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Magnet Technology MAGNET TECHNOLOGY Franz Bødker Physics Design Danfysik A/S, Denmark NPAS, 17-8-2017 Danfysik today Staff: 85, including 4 physicists and 35 engineers Ownership: subsidiary of Danish Technological Institute Mission We provide high performance particle accelerators and related equipment for research, health care and industry globally Accelerating Technology Business -> www.danfysik.com Outline • Basic magnet concepts – Magnetic field and basic magnet types – Pole shapes and magnetic steel – Excitation current – Ramped or pulsed magnets • Magnetic field measurement • Maxlab compact girder concept • Superconducting magnets • Permanent magnet technology • Insertion devices Magnet Technology, NPAS 17-8-2017 3 Beam deflection in a magnetic field Lorentz force on a charged beam in a magnetic field q = charge [C] v = velocity [m/s] B = magnetic field induction [Tesla] Lorentz force with pointing out of the figure Right hand rule for the Lorentz force direction Magnet Technology, NPAS 17-8-2017 4 Magnetic field generation Accelerator magnets are usually made as electromagnets with the magnetic field generated by a current through a conductor but permanent magnets can also be used The right-hand rule is useful Low field accelerator magnets can be made as air core magnets but normal conducting magnets are typically iron dominated with iron cores as this gives a higher magnetic field Bgap for given Ampere-turns and good field homogeneity in is easy to achieve Iron dominated electromagnet Iron dominated permanent magnet Air core electromagnet Flux circuit NI/2 Yoke t e N n N g a m Bgap t Pole gap Coil n e n S a S m r e p Magnet Technology, NPAS 17-8-2017 5 Magnetic field Spherical field harmonics from Maxwell’s equation in polar coordinates = sin + cos Complete field description in current & iron free region Multipole coefficients: = cos sin bn: normal, an: skew − Multipole expansion in Cartesian coordinates + + = + = + + Vertical field for simplified case without skew An terms = + + + + ….. Taylor series in the y=0 −center plane − 3 = + + + + ….. Dipole Quadrupole Sextupole Octupole Magnet Technology, NPAS 17-8-2017 6 Dipole magnet Dipole magnets are used to bend or steer the beam Pole equation: y = ± r (fixed gap h = 2r) Constant field: By = Bo Classic dipole types: C-type H-type O-type or Window frame Combined function: dipole & gradient By = Bo + x·B’ Racetrack coils Saddle coils Magnet Technology, NPAS 17-8-2017 7 Quadrupole magnet Quadrupole magnets are used for beam focusing 2 Pole equation: 2xy = ± r (r is the aperture radius) Constant gradient: By = B2x, B2 = Field amplitude constant on a circle: |B| = · Classic quadrupole types: High field type Cost optimal Figure-8 Panofsky quadrupole Magnet Technology, NPAS 17-8-2017 8 Sextupole and octupole magnets Sextupole magnets for beam chromaticity correction: 2 3 2 2 Pole equation, sextupole: 3x y - y = ± Constant sextupole gradient: By = B3(x - y ) , B3 = 2 For y=0: By = x Octupole magnets for higher order corrections: 3 3 3 2 Pole equation: 4(x y - xy ) = ± Constant octupole gradient: By = B4(x - 3xy ) , B4 = Magnet Technology, NPAS 17-8-2017 9 Excitation current for a dipole We use Ampère's law , where = and Assuming B is constant (i.e. Bgap=Biron) around the loop and h this gives iron 2 The pole gap field is therefore gap = pole gap ℎ Bgap 2 ≫ 1 When the relative permeability is large we can ignore the iron reluctance Bgap ≫ 1 Magnet Technology, NPAS 17-8-2017 10 Effect of the magnetic iron yoke 3 5 Magnetic soft core material is highly non-linear: _ : 10 – 10 , typically 2000-6000 Saturation _ Hysteresis B-H slope: = = Remanence Saturation H The hysteresis changes typically the magnet field on the 0.1-1% level To get a stable B(I) the excitation current is cycled up/down 3 times: Imax t n Degaussing current cycling e r r u Imax C Imin t Time n e r r u At I=0 there is a small residual remanence field on the mT level due C to the iron remanence Br which can be suppressed by degaussing -I max Time Magnet Technology, NPAS 17-8-2017 11 ~1.8T in the pole the in ~1.8T and yoke in the if~1.5T possiblebebelowshould levels Field loss. iron as known B(I)decay non-linearin a resulting ~2T at typically saturates iron Magnet The calculated relative permeability drops to 350 in main parts of the pole ->ofironin loss3% relativetopartspolethe calculateddrops permeability The main350 Model calculation of top half of dipole magnet at 1.44 T current1.44atT dipolemagnetatfieldhalfcentertopmaximumof of calculation Model Iron saturation Iron saturation in high field magnets 1.44 1.44 T 5000 1.7 1.7 T 0.9 T 350 Magnet Technology, NPAS 17-8-2017 1.55 1.55 T 800 Deviation from linearity (%) Measured center field (T) 0.0 0.5 1.0 1.5 -3.5 -3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 Relative permeability for the steel (EBG 1200)(EBG steeltheRelativeforpermeability 0 0 Deviation dB from a linear fit toB fitdBlinear toB(I) from Deviation relativea Measured center field vs. excitationfieldcentercurrentMeasuredvs. 1.5 1.5 mT dB/Bmax 0.2% 0.2% Up/down hysteresis 500 500 Current Current (A) Current (A) Current 3% iron loss 1000 1000 12 B B (T) max Field quality improvement by pole shimming The finite pole width reduces the field quality which for a dipole is defined as = (0) (0) Low ⁄dB/B requires − pole overhang a which can be estimated as Dipole shims ln / (no shims) ≈ −0.18 − 0.45 ℎ So-called rose shims can be used to reduce the needed pole width Quadrupole shims Magnet Technology, NPAS 17-8-2017 13 Fringe field effects Dipole field integral is important = 0 Fringe field as it determines the beam deflection ∫ Iron pole ∫ Beam Effective magnetic length: 1 ∞ lefb = B(s)ds ∫ Fringe field Fringe field B(0) 0 Center field: B(0) The magnetic length is longer than the iron length due to the fringe fields: Iron length, ~ (geometry dependent) Effective magnetic length, This is very important + ℎ for short magnets The magnetic shim rotation angle can be Shim rotation angle used to optimized the beam focusing Magnetic field quality should ideally be evaluated based on field integral quality rather than just the center field quality Effective Field Effective Field Boundary Boundary Magnet Technology, NPAS 17-8-2017 14 value are favored when total lifetime cost is is minimized cost total lifetime when are favored value j increases. Low cost and power running consumption j increasing but with reduced and is Magnet size cost are possible be but risky can higher values j with 3-10of typical coils A/mm cooled Water Air cooled coils for current densities =1-2 j of current A/mm for cooled coils Air Current Current conductors Magnet Technology, NPAS 17-8-2017 2 2 1.86 1.86 T High power PT dipole example dipole Glass tape wrapped & epoxy impregnated & epoxy wrapped tape Glass , , 25 ton, ton, 25 Lacquer insulated solid Cu wire Cu solid insulated Lacquer j=11 j=11 A/mm 2 , 300 300 , kW, 170 l/min 15 AC operation Induction: The needed drive voltage over the coil terminals will increase with ramping speed as U = RI + L , where the inductance L is = / where A is the total≈ area of flux, h≫ is1 the height of the pole gap and the flux ℎ + ℎ circuit length. N is the number of coil turns. Power supply: The magnet and its power supply tend to become integrated units. High voltage protection around the current terminals is often needed Eddy currents: are generated by field ramping and can result in saturation of the yoke and ramping speed dependent field lag both during ramping and some time after end ramping. Eddy currents in, for example, a conductive vacuum pipe can degrade the field quality and result in heating of the pipe Core loss: In each current cycle there will be hysteresis losses in the core proportional to the enclosed area of the BH-curve resulting in a core heating Skin-depth: for sinusoidal currents the penetration depth into the conductor will decay with frequency f with a characteristic length = ( ), ρ is the conductor resistivity. The effective resistance therefore increases when becomes smaller than the conductor width. There is also a⁄ magnetic field skin-depth effect for the core Magnet Technology, NPAS 17-8-2017 16 Core material options Solid iron magnets: Basically for dc operation with field variation limited to frequencies up to 0.01 - 0.1 Hz due to eddy current effects. Lamination direction Laminated magnets: Cores of stacked steel laminates that are coated for electrical insulation allow field ramping while limiting eddy current losses. Hysteresis core losses are further minimized by using silicon steel laminates due to its enhanced resistivity. Lamination thickness is usually 0.5 - 1 mm at 10 Hz operation and 0.35 - 0.65 mm at 50 Hz. Faster ramp rates are possible Beam dump in 0.2ms with when operated in pulsed operation with time delays between pulses. 0.35mm laminate thickness Laminates are shuffled during production to get uniform magnet strength for series operation. Laminated magnets are typically costly but can in larger series productions be cost effective. Power cores: Can be used for intermediate frequency but has reduced saturation fields of 0.6 – 0.8 T. Ferrite magnets: The very high resistivity of ferrite allow MHz operation but the design is limited by the modest 0.25 – 0.5 T saturation magnetization of ferrite. The brittle ceramic ferrite (mostly MnZn or NiZn) core is mostly used in the form of blocks.
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