Lecture 2: Magnets & training, plus fine filaments Magnets the ATLAS magnet at CERN • magnetic fields above 2 Tesla • coil shapes for solenoids, dipoles and quadrupoles • engineering current density • load lines Degradation & Training • causes of training - release of energy within the magnet • reducing training - stability and minimum quench energy MQE • need copper and fine filaments for low MQE Flux Jumping • need for fine filaments JUAS February 2013 Martin Wilson Lecture 2 slide1
Fields and ways to create them: conventional • conventional electromagnets have an iron yoke - reduces magnetic reluctance - reduces ampere turns required - reduces power consumption • iron guides and shapes the field I I B 1.6 T B H -100A/m 100A/m Iron electromagnet – for accelerators, motors, transformers, generators etc -1.6T for higher fields we cannot rely on iron BUT iron saturates at ~ 2T field must be created and shaped by the winding JUAS February 2013 Martin Wilson Lecture 2 slide2
Solenoids B t • no iron - field shape depends only on the winding a • azimuthal current flow, eg wire wound on bobbin, axial field 2b • the field produced by an infinitely long solenoid is where N = number of turns/unit I μ μ B NI J t o o e length, I = current , J e = engineering current density 1 1 • so high J e thin compact economical winding .9 .8 • in solenoids of finite length the central field is t 0.1 .7 t 1 b .6 μ β,τ f( bt B J t f b o e .5 t 3 b .4 where b b/a t = t/a .3 .2 • field uniformity and the ratio of peak field to .1 central field get worse in short fat solenoids 0 0 0.1 1 10 1 10 0.1 b b JUAS February 2013 Martin Wilson Lecture 2 slide3
Superconducting solenoids Superconducting solenoid for Delphi solenoid for HEP experiments at CERN research 1.2T 5.5m dia 6.8m long 110MJ JUAS February 2013 Martin Wilson Lecture 2 slide4
Accelerators need transverse fields simplest winding • some iron - but field shape is set 'saddle' coils make uses racetrack mainly by the winding better field coils • used when the long dimension is shapes transverse to the field, eg accelerator magnets • known as dipole magnets (because the iron version has 2 poles) special winding cross sections for good uniformity I I I B LHC has 'up' & 'down' dipoles side by side JUAS February 2013 Martin Wilson Lecture 2 slide5
Dipole field from overlapping cylinders J B Ampere's law for the field inside a cylinder carrying uniform current density B J r o 2 2 π μ μ π B.ds rB I r J B o o 2 • two cylinders with opposite currents • push them together J J J J J J J • currents cancel where they overlap aperture B B B B B B B B B B r 1 B r 2 B • fields in the aperture: B B B q 1 q 2 μ μ t t J Jt t o cos θ cos θ o B r r y 1 1 2 2 2 2 μ J o sin θ sin θ B r r 0 x 1 1 2 2 2 • same trick with ellipses • thus the overlapping μ J t o e B cylinders give a y 2 perfect dipole field • circular aperture JUAS February 2013 Martin Wilson Lecture 2 slide6
Windings of distributed current density Analyse thin current sheets flowing on the surface of a cylinder using complex algebra. Let the linear current density (Amps per m of circumference) be g n = g o cos(n q (Am -1 ) For n = 1 we find a pure dipole field inside the cylinder, n = 2 gives a quadrupole etc. Now superpose many cylinders of increasing radius to get a thick walled cylinder carrying an (area) current density (Am -2 ) J n = J o cos(n q q q q θ n=1 ( ) cos J J J ( ) J cos 2 n=2 0 0 1 2 J J b b B 0 0 B J ( b a ) / 2 J t / 2 o 0 o ln B x ln B y x y o 0 o 0 y x 2 2 a a B gradient t a b JUAS February 2013 Martin Wilson Lecture 2 slide7
Summary of simplified dipole windings 60 ° sector Cos ( q Overlapping circles Overlapping ellipses μ o B J t μ 2 μ B J t o o o 2 o o o B J t B J t Sin(60 ) o o π 2 where c / (b + c) t = winding thickness J o = best estimate engineering current density o 2 c = height of ellipse of forces Sin(60 ) 0.55 π b = width best estimate of peak field LHC B dipole winding recap solenoid μ β,τ B J t f o e I JUAS February 2013 Martin Wilson Lecture 2 slide8
Importance of (engineering) current density in dipoles I field produced J e = 37.5 Amm -2 by a perfect I I dipole is B t B J o e 2 LHC dipole J e = 375 Amm -2 120mm 660mm 9.5x10 5 Amp turns 9.5x10 6 Amp turns =1.9x10 6 A.m per m =1.9x10 7 A . m per m JUAS February 2013 Martin Wilson Lecture 2 slide9
Dipole Magnets I I I B JUAS February 2013 Martin Wilson Lecture 2 slide10
Electromagnetic forces in dipoles • forces in a dipole are horizontally outwards and vertically towards the median plane • unlike a solenoid, the bursting F y F x forces cannot be supported by tension in the winding a • the outward force must be F x supported by an external structure F y • both forces cause compressive stress and shear in the conductor and insulation • apart from the ends, there is no tension in the conductor • simple analysis for thin windings 2 2 B 4 a B 4 a i i F F x y 2 3 2 3 o o JUAS February 2013 Martin Wilson Lecture 2 slide11
Estimating the iron shield thickness no iron with iron some flux returns close to the coil almost all flux returns through the iron flux through ½ coil aperture return flux through iron (one side) f c B o a f i B sat t a = coil radius t = iron thickness f i ~ f c t ~ a B o / B sat so JUAS February 2013 Martin Wilson Lecture 2 slide12
Quadrupole windings I I B y = kx B x = ky JUAS February 2013 Martin Wilson Lecture 2 slide13
Critical surface and 600 7 resistive magnet load lines superconducting -2 . Engineering current density Amm * 500 magnet 400 aperture field 300 Engineering Current 200 density Amm -2 magnet 100 peak field 0 2 2 * 4 0 2 4 6 8 4 Field T 6 6 8 8 • load line relates magnet field to current 10 12 • peak field > aperture (useful) field 14 16 • we expect the magnet to go resistive 'quench' where the peak field load line crosses the critical current line * JUAS February 2013 Martin Wilson Lecture 2 slide14
Degraded performance and ‘training’ of magnets • early disappointment for magnet makers when they ramped up the magnet current for the first time • instead of going up to the critical line, it ‘quenched’ quench (went resistive) at less than the expected current field • at the next try it did better • known as training 250 critical time 200 quench current • after a quench , the stored energy of the 150 magnet is dissipated in the magnet, raising 100 its temperature way above critical • you must wait for it to cool down and then 50 try again 0 • well made magnets are better than 0 5 10 15 20 poorly made quench number JUAS February 2013 Martin Wilson Lecture 2 slide15
‘Training’ of magnets • it's better than the 10.0 old days, but training is still with us 9.5 field acheived . • it seems to be affected by the construction 9.0 technique of the magnet stainless steel collars stainless steel collars • it can be wiped 8.5 aluminium collars operating field out if the magnet is warmed to room temperature 8.0 • 'de-training is the 0 5 10 15 20 25 30 35 40 45 quench number most worrysome feature Training of LHC short prototype dipoles (from A. Siemko) JUAS February 2013 Martin Wilson Lecture 2 slide16
Causes of training: 10 2 (1) low specific heat 10 2 • the specific heat of all substances Specific Heat Joules / kg / K falls with temperature 10 • at 4.2K, it is ~2,000 times less than at room temperature • a given release of energy within 1 the winding thus produce a temperature rise 2,000 times greater than at room temperature 300K • the smallest energy release can 10 -1 therefore produce catastrophic effects 4.2K 10 -2 10 100 1000 1 temperature K JUAS February 2013 Martin Wilson Lecture 2 slide17
Causes of training: (2) J c decreases with temperature 800 2T 4T 6T 700 8T -2 . engineering current density Amm J c 600 500 400 2 2 2 2 4 4 4 4 * 6 6 6 6 300 * 8 8 8 8 10 10 200 10 10 12 12 14 14 16 16 100 0 3 4 5 6 7 temperature K at any field, J c of NbTi falls ~ linearly with temperature - so any temperature rise drives the conductor towards the resistive state JUAS February 2013 Martin Wilson Lecture 2 slide18
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