AC Magnet Systems. Ben Shepherd Magnetics and Radiation Sources Group. Daresbury Laboratory.

Transcription

1 AC Magnet Systems Ben Shepherd Magnetics and Radiation Sources Group ASTeC Daresbury Laboratory Ben Shepherd, ASTeC Cockcroft Institute: AC Magnets, Autumn

2 Philosophy 1. How do AC lattice magnets differ from DC magnets? 2. Typical qualities of steel used in lattice magnets 3. Qualitative overview of injection and extraction techniques as used in circular machines 4. Standard designs for kicker and septum magnets and their associated power supplies Ben Shepherd, ASTeC Cockcroft Institute: AC Magnets, Autumn

3 Contents a) Variations in design and construction for AC magnets Effects of eddy current in vac vessels and coils Properties and choice of steel b) Methods of injecting and extracting beam Single turn injection/extraction Multi-turn injection/extraction Magnet requirements c) Fast magnets Kicker magnets: lumped and distributed power supplies Septum magnets: active and passive septa Some modern examples Ben Shepherd, ASTeC Cockcroft Institute: AC Magnets, Autumn

4 Differences to DC magnets AC magnets differ in two main respects to DC magnets: 1. In addition to DC ohmic loss in the coils, there will be AC losses (eddy and hysteresis); design goals are to correctly calculate and minimise AC losses. 2. Eddy currents will generate perturbing fields that will affect the beam. Excitation voltage now includes an inductive (reactive) component; this may be small, major or dominant (depending on frequency); this must be accurately assessed. Ben Shepherd, ASTeC Cockcroft Institute: AC Magnets, Autumn

5 Equivalent circuit of AC magnet R ac L m R dc I m C leakage Ben Shepherd, ASTeC Cockcroft Institute: AC Magnets, Autumn

6 AC Magnet Design Additional Maxwell equation for magneto-dynamics: EE = dddd dddd Applying Stoke s theorem around any closed path s enclosing area A EE. ddaa = EE. dddd = VV llllllll where V loop is the voltage around path s ddbb ddφ. dddd = dddd dddd where Φ is the total flux cutting A So: VV llllllll = ddφ dddd Thus, eddy currents are induced in any conducting material in the alternating field. This results in increased loss, and modification to the field strength and quality. Ben Shepherd, ASTeC Cockcroft Institute: AC Magnets, Autumn

7 Eddy Currents in a Conductor I Rectangular cross section resistivity ρ, breadth 2a thickness τ, length λ BBssssss ωωωω cut normally by field BBBBBBBB ωωωω Consider a strip at +x, width δx, returning at x (λλ xx): Peak volts in circuit VV pppppppp = 2xxxxxxxx Resistance of circuit RR = 2λλλλ ττ δδδδ Peak current in circuit II pppppppp = xxxxxxxx ρρ Integrate this to give total Amp-turns in block. Peak instantaneous power in strip PP pppppppp,ssssssssss = 2xx2 λλ ωω 2 BB 2 ττ δδδδ ρρ Integrate w.r.t. x between 0 and a to obtain peak instantaneous power in block Cross section area AA = 2aaaa Average power is ½ of above PP pppppppp,bbbbbbbbbb = 2 3 aa 3 λλωω 2 BB 2 ττ ρρ Power loss/unit length PP llllllll = ωω2 BB 2 AAaa 2 A 10x10 mm² Cu conductor in a 1 T peak 50Hz sinusoidal field P loss = 1.7 kw/m Ben Shepherd, ASTeC Cockcroft Institute: AC Magnets, Autumn τ -a -x 0 x a δx 6ρρ λ Cross section A

8 Perturbation field generated by eddy currents Note: that if the vacuum vessel is between the poles of a a ferromagnetic yoke, the eddy currents will couple to that yoke; the yoke geometry therefore determines the perturbing fields; this analysis assumes that the perturbing field is small compared to the imposed field. Using: BB ee = μμ 0II ee gg g μ = Magnet geometry around vessel, radius R Amplitude ratio between perturbing and imposed fields at X = 0 is: BB ee (0) = 2μμ 0ωωωωRR 2 BB ρρρρ Phase of perturbing field w.r.t. imposed field is: θθ ee = arctan 2μμ 0ωωωωRR 2 ρρρρ R 0 x Ben Shepherd, ASTeC Cockcroft Institute: AC Magnets, Autumn

9 Distributions of perturbing fields Cylindrical vessel (radius R): BB ee xx = 2μμ 0RRRRRR BB cccccc ωωωω ρρρρ variation with horizontal position x = 2μμ 0RR 2 ττττ BB cccccc ωωωω ρρρρ RR 2 xx 2 1 xx2 2RR 2 xx4 8RR 4 xx6 16RR 6 5xx8 128RR 8 Ben Shepherd, ASTeC Cockcroft Institute: AC Magnets, Autumn

10 Perturbation field generated by eddy currents Note, eddy currents in vacuum vessels: In all cases, the first order field perturbation is (aa 2 xx 2 ) or aa 2 xx 2 reduction in dipole field and negative sextupole leading to negative chromaticity. Cylindrical and elliptical vessels also have 10, pole Ben Shepherd, ASTeC Cockcroft Institute: AC Magnets, Autumn

11 Stainless steel vessels amplitude loss Example: Ratio of amplitude of perturbing eddy current dipole field to amplitude of imposed field as a function of frequency for three values of stainless steel vessel wall thickness (RR = gg/2) 1 Perturbation/imposed field thickness = 1 mm thickness = 0.5 mm thickness= 0.25 mm Calculation invalid in this region Frequency (Hz) Ben Shepherd, ASTeC Cockcroft Institute: AC Magnets, Autumn

12 Stainless steel vessels phase Phase change (lag) of dipole field applied to beam as a function of frequency for three values of vessel wall thickness (RR = gg/2) Phase change in field applied to beam [ ] thickness = 1 mm thickness = 0.5 mm thickness = 0.25 mm Calculation invalid in this region Frequency (Hz) Ben Shepherd, ASTeC Cockcroft Institute: AC Magnets, Autumn

13 AC effects in steel yokes Steel yokes will have: eddy current power loss - with distortion of B hysteresis losses So have to be laminated like a mains transformer Laminated layers Ben Shepherd, ASTeC Cockcroft Institute: AC Magnets, Autumn

14 Steel Yoke Eddy Losses. To limit eddy losses, the laminations in the steel core are coated with a thin layer (~2 µm) of insulating material, usually just on one side of each lamination. At 10 Hz lamination thicknesses of 0.5mm to 1 mm can be used. At 50Hz, lamination thicknesses of 0.35mm to 0.65mm are standard. Laminations also allow steel to be shuffled during magnet assembly, so each magnet contains a fraction of the total steel production this is used also for DC magnets. Ben Shepherd, ASTeC Cockcroft Institute: AC Magnets, Autumn

15 Steel hysteresis loss Steel also has hysteresis loss caused by the finite area inside the B/H loop: Loss is proportional to BB. dddd integrated over the area within the loop. Ben Shepherd, ASTeC Cockcroft Institute: AC Magnets, Autumn

16 Steel loss data Manufacturers give figures for total loss (in W/kg) in their steel catalogues: for a sin waveform at a fixed peak field (Euro standard is at 1.5 T) and at fixed frequency (50 Hz in Europe, 60 Hz in USA) at different lamination thicknesses (0.35, 0.5, 0.65 & 1.0 mm typically) they do not give separate values for eddy and hysteresis loss Accelerator magnets will have: 3 different waveforms (unidirectional!) different DC bias values 0 different frequencies (0.2 Hz up to 50 Hz) 0 10 How does the designer calculate steel loss? Ben Shepherd, ASTeC Cockcroft Institute: AC Magnets, Autumn

17 Eddy and hysteresis loss in steel Variation with Eddy loss Hysteresis loss AC frequency AC amplitude Square law Linear Square law Nonlinear, depends on level DC bias No effect Increases nonlinearly Total volume of steel Linear Linear Lamination thickness Square law No effect Ben Shepherd, ASTeC Cockcroft Institute: AC Magnets, Autumn

18 Choice of steel grain oriented Electrical steel is either grain oriented or non-oriented Grain oriented: strongly anisotropic very high quality magnetic properties and very low AC losses in the rolling direction normal to rolling direction is much worse than nonoriented steel stamping and machining causes loss of quality and the stamped laminations must be annealed before final assembly Ben Shepherd, ASTeC Cockcroft Institute: AC Magnets, Autumn

19 Choice of steel non-oriented Non-oriented steel: some anisotropy (~5%) manufactured in many different grades, with different magnetic and loss figures losses controlled by the percentage of silicon included in the mix high silicon gives low losses (low coercivity), higher permeability at low flux density but poorer magnetic performance at high field low (but not zero) silicon gives good performance at high B silicon mechanically stabilises the steel, prevents aging Ben Shepherd, ASTeC Cockcroft Institute: AC Magnets, Autumn

20 Solid steel Low carbon/high purity steels: usually used for solid DC magnets good magnetic properties at high fields but hysteresis loss not as low as high silicon steel accelerator magnets are seldom made from solid steel (laminations preferred to allow shuffling and reduce eddy currents) Ben Shepherd, ASTeC Cockcroft Institute: AC Magnets, Autumn

21 Steel comparisons Property DK-70 CK M 3 XC06 Type Non-oriented Non-oriented Grain-oriented Non-oriented Silicon content Low High - Very low Lamination thickness 0.65 mm 0.35 mm 0.27 mm Solid AC loss (50 Hz) at 1.5 T peak 6.9 W/kg 2.25 W/kg 0.79 W/kg Not suitable Permeability at B = 1.5 T 1, >10,000 >1,000 at B = 1.8 T ,100 >160 Ben Shepherd, ASTeC Cockcroft Institute: AC Magnets, Autumn

22 The problem with grain oriented steel In spite of the obvious advantage, grain oriented is seldom used in accelerator magnets because of the mechanical problem of keeping B in the direction of the grain. B Rolling direction Difficult (impossible?) to make each limb out of separate strips of steel Ben Shepherd, ASTeC Cockcroft Institute: AC Magnets, Autumn

23 The Injection/Extraction problem Single turn injection/extraction: a magnetic element inflects beam into the ring and turn-off before the beam completes the first turn (extraction is the reverse). Multi-turn injection/extraction: the system must inflect the beam into the ring with an existing beam circulating without producing excessive disturbance or loss to the circulating beam Accumulation in a storage ring: A special case of multi-turn injection - continues over many turns (with the aim of minimal disturbance to the stored beam) injected beam straight section magnetic element Ben Shepherd, ASTeC Cockcroft Institute: AC Magnets, Autumn

24 Single turn simple solution A kicker magnet with fast turn-off (injection) or turn-on (extraction) can be used for single turn injection field injection fast fall extraction fast rise Problems: rise or fall will always be non-zero loss of beam single turn inject does not allow the accumulation of high current in small accelerators revolution times can be << 1 µs magnets are inductive fast rise (fall) means (very) high voltage time Ben Shepherd, ASTeC Cockcroft Institute: AC Magnets, Autumn

25 Multi-turn injection solutions Beam can be injected by phase-space manipulation (a) Inject into an unoccupied outer region of phase space with non-integer tune which ensures many turns before the injected beam re-occupies the same region (electrons and protons): e.g. Horizontal phase space at Q = ¼ integer: x septum x 0 field deflect. field turn 1 first injection turn 2 turn 3 turn 4 last injection Ben Shepherd, ASTeC Cockcroft Institute: AC Magnets, Autumn

26 Multi-turn injection solutions (b) Inject into outer region of phase space - damping coalesces beam into the central region before re-injecting (high energy leptons only): dynamic aperture stored beam injected beam next injection after 1 damping time (c) inject negative ions through a bending magnet and then strip to produce a proton after injection (H - to p + only) Ben Shepherd, ASTeC Cockcroft Institute: AC Magnets, Autumn

27 Multi-turn extraction solution Shave particles from edge of beam into an extraction channel whilst the beam is moved across the aperture: extraction channel beam movement septum Points: Some beam loss on the septum cannot be prevented Efficiency can be improved by blowing up on 1/3rd or 1/4 th integer resonance Ben Shepherd, ASTeC Cockcroft Institute: AC Magnets, Autumn

28 Magnet requirements Magnets required for injection and extraction systems Kicker magnets: pulsed waveform rapid rise or fall times (usually << 1 µs) flat-top for uniform beam deflection Septum magnets: pulsed or DC waveform spatial separation into two regions one region of high field (for injection deflection) one region of very low (ideally 0) field for existing beam septum to be as thin as possible to limit beam loss Septum magnet schematic Ben Shepherd, ASTeC Cockcroft Institute: AC Magnets, Autumn

29 Fast Magnet & Power Supplies Because of the demanding performance required from these systems, the magnet and power supply must be strongly integrated and designed as a single unit Two alternative approaches to powering these magnets: Distributed circuit: magnet and power supply made up of delay line circuits Lumped circuits: magnet is designed as a pure inductance; power supply can be use delay line or a capacitor to feed the high pulse current Ben Shepherd, ASTeC Cockcroft Institute: AC Magnets, Autumn

30 High Frequency Kicker Magnets Kicker Magnets: used for rapid deflection of beam for injection or extraction usually located inside the vacuum chamber rise/fall times << 1µs yoke assembled from high frequency ferrite single turn coil pulse current 10 4 A pulse voltages of many kv Typical geometry Ferrite Core beam Conductors Ben Shepherd, ASTeC Cockcroft Institute: AC Magnets, Autumn

31 Kickers - Distributed System Standard (CERN) delay line magnet and power supply: L, C L, C dc Z 0 Power Supply Thyratron Magnet Resistor The power supply and interconnecting cables are matched to the surge impedance of the delay line magnet Ben Shepherd, ASTeC Cockcroft Institute: AC Magnets, Autumn

32 Distributed System mode of operation The first delay line is charged by the DC supply to a voltage V The thyratron triggers a voltage wave: V/2 which propagates into the magnet This gives a current wave of VV 2ZZ propagating into the magnet The circuit is terminated by pure resistor Z, to prevent reflection Ben Shepherd, ASTeC Cockcroft Institute: AC Magnets, Autumn

33 Kickers Lumped Systems The magnet is (mainly) inductive - no added distributed capacitance The magnet must be very close to the supply (minimises inductance) R dc L II = VV RR RRRR 1 exp LL i.e. the same waveform as distributed power supply, lumped magnet systems.. Ben Shepherd, ASTeC Cockcroft Institute: AC Magnets, Autumn

34 Improvement on above C R dc L The extra capacitor C improves the pulse substantially. Ben Shepherd, ASTeC Cockcroft Institute: AC Magnets, Autumn

35 Resulting Waveform Example calculated for the following parameters: mag inductance L = 1 µh rise time t = 0.2 µs resistor R = 10 Ω trim capacitor C = 4000 pf The impedance in the lumped circuit is twice that needed in the distributed! The voltage to produce a given peak current is the same in both cases Pulse Waveform Time [µs] Performance: at t = 0.1 µs, current amplitude = of peak at t = 0.2 µs, current amplitude = 1.01 of peak The maximum overswing is 2.5%. This system is much simpler and cheaper than the distributed system. Ben Shepherd, ASTeC Cockcroft Institute: AC Magnets, Autumn

36 An EMMA kicker magnet ferrite cored lumped system Ben Shepherd, ASTeC Cockcroft Institute: AC Magnets, Autumn

37 EMMA Injection Kicker Magnet Waveform Ben Shepherd, ASTeC Cockcroft Institute: AC Magnets, Autumn

38 Septum Magnets classic design Often (not always) located inside the vacuum and used to deflect part of the beam for injection or extraction: The thin 'septum' coil on the front face gives: high field within the gap, low field externally; Yoke Beam Problems: The thickness of the septum must be minimised to limit beam loss the front septum has very high current density and major heating problems Single turn coil Ben Shepherd, ASTeC Cockcroft Institute: AC Magnets, Autumn

39 Septum Magnet eddy current design uses a pulsed current through a backleg coil (usually a poor design feature) to generate the field the front eddy current shield must be, at the septum, a number of skin depths thick; elsewhere at least ten skin depths high eddy currents are induced in the front screen; but this is at earth potential and bonded to the base plate heat is conducted out to the base plate field outside the septum are usually ~ 1% of field in the gap - + Single or multi turn coil Eddy current shield Ben Shepherd, ASTeC Cockcroft Institute: AC Magnets, Autumn

40 Comparison of the two types Classical septum Eddy current septum Excitation DC or low frequency pulse Pulse at >10 khz Coil Cooling Single turn including front septum Complex: water spirals in thermal contact with septum Single or multi-turn on backleg, room for large cross-section Heat generated in shield is conducted to base plate Yoke Conventional steel High frequency material (ferrite or thin steel laminations) Ben Shepherd, ASTeC Cockcroft Institute: AC Magnets, Autumn

41 Example Skin depth in material: resistivity ρ relative permeability µ r at frequency ω is given by: dd = ωωμμ rr μμ 0 Example: EMMA injection and extraction eddy current septa: Screen thickness (at beam height): 1 mm Screen thickness (elsewhere) up to 10 mm Excitation 25 µs, half sinewave Skin depth in copper at 20 khz 0.45 mm 2ρρ Ben Shepherd, ASTeC Cockcroft Institute: AC Magnets, Autumn

42 Location of EMMA septum magnets Ben Shepherd, ASTeC Cockcroft Institute: AC Magnets, Autumn

43 Design of the EMMA septum magnet Inner steel yoke is assembled from 0.1 mm thick silicon steel laminations, insulated with 0.2 µm coatings on each side. Ben Shepherd, ASTeC Cockcroft Institute: AC Magnets, Autumn