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Superconducting Magnets for Accelerators Lecture

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Superconducting Magnets for Accelerators Lecture Superconductivity for accelerators - why bother? Abolish Ohm's Law • no power consumption (although do need refrigeration power) • high current density compact windings, high gradients • ampere turns are cheap, so don’t need iron (although often use it for shielding) Consequences • lower power bills • higher magnetic fields mean reduced bend radius smaller rings reduced capital cost new technical possibilities (eg muon collider) • higher quadrupole gradients higher luminosity Martin Wilson Lecture 1 slide 1 JUAS February 2013 Plan of the Lectures 1 Introduction to Superconductors 4 Quenching and Cryogenics • critical field, temperature & current • the quench process • superconductors for magnets • resistance growth, current decay, temperature rise • manufacture of superconducting wires • quench protection schemes • high temperature superconductors HTS • cryogenic fluids, refrigeration, cryostat design 2 Magnetization, Cables & AC losses 5 Practical Matters • superconductors in changing fields • filamentary superconductors and magnetization • LHC quench protection • coupling between filaments magnetization • current leads • why cables, coupling in cables • accelerator magnet manufacture • AC losses in changing fields • some superconducting accelerators 3 Magnets, ‘Training’ & Fine Filaments Tutorial 1: Fine Filaments • coil shapes for solenoids, dipoles & quadrupoles • how filament size affects magnetization • engineering current density & load lines Tutorial 2: Quenching • degradation & training minimum quench energy • current decay and temperature rise • critical state model & fine filaments get a feel for the numbers, bring a calculator Martin Wilson Lecture 1 slide 2 JUAS February 2013 The critical surface of niobium titanium • NbTi is the standard commercial ‘work horse’ of the superconducting magnet business Current • critical surface is the density boundary between J Amm-2 superconductivity and normal resistivity in J, B, q space 10000 • superconductivity prevails everywhere below the 8000 surface, resistance everywhere above it 6000 8000-10000 • upper critical 6000field-8000 Bc2 (at zero temperature and current) 4000 4000-6000 2000-4000 • critical temperature qc (at zero 2000 field and current)0-2000 Bc qc 2 • Bc2 and qc are characteristic 0 0.0 of the alloy composition 0 2.0 2 4.0 4 • critical current density Jc 6 6.0 8 8.0 depends on processing Temperature Field B (T) 10 10.0 12 qT (K) 14 • keep it cold! Martin Wilson Lecture 1 slide 3 JUAS February 2013 The critical line at 4.2K 10000 niobium titanium • magnets usually work in niobium tin boiling liquid helium, so the critical surface is often represented by a curve of 1000 current versus field at 4.2K • niobium tin Nb Sn has a ) 3 -2 much higher performance than NbTi (A mm c 100 • but Nb3Sn is a brittle intermetallic compound with poor mechanical properties 10 conventional iron • both the field and current electro-magnets density of both Critical current Critical J density superconductors are way above the capability of conventional electromagnets 1 0 10 20 30 Field (T) Martin Wilson Lecture 1 slide 4 JUAS February 2013 Two kinds of superconductor: type 1 • the materials first discovered by Kammerlingh Onnes in 1911 - soft metals like lead, tin mercury • sphere of metal at room temperature • apply magnetic field • reduce the temperature - resistance decreases • reduce the temperature some more - resistance decreases some more • at the critical temperature qc the field is pushed out - the Meissner effect - superconductivity! • increase the field - field is kept out • increase the field some more - superconductivity is extinguished and the field jumps in • thermodynamic critical field Bc is trade off between reducing energy via condensation to superconductivity and increasing energy by pushing out field ~ 0.1T useless for magnets! Martin Wilson Lecture 1 slide 5 JUAS February 2013 Two kinds of superconductor: type 2 • apply magnetic field • reduce the temperature - resistance decreases • at the critical temperature qc the field is pushed out • increase the field - field jumps back in without quenching superconductivity • it does so in the form of quantized fluxoids • lower critical field Bc1 • supercurrents encircle the resistive core of the fluxoid thereby screening field from the bulk material • higher field closer vortex spacing • superconductivity is extinguished at the (much higher) upper critical field Bc2 Martin Wilson Lecture 1 slide 6 JUAS February 2013 Type 1 and type 2 superconductors • Meissner effect is not total • magnetic field penetrates a small distance l • the London Penetration Depth. l • another characteristic distance is the coherence length z - the minimum distance over which the electronic state can change from superconducting to normal • theory of Ginsburg, Landau, Abrikosov and Gorkov GLAG defines the ratio k = l / x x if k < 1/2 x if k > 1/2 material is material is Type 1 Type 2 l l Martin Wilson Lecture 1 slide 7 JUAS February 2013 Critical fields of type 2 superconductors • recap thermodynamic critical field Bc • lower critical field Bc1 = Bc / k • above Bc1 magnetic field penetrates as discrete quantized fluxoids a fluxoid encloses flux human hair o h = = 2 1015Wb in earth's o 2e magnetic I field ~ 50o h = Planck's constant e = electronic charge upper 1 in the where n is the critical field Bc2 = 2k Bc 6 2 ‘dirty limit' k 2.410 n normal state resistivity - best superconductors 3 thus the upper critical field Bc2 = 3.110 nqc are best resistors! -3 -2 -8 for NbTi: ~ 900 J m K n ~ 65 x10 W m qc = 9.3 K hence Bc2 ~ 18.5 T Sommerfeld coefficient of electronic specific heat Ce = q Martin Wilson Lecture 1 slide 8 JUAS February 2013 Critical current density: type 2 superconductors • fluxoids consist of resistive cores with supercurrents circulating round them. precipitates of a Ti in Nb Ti spacing between the fluxoids is:- 1 2 2 d = o = 22nm at 5T 3 B • each fluxoid carries one unit of flux, so density of fluxoids = average field uniform density uniform field zero J (because Curl B = moJ ) • to get a current density we must produce a gradient in the density of fluxoids • fluxoids like to distribute uniformly fluxoid lattice at 5T on the same scale • so we must impose a gradient by inhomogeneities in the material, eg dislocations or precipitates Martin Wilson Lecture 1 slide 9 JUAS February 2013 Critical properties 12 10 Bc2 8 qc • Critical temperature qc: choose the right material to have a large 6 energy gap or 'depairing energy' property of the material 4 • Upper Critical field Bc2: choose a critical temperature / field at 4K 2 Type 2 superconductor with a high critical temperature and a high normal 0 20 40 60 80 2 state resistivity - weight % Ti 4000 property of the material Amm c 3000 at 5T • Critical current density Jc: mess 2000 up the microstructure by cold working and precipitation heat treatments hard work by the producer 1000 at 8T critical critical J current density 0 5 10 15 20 25 volume % of aTi precipitate Martin Wilson Lecture 1 slide 10 JUAS February 2013 Critical field & temperature of metallic superconductors Note: of all the metallic superconductors, only NbTi is ductile. All the rest are brittle intermetallic compounds Martin Wilson Lecture 1 slide 11 JUAS February 2013 Critical field & temperature of metallic superconductors 30 To date, all superconducting accelerators have 20 used NbTi. T . T c2 Nb3Sn NbTi Of the intermetallics, only Nb3Sn has critical field B field critical 10 found significant use in magnets 0 0 5 10 15 20 temperature K Martin Wilson Lecture 1 slide 12 JUAS February 2013 Practical wires for magnets • some 40 years after its development, NbTi is still the most popular magnet conductor, with Nb3Sn being used for special high field magnets and HTS for some developmental prototypes. • 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 = 5 - 50mm • for electromagnetic reasons, the composite wires are twisted so that the filaments look like a rope (see Lecture 3) Martin Wilson Lecture 1 slide 13 JUAS February 2013 NbTi manufacture • vacuum melting of NbTi billets • hot extrusion of the copper NbTi composite • sequence of cold drawing and intermediate heat treatments to precipitate aTi phases as flux pinning centres • for very fine filaments, must avoid the formation of brittle CuTi intermetallic compounds during heat treatment - usually done by enclosing the NbTi in a thin Nb shell • twisting to avoid coupling - see lecture 2 Martin Wilson Lecture 1 slide 14 JUAS February 2013 Filamentary Nb3Sn wire via the bronze route Nb3Sn is a brittle material At final size the wire is The remaining copper still and cannot be drawn down. heated (~700C for some contains ~ 3wt% tin and has a high Instead must draw down days) tin diffuses through resistivity ~ 610-8Wm. pure niobium in a matrix of the Cu and reacts with So include 'islands' of pure copper bronze (copper tin) the Nb to form Nb3Sn surrounded by a diffusion barrier • BUT maximum ductile bronze is ~13wt% tin, • reaction slows at ~ 3wt% • so low engineering Jc Martin Wilson Lecture 1 slide 15 JUAS February 2013 Nb3Sn with higher engineering Jc Cu sheathed Powder in tube PIT Nb rods NbSn2 powder tin in extrude Cu jacket centre Nb tube stack & extrude draw to heat treat stack & draw to wire wire extrude heat treat to form 'macro both make filaments' high Jeng of Nb3Sn (RRP is the highest) but large filaments Martin Wilson Lecture 1 slide 16 JUAS February 2013 Measurement of critical current • spiral sample with current leads and voltage taps I • place in the bore of a I superconducting solenoid • put in cryostat B • immerse in liquid helium • at each field level slowly increase the current is and measure the voltage across the test section Martin Wilson Lecture 1 slide 17 JUAS February 2013 Resistive transition 1 When measured sensitively, the boundary between superconducting and resistive states is not sharp, but slightly blurred.
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