcor zero 'Pulsed Superconducting Magnets' CERN Academic Training May 2006

  25. The flux penetration process B fully penetrated plot field profile across the slab field increasing from zero field decreasing through zero 'Pulsed Superconducting Magnets' CERN Academic Training May 2006

  26. The flux penetration process B fully penetrated plot field profile across the slab field increasing from zero field decreasing through zero 'Pulsed Superconducting Magnets' CERN Academic Training May 2006

  27. Lecture 1: concluding remarks • superconducting magnets burn no power (dc); they produce high fields and high gradients • - but in changing fields they suffer ac losses • three types of superconductor • - type 1: unsuitable for high field • - type 2: good for high field - but must work hard to get current density • - HTS: good for high field & temperature - but current density still a problem in field • all superconducting accelerators to date use type 2, usually NbTi (45 years after its discovery) • performance of type 2 superconductors is described by the critical surface in B q J space, • - properties inB andqspace are reversible properties determined by the chemistry • - properties in J space are irreversible and lossy, determined by flux pinning inhomogeneities • engineering current density is what counts for magnet performance • changing magnet fields induce persistent currents in superconductors • persistent currents may be described by the Bean critical state model, • - we shall see they are a major cause of ac losses 'Pulsed Superconducting Magnets' CERN Academic Training May 2006

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