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Warm Magnets CAS Chavannes de Bogis, 28-Sept-2021, warm magnets, GdR Gijs de Rijk CERN CAS Chavannes de Bogis, Switzerland 28th September 2021 1
Copyright statement and speaker’s release for video publishing CAS Chavannes de Bogis, 28-Sept-2021, warm magnets, GdR The author consents to the photographic, audio and video recording of this lecture at the CERN Accelerator School. The term “lecture” includes any material incorporated therein including but not limited to text, images and references. The author hereby grants CERN a royalty-free license to use his image and name as well as the recordings mentioned above, in order to post them on the CAS website. The author hereby confirms that to his best knowledge the content of the lecture does not infringe the copyright, intellectual property or privacy rights of any third party. The author has cited and credited any third-party contribution in accordance with applicable professional standards and legislation in matters of attribution. Nevertheless the material represent entirely standard teaching material known for more than ten years. Naturally some figures will look alike those produced by other teachers. 2
Contents • Introduction: magnetic field and warm magnet principles CAS Chavannes de Bogis, 28-Sept-2021, warm magnets, GdR • Field description and magnet types • Practical magnet design & manufacturing • Permanent magnets • Examples of accelerator magnets from the early times until the present • Literature on warm Magnets 3
Magnet types, technological view We can also classify magnets based on their technology CAS Chavannes de Bogis, 28-Sept-2021, warm magnets, GdR electromagnet permanent magnet iron dominated coil dominated normal conducting superconducting (resistive) cycled / ramped static fast pulsed slow pulsed 4
Earth magnetic field In Geneva, on 06/09/2021, the (estimated) magnetic field (flux density) is |B| = 47672 nT = 0.047672 mT = 4.7672·10-5 T ≈ 0.5 Gauss. Bhorizontal = 22259 nT CAS Chavannes de Bogis, 28-Sept-2021, warm magnets, GdR 5
Maxwell equations Integral form Differential form CAS Chavannes de Bogis, 28-Sept-2021, warm magnets, GdR ර Ԧ = න Ԧ + Ԧ Ampere’s law = Ԧ + ර Ԧ = − න Ԧ Faraday’s equation = − න Ԧ = 0 Gauss’s law for = 0 magnetism න Ԧ = න = Gauss’s law With: = = 0 = 0 + = = 0 + Ԧ = + . 6
Magnetostatics Let’s have a closer look at the 3 equations that describe magnetostatics CAS Chavannes de Bogis, 28-Sept-2021, warm magnets, GdR Gauss law of magnetism (1) div = 0 always holds Ampere’s law with no time dependencies (2) rot = Ԧ holds for magnetostatics Relation between field and the flux (3) = 0 holds for linear materials density 7
Magnetic fields From Ampere’s law with no time dependencies (Integral form) ò C B × dl = m0 I encl. CAS Chavannes de Bogis, 28-Sept-2021, warm magnets, GdR We can derive the law of Biot and Savart m0 I B= ĵ 2p r If you wanted to make a B = 1.5 T magnet with just two infinitely thin wires placed at 100 mm distance in air one needs : I = 187500 A • To get reasonable fields ( B > 1 T) one needs large currents • Moreover, the field homogeneity will be poor 8
Iron dominated magnets With the help of an iron yoke we can get fields with less ò C H × dl = N × I current N × I = H iron × liron + H airgap × lairgap Þ CAS Chavannes de Bogis, 28-Sept-2021, warm magnets, GdR B B N ×I = × liron + × lairgap Þ Example: C shaped dipole for accelerators m0mr m0 lairgap × B This is valid as mr >> 1 in N ×I = Yoke m0 the iron : limited to B < 2 T coil B = 1.5 T mr as func on of B for low carbon magnet steel (Magne l BC) Gap = 50 mm 9000 8000 N . I = 59683 A 7000 6000 mr 5000 2 x 30 turn coil 4000 I = 994 A 3000 2000 @5 A/mm2, 200 mm2 1000 0 0 0.5 1 1.5 2 14 x 14 mm Cu B (T) 9
Comparison : iron magnet and air coil Imagine a magnet with a 50 mm vertical gap ( horizontal width ~100 mm) Iron magnet wrt to an air coil: – Up to 1.5 T we get ~6 times the field CAS Chavannes de Bogis, 28-Sept-2021, warm magnets, GdR – Between 1.5 T and 2 T the gain flattens of : the iron saturates – Above 2 T the slope is like for an air-coil: currents become too large to use resistive coils 8 7 6 5 B [T] 4 These two curves are the 3 transfer functions – B field vs. current – for the two cases 2 with iron 1 without iron iron, infinite permeability 0 0 100 200 300 400 500 600 700 800 900 1000 NI [kA] Courtesy A. Milanese, CERN 10
Magnetic field quality: multipole description ∞ −1 −4 + + = 10 1 ൫ + ) =1 CAS Chavannes de Bogis, 28-Sept-2021, warm magnets, GdR ℎ: = + , ℎ ℎ , ℎ ℎ , 1 ℎ ℎ , ℎ ℎ , ℎ ℎ . The “wanted” or is equal to 1 In a ring-shaped accelerator, where the beam does multiple passes, one typically demands : , ≤ 1 10−4 11
Magnetic Length In 3D, the longitudinal dimension of the magnet is described by a magnetic length CAS Chavannes de Bogis, 28-Sept-2021, warm magnets, GdR ∞ 0 = න −∞ lmag Courtesy A. Milanese, CERN magnetic length Lmag as a first approximation: • For dipoles Lmag = Lyoke + d d = pole distance • For quadrupoles: Lmag = Lyoke + r r = radius of the inscribed circle between the 4 poles 12
Magnets in an accelerator: power convertor and circuit Cu (or Al) B (flux density) cables or busbars CAS Chavannes de Bogis, 28-Sept-2021, warm magnets, GdR beam power Convertor (current Vacuum source) chamber • B field stability in time: ~10-5 - 10-6 Cu or Al coil Steel yoke • Typical R of a magnet ~20mW - 60mW Then the Power Convertor has to • Typical L of a magnet ~20mH – 200mH Supply : 0-500 A with a stability of • Powering cable (for 500A): Cu 250 mm 2 a few ppm. (Cu: 17 nW.m) R = 70 mW/m, for 200m: Voltage up to 40 V (resitive) R= 13mW And 100 V (inductive) • Take a typical rise time 1s 13
Types of magnetic fields for accelerators CAS Chavannes de Bogis, 28-Sept-2021, warm magnets, GdR Courtesy D. Tommasini, CERN 14
fluxlines in magnets Dipole Quadrupole sextupole CAS Chavannes de Bogis, 28-Sept-2021, warm magnets, GdR 0 0.8 1.6 0 0.8 1.6 0 0.5 1.0 T T T T T T 15
Symmetry and allowed harmonics In a fully symmetric magnet certain field harmonics are natural. CAS Chavannes de Bogis, 28-Sept-2021, warm magnets, GdR Magnet type Allowed harmonics bn n=1 Dipole n=3,5,7,... n=2 Quadrupole n=6,10,14 n=3 Sextupole n=9,15,21 n=4 Octupole n=12,20,28 Non-symmetric designs and fabrication errors give rise to non allowed harmonics: bn with n other than listed above and an with any n NB: For “skew” magnets this logic is inverted ! 16
CAS Chavannes de Bogis, 28-Sept-2021, warm magnets, GdR Courtesy D. Tommasini, CERN Basic magnet types 17
Practical magnet design & manufacturing Steps in the process: CAS Chavannes de Bogis, 28-Sept-2021, warm magnets, GdR 1. Specification 2. Conceptual design 3. Detailed design 1. Yoke: yoke size, pole shape, FE model optimization 2. Coils: cross-section, geometry, cooling 3. Raw material choice 4. Yoke ends, coil ends design 4. Yoke manufacturing, tolerances, alignment, structure 5. Coil manufacturing, insulation, impregnation type 6. Magnetic field measurements 18
Specification Before you start designing you need to get from the accelerator designers: • B(T) or G (T/m) (higher orders: G3(T/m2), etc) • Magnet type: C-type, H-type, DC (slow ramp) or AC (fast ramp) CAS Chavannes de Bogis, 28-Sept-2021, warm magnets, GdR • Aperture: – Dipole : “good field region“ airgap height and width – Quads and higher order: “good field region“ aperture inscribed circle • Magnetic length and estimated real length • Current range of the power convertor (and the voltage range: watch out for the cables ) • Field quality: ∆ ∆ : , : , = 1,2,3,4,5, … • Cooling type: air, water (Pmax , Dpmax and Qmax (l/min)) • Jacks and Alignment features • Vacuum chamber to be used fixations, bake-out specifics These need careful negotiation and often iteration after conceptual (and detailed) design, and will probably be a compromise. 19
Conceptual design • From B and l you get NI (A) = Yoke 0 Wyoke Wpole • From NI (A) and the power convertor Imax you 1 CAS Chavannes de Bogis, 28-Sept-2021, warm magnets, GdR NI coil 2 get N • Then you decide on a coil X-section using: Wyoke B = 5 ൗ 1 2 2 NI = 1 Τ 2 • This defines the coil cavity in the yoke (you add 0.5 mm insulation around each conductor and 1 mm ground insulation around the coil) and select the best fitting rectangular • You can the draw the draft X-section using: = ℎ 1.5 < < 2 • Decide on the coil ends: racetrack, bedstead • You now have the rough magnet cross section and envelope 20
Power generated Power generated by coil • DC: from the length of the conductor N∙Lturn , the cross-section s and the specific resistivity r of the material one gets the spent Power in the coil CAS Chavannes de Bogis, 28-Sept-2021, warm magnets, GdR = 1.72 1 + 0.0039 − 20 10−8 Ω Τ Τ = 2 ℎ: = 2.65 1 + 0.0039 − 20 10−8 Ω For AC: take the average I2 for the duty cycle Power losses due to hysteresis in the yoke: (Steinmetz law up to 1.5 T) Τ = 1.6 ℎ = 0.01 0.1, ≈ 0.02 Power losses due to eddy currents in the yoke 2 Τ = 0.05 10 with the lamination thickness in mm, ℎ Courtesy D. Tommasini, CERN 21
Cooling circuit parameters Aim: to design dcooling , Pwater[bar], DP[bar], Q[l/min] Choose a desired DT CAS Chavannes de Bogis, 28-Sept-2021, warm magnets, GdR • (20ºC or 30ºC depending on the Tcooling water ) • with the heat capacity of water (4.186 kJ/kgºC) we now know the required water flow rate: Q(l/min) • The cooling water needs to be in moderately turbulent regime (with laminar flow the flow speed is zero on the wall !): Reynolds > 2000 = ~ 140 Τ ~40° • A good approximation for the pressure drop in smooth pipes can be derived from the Blasius law, giving: Τ 1.75 Δ = 60 4.75 Courtesy D. Tommasini, CERN 22
Theoretical pole shapes The ideal poles for dipole, quadrupole, sextupole, etc. are lines of constant scalar potential CAS Chavannes de Bogis, 28-Sept-2021, warm magnets, GdR Dipole = ±ℎ/2 straight line quadrupole 2 = ± 2 hyperbola sextupole 3 2 − 3 = ± 3 23
Practical pole shapes: shims and alignment features • Dipole example: below a lamination of the LEP main bending magnets, with the pole shims well visible CAS Chavannes de Bogis, 28-Sept-2021, warm magnets, GdR • Quadrupoles: at the edge of the pole one can put a combination a shim and alignment feature (examples: LHC-MQW, SESAME quads, etc) • This then also allows to measure the pole distances : special instrumentation can be made for this 24
Finite Element electromagnetic models • Aim of the electromagnetic FE models: – The exact shape of the yoke needs to be designed • Optimize field quality: adjust pole shape, minimize high saturation CAS Chavannes de Bogis, 28-Sept-2021, warm magnets, GdR zones • Minimize the total steel amount ( magnet weight, raw material cost ) – Calculate the field: needed for the optics and dynamic aperture modelling • transfer function Bxsection(I) , න , magnetic length • multipoles (in the centre of the magnet and integrated) bn and an • Some Electromagnetic FE software packages that are often used: – Opera from Cobham: 2D and 3D commercial software see: http://operafea.com/ – “Good old” Poisson, 2D: now distributed by LANL-LAACG see: http://laacg.lanl.gov/laacg/services/download_sf.phtml – ROXIE (CERN) 2D and 3D, specialized for accelerator magnets; single fee license for labs & universities see: ttps://espace.cern.ch/roxie/default.aspx – ANSYS Maxwell: 2D and 3D commercial software see: http://www.ansys.com/Products/Electronics/ANSYS-Maxwell 25
FE models: steel curves You can use a close ‘generic’ B(H) curve for a first cut design You HAVE to use a measured, and smoothed, curve to properly calculate Bxsection(I) , න , bn and an CAS Chavannes de Bogis, 28-Sept-2021, warm magnets, GdR As illustration the curves for several types of steel: 2.5 End slope is m0 2 1.5 B(T) Magnetil LAF 1.5 mm 1 Iron AC37 St-Petersburg 0.75 mm ISR 1.5 mm slope is mrm0 steel Ru 21848 Si 3.25% 0.5 Magnetil LAC 1.5 mm 0 0 5000 10000 15000 20000 25000 30000 35000 H (/m) 26
Yoke shape, pole shape: FE model optimization Use symmetry and the thus appropriate boundary conditions to model only ¼th (dipoles, quadrupoles ) or even 1/6th sextupoles. CAS Chavannes de Bogis, 28-Sept-2021, warm magnets, GdR Meshing needs attention in the detailed areas like poles, slits, etc 27
Yoke manufacturing • Yokes are nearly always laminated to reduce eddy currents during ramping • Laminations can be coated with an inorganic (oxidation, phosphating, Carlite) or organic (epoxy) layer to increase the resistance CAS Chavannes de Bogis, 28-Sept-2021, warm magnets, GdR • Magnetic properties: depend on chemical composition + temperature and mechanical history • Important parameters: coercive field Hc and the saturation induction. – Hc has an impact on the remnant field at low current • Hc < 80 A/m typical • Hc < 20 A/m for magnets ranging down also to low field B < 0.05 T – low carbon steel (C content < 0.006%) is best for higher fields B > 1 T Field Strength [A/m] Minimum Field Strength H Minimum Induction [T] Example [A/m] Induction B [T] Example 40 0.20 specification for 100 0.07 specification for 60 0.50 1.5 mm thick 300 1.05 0.5 mm thick 120 0.95 oxide coated 500 1.35 epoxy coated 500 1.4 1 200 1.5 steel for the LHC 1000 1.50 steel for LHC 2 500 1.62 warm separation 2500 1.62 transfer line 5000 1.72 5 000 1.71 magnets, corrector magnet 10000 1.82 10 000 1.81 Bmax= 1.53 T Bmax=0.3 T 24 000 2.00 28
Yoke manufacturing Stacking an MBW dipole yoke stack Stacking an MQW quadrupole yoke stack CAS Chavannes de Bogis, 28-Sept-2021, warm magnets, GdR MQW yoke assembly 29
Yoke stack manufacturing Double aperture LHC quadrupole MQW Stacking on a precision table CAS Chavannes de Bogis, 28-Sept-2021, warm magnets, GdR Welding the structural plates Finished stack 30
Yokes: holding a laminated stack together • Yokes are either – Glued , using epoxy coated laminations – Welded, full length plates are welded on the outside CAS Chavannes de Bogis, 28-Sept-2021, warm magnets, GdR Corrector dipole in TI2 and TI8 LHC injection lines – Compressed by tie rods in holes Magnet with gluedoflaminated or a combination all these yokes assembled with bolts. • To be able to keep the yoke (or yoke stack) stable you probably need end plates (can range from ± 1 cm to 5 cm depending on the size) • The end plates have pole chamfers and often carry end shims Glued yoke (MCIA LHC TL) Welded stack Tie rod Main parameters Name MCIA V Type Vertical correcting dipole Nominal peak field [T] 0.26 Imax [A] 3.5 N. Of turns 1014 Résistance [Ω] 13.9 Yoke lenght [mm] 450 Gap [mm] 32.5 Total weight [kg] 300 31
Coil manufacturing, insulation, impregnation type • Winding Cu conductors is an well established technique • When the Cu conductor is thick it is best to use “dead soft” Cu (T treatment) • Insulation of the coil CAS Chavannes de Bogis, 28-Sept-2021, warm magnets, GdR – Glass fibre – epoxy impregnated • Individual conductor 0.5 mm glass fibre, 0.25 mm tape wound half lapped • Impregnated with radiation resistant epoxy, total glass volume ratio >50% – For thin conductors: Cu emanel coated, possibly epoxy impregnated afterwards 32
Coil ends For dipoles some main types are racetrack of bedstead CAS Chavannes de Bogis, 28-Sept-2021, warm magnets, GdR Quadrupoles 33
Coil manufacturing MQW Glass fibre tape wrapping. CAS Chavannes de Bogis, 28-Sept-2021, warm magnets, GdR Winding the hollow Cu conductor 34
Coil manufacturing Mounted coil coil electrical test (under water !) CAS Chavannes de Bogis, 28-Sept-2021, warm magnets, GdR Dipoles racetrack coil MBXW Coil winding Finished MBXW coil 35
Magnetic field measurements Several Magnetic Measurements techniques can be applied, e.g.: • Rotating coils: multipoles and integrated field or gradient in all magnets • Stretched wire: magnetic centre and integrated gradient for n > 1 magnets CAS Chavannes de Bogis, 28-Sept-2021, warm magnets, GdR • Hall probes: field map • Pickup coils: field on a current ramp • Example below : MQW : double aperture quadrupole for the LHC. The radial coil Mole assembly 1 Flux in a Radial Coil: R2 F(q ) = NL ò Bq (r ,q )dr Y R1 q = q 0 + wt B AS Budapest, 7-Oct-2016, warm magnets, GdR Mole Assembly R2 Side View Induced Voltage: R1 X Gravity Sensor Pneumatic Break Incremental Encoder Slip Rings Harmonic Coils æ ¶F ö V (t ) = -ç ÷ è ¶t ø Integrated Voltage: Mole Assembly Top View 36 Rotating radial coil Cross section of a radial coil
Sextupoles • These are sextupoles (with embedded correctors) of the main ring of the SESAME light source CAS Chavannes de Bogis, 28-Sept-2021, warm magnets, GdR Courtesy A. Milanese, CERN 37
Permanent magnets Linac4 @ CERN permanent magnets , quadrupoles CAS Chavannes de Bogis, 28-Sept-2021, warm magnets, GdR Permanent Magnets : LINAC 4 DTL tank Pictured : Cell-Coupled Drift Tube Linac module. • Permanent magnet because of space between DTL tanks • Sm2Co17 permanent magnets • Integrated gradient of 1.3 to 1.6 Tesla • 15 magnets • Magnet length 0.100 m • Field quality/amplitude tuning blocks Courtesy D. Tommasini, CERN Sextupole Hallback Array 38 Introduction to accelerator physics Varna, 19 September, 1 October 2010 Davide Tommasini : Magnets (warm)25
Hybrid magnets CLIC final focus, Hybrid Magnets : CLIC final focus CAS Chavannes de Bogis, 28-Sept-2021, warm magnets, GdR Gradient: > 530 T/m Aperture Ø: 8.25 mm Tunability: 10-100% Courtesy D. Tommasini, CERN 39 Introduction to accelerator physics Varna, 19 September, 1 October 2010 Davide Tommasini : Magnets (warm)
CAS Chavannes de Bogis, 28-Sept-2021, warm magnets, GdR Examples; Some history, some modern regular magnets and some special cases 40
The 184’’ (4.7 m) cyclotron at Berkeley (1942) CAS Chavannes de Bogis, 28-Sept-2021, warm magnets, GdR Courtesy A. Milanese, CERN 41
Cyclotrons CAS Chavannes de Bogis, 28-Sept-2021, warm magnets, GdR A modern synchrocyclotron for medical application – IBA S2C2 Harvard 1948 ® at the same energy synchrocyclotrons can be build more compact and with lower cost than sector cyclotrons; however, the achievable current is significantly lower energy 230 MeV Feb/2013, courtesy: current 20 nA P.Verbruggen,IBA dimensions Æ2.5 m x 2 m weight < 50 t extraction radius 0.45 m s.c. coil strength 5.6 Tesla RF frequency 90…60 MHz repetition rate 1 kHz 1974 20 42
Some early magnets (early 1950-ies) Bevatron (Berkeley) CAS Chavannes de Bogis, 28-Sept-2021, warm magnets, GdR 1954, 6.2 GeV Cosmotron (Brookhaven) 1953, 3.3 GeV Aperture: 20 cm x 60 cm 43
No. of non-linear lenses 20 pairs Harmonic number 20 Frequency range 2.9–9.55 MHz PS combined function dipole Power per cavity 6 kW Magnet and Power Supply Magnetic field: Injection at injection 147 G for 24.3 GeV 1.2 T Injection energy 50 ± 0.1 MeV CAS Chavannes de Bogis, 28-Sept-2021, warm magnets, GdR maximum 1.4 T Injection field 147 G Weight of one magnet unit 38 t Length of linear accelerator 30 m Total weight Gradient @1.2ofT coils (alumin.) : 5 T/m 110 t RF power 5 MW at 202.5 MH Total weight of iron 3400 t during 200 ms Rise timewith Equipped to 1.2 T pole-face 1s windings No. for higher of cycles order (1.2 T per minute Fig. 10: Model with movable plates to determine final Fig. 11: The ‘n’ values of open and c Water cooled Al race- profile. the remanent field show corrections operation) 20 track coils Vacuum System difference. The acceptab thickness determined e xperim Peak power to energize the The final form of the magnet block is given in Fig. 12. The construction of the 1 magnet 34 600 kW Vacuum chamber length entrusted to Ansaldo Fig. 9: Final in Genoa with pole steel profile. 628 laminations produced mnearby fact in the (Fig. 13). Ansaldo won the contract because of the higher precision of their punching Stored energy 107 J Vacuum chamber with those madesection by other European manufacturers. 7 ´ 14 cm Paying extreme attention to tolerances and in general to very sound engineer Mean dissipated power 1500 kWcomponent was,Wall thickness I believe, (stainless of capital importance steel) not only for the success 2 mm of the PS b Magnet gap at equilibrium orbit Vacuumat pumps 10 cm subsequent machines (ø 10 cm) 4 CERN. It taught all of us how to tackle technical design and+ 67 stations the basis of Pressure, an attitude better which was thanone of the facets of J. B. Adams’s 10–5 mmHg personality pessimism’, just the opposite of ‘blind optimism’. Indeed John was a pessimist not in but in the sense that he believed that Nature had no reason to make gifts to accel Therefore the correct attitude consisted in understanding the finest details of each pro make a design leaving nothing to chance on the way to success. Some people co conservatism and overcautiousness. But how can one consider as conservative o extraordinary engineers of our time, a man who undertook to construct the first proton in the world, the first underground large accelerator and, finally, the first pp collider? Fig. 12: Final form of the magnet blocks. The apparent simplicity of the magnet system masked a fair degree of sophist many studies and a lot of experimental work. Complication Courtesy was due to:CERN 44 D. Tommasini,
CPS booster PS Booster Magnets 4 accelerator rings in a common yoke. (increase total beam intensity by 4 in presence of space charge limitation at low Spare energy): Booster Dipole B=1.48 T @Booster Installed 2 GeV Dipole 1.4 GeV Magnet Cycle Was originaly designed for 0.8 GeV ! CAS Chavannes de Bogis, 28-Sept-2021, warm magnets, GdR 32 Dipole magnets for Booster Ring Magnet Weight - 12000 Kg Core Length - 1537 mm ‘Thick’ End Plate Aperture - 103 mm BDL correction Windings Magnetic flux @ 1.4 GeV operation 1.064 T compensate the 1% difference between the inner and outer rings. Yoke construction: Laminated core stacked between Laminations ‘thick’ end plates assembled using external welded tie bars. Lamination insulation achieved through a phosphatizing process. Welded tie Bars Courtesy D. Tommasini, CERN Booster Ring 4 Booster to PS LINAC to Booster 3 2 1 45
dipole magnet : SPS dipole CAS Chavannes de Bogis, 28-Sept-2021, warm magnets, GdR H magnet s of bending magnets oftype MBB the SPS. B = 2.05 T Coil : 16 turns I max = 4900 A Aperture = 52 × 92 mm2 L = 6.26 m Weight = 17 t 46
Quadrupole magnet : SPS quadrupole CAS Chavannes de Bogis, 28-Sept-2021, warm magnets, GdR type MQ G = 20.7 T/m Coil : 16 turns I max = 1938 A Aperture inscribed radius = 44 mm Lcoil = 3.2 m Weight = 8.4 t 47
CAS Chavannes de Bogis, 28-Sept-2021, warm magnets, GdR MBW LHC warm separation dipole (1) 48
CAS Chavannes de Bogis, 28-Sept-2021, warm magnets, GdR MQW: LHC warm double aperture quadrupole 49
CAS Chavannes de Bogis, 28-Sept-2021, warm magnets, GdR • . Elena, anti proton decelerator 50
Soleil, synchrotron light-source CAS Chavannes de Bogis, 28-Sept-2021, warm magnets, GdR Courtesy A. Dael, CEA 51
Literature on warm accelerator magnets • Books – G.E.Fisher, “Iron Dominated Magnets” AIP Conf. Proc., 1987 -- Volume 153, pp. 1120-1227 CAS Chavannes de Bogis, 28-Sept-2021, warm magnets, GdR – J. Tanabe, “Iron Dominated Electromagnets”, World Scientific, ISBN 978-981-256- 381-1, May 2005 – P. Campbell, Permanent Magnet Materials and their Application, ISBN-13: 978- 0521566889 – S. Russenschuck, Field computation for accelerator magnets : analytical and numerical methods for electromagnetic design and optimization / Weinheim : Wiley, 2010. - 757 p. • Schools – CAS Bruges, 2009, specialized course on magnets, 2009, CERN-2010-004 – CAS Frascati 2008, Magnets (Warm) by D. Einfeld – CAS Varna 2010, Magnets (Warm) by D. Tommasini • Papers and reports – D. Tommasini, “Practical definitions and formulae for magnets,” CERN,Tech. Rep. EDMS 1162401, 2011 52
Acknowledgements For this lecture I used material from lectures, seminars, reports, etc. from the many colleagues. Special thanks goes to: Davide Tommasini, Attilio Milanese, Antoine Dael, Stephan Russenschuck, CAS Chavannes de Bogis, 28-Sept-2021, warm magnets, GdR Thomas Zickler And to the people who taught me, years ago, all the fine details about magnets ! 53
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