1. Neil Marks; ASTeC, CI.‘AC Magnets’; CI School 2013. A.C. Magnet Systems Neil Marks, ASTeC, Cockcroft Institute, Daresbury, Warrington WA4 4AD, neil.marks@stfc.ac.uk Tel: (44) (0)1925 603191 Fax: (44) (0)1925 603192

2. Neil Marks; ASTeC, CI.‘AC Magnets’; CI School 2013. Philosophy 1.Present practical details of how a.c. lattice magnets differ from d.c. magnets. 2.Present details of the typical qualities of steel used in lattice magnets. 3.Give a qualitative overview of injection and extraction techniques as used in circular machines. 4.Present the standard designs for kicker and septum magnets and their associated power supplies.

3. Neil Marks; ASTeC, CI.‘AC Magnets’; CI School 2013. Contents a) Variations in design and construction for a.c. 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.

4. Neil Marks; ASTeC, CI.‘AC Magnets’; CI School 2013. Differences to d.c. magnets A.c magnets differ in two main respects to d.c. magnets: 1.In addition to d.c ohmic loss in the coils, there will be ‘ac’ losses (eddy and hysteresis); design goals are to correctly calculate and minimise a.c. losses. 2.Eddy currents will generate perturbing fields that will affect the beam. 3.Excitation voltage now includes an inductive (reactive) component; this may be small, major or dominant (depending on frequency); this must be accurately assessed.

5. Neil Marks; ASTeC, CI.‘AC Magnets’; CI School 2013. Equivalent circuit of a.c. magnet LmLm R dc C leakage ImIm R ac

6. Neil Marks; ASTeC, CI.‘AC Magnets’; CI School 2013. Additional Maxwell equation for magneto-dynamics: curl E = -dB/dt. Applying Stoke’s theorem around any closed path s enclosing area A:  curl E.dA =  E.ds = V loop where V loop is voltage around path s;  - (dB /dt).dA = - d  /dt; Where  is total flux cutting A; So:V loop = -d  /dt 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. A.C. Magnet Design

7. Neil Marks; ASTeC, CI.‘AC Magnets’; CI School 2013. Eddy Currents in a Conductor I Rectangular cross section resistivity , breadth 2 a, thickness , length, cut normally by field B sin  t. Consider a strip at +x, width  x, returning at –x (  >>x). Peak volts in circuit = 2 x  B Resistance of circuit = 2  /(   x ) Peak current in circuit = x  B   x /  Integrate this to give total Amp-turns in block. Peak instantaneous power in strip = 2 x 2  2 B 2   x /  Integrate w.r.t. x between 0 and a to obtain peak instantaneous power in block = (2/3) a 3  2 B 2   /  Cross section area A = 2 a  Average power is ½ of above. Power loss/unit length =  2 B 2 A a 2 /(6  )W/m; xx  -a -x 0 x a B sin  t Cross section A a 10x10 mm 2 Cu conductor in a 1T peak 50Hz sin. field, loss = 1.7 kW/m

8. Neil Marks; ASTeC, CI.‘AC Magnets’; CI School 2013. Perturbation field generated by eddy currents Magnet geometry around vessel radius R. g  =  R x 0 Note: that if the vacuum vessel is between the poles of a a ferro-magnetic 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: B e =  0 I e /g; Amplitude ratio between perturbing and imposed fields at X = 0 is: B e (0)/B = - 2  0   R 2 /  g; Phase of perturbing field w.r.t. imposed field is:  e = arctan (- 2  0   R 2 /  g )

9. Neil Marks; ASTeC, CI.‘AC Magnets’; CI School 2013. Distributions of perturbing fields Cylindrical vessel (radius R): Be(X) Rectangular vessel (semi axies a, b): Be(X) Elliptical vessel (semi axies a, b): Be(X) variation with horizontal position X

10. Neil Marks; ASTeC, CI.‘AC Magnets’; CI School 2013. Perturbation field generated by eddy currents. Note, eddy currents in vacuum vessels: In all cases, the first order field perturbation is (a -X 2 ) ; → reduction in dipole field and negative sextupole adding to negative chromaticity. cylindrical and elliptical vessels also have 10, 14.. pole.

11. Neil Marks; ASTeC, CI.‘AC Magnets’; CI School 2013. 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 s.s. vessel wall thickness (R = g/2): Calculation invalid in this region.

12. Neil Marks; ASTeC, CI.‘AC Magnets’; CI School 2013. 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 (R = g/2): Calculation invalid in this region.

13. Neil Marks; ASTeC, CI.‘AC Magnets’; CI School 2013. 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.

14. Neil Marks; ASTeC, CI.‘AC Magnets’; CI School 2013. Steel Yoke Eddy Losses. At 10 Hz lamination thickness of 0.5mm to 1 mm can be used. At 50Hz, lamination thickness 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; - used also for d.c. magnets. 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.

15. Neil Marks; ASTeC, CI.‘AC Magnets’; CI School 2013. Steel hysteresis loss Steel also has hysteresis loss caused by the finite area inside the B/H loop: Loss is proportional to  B.dH integrated over the area within the loop.

16. Neil Marks; ASTeC, CI.‘AC Magnets’; CI School 2013. Steel loss data Manufacturers give figures for total loss (in W/kg) in their steels 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: different waveforms (unidirectional!); different d.c. bias values; different frequencies (0.2 Hz up to 50 Hz). How does the designer calculate steel loss?

17. Neil Marks; ASTeC, CI.‘AC Magnets’; CI School 2013. Comparison between eddy and hysteresis loss in steel: Variation with: Eddy loss Hysteresis loss A.c. frequency: Square law Linear; A.c. amplitude: Square law Non-linear-depends on level; D.c. bias: No effect Increases non-linearly; Total volume of steel: Linear Linear; Lamination thickness: Square law No effect.

18. Neil Marks; ASTeC, CI.‘AC Magnets’; CI School 2013. Choice of steel 'Electrical steel' is either 'grain oriented' or 'non-oriented‘: Grain oriented: strongly anisotropic, very high quality magnetic properties and very low a.c losses in the rolling direction; normal to rolling direction is much worse than non-oriented steel; stamping and machining causes loss of quality and the stamped laminations must be annealed before final assembly.

19. Neil Marks; ASTeC, CI.‘AC Magnets’; CI School 2013. Choice of steel (cont). 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.

20. Neil Marks; ASTeC, CI.‘AC Magnets’; CI School 2013. Solid steel Low carbon/high purity steels: usually used for solid d.c. 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)

21. Neil Marks; ASTeC, CI.‘AC Magnets’; CI School 2013. Comparisons Property: DK-70:CK-27: 27 M 3: XC06 : Type Non- Non- Grain- Non- orientedoriented oriented oriented Silicon content LowHigh - Very low Lam thickness 0.65 mm0.35 mm 0.27 mm Solid a.c. loss (50 Hz): at 1.5 T peak 6.9 W/kg2.25 W/kg 0.79 W/kg Not suitable Permeability: at B=1.5 T 1,680990 > 10,000 >1,000 at B=1.8 T 184122 3,100 >160

22. Neil Marks; ASTeC, CI.‘AC Magnets’; CI School 2013. 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. Difficult (impossible?) to make each limb out of separate strips of steel.

23. Neil Marks; ASTeC, CI.‘AC Magnets’; CI School 2013. 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). straight section injected beam magnetic element

24. Neil Marks; ASTeC, CI.‘AC Magnets’; CI School 2013. Single turn – simple solution A ‘kicker magnet’ with fast turn-off (injection) or turn-on (extraction) can be used for single turn injection. injection – fast fallextraction – fast rise Problems: i) rise or fall will always be non-zero  loss of beam; ii) single turn inject does not allow the accumulation of high current; iii) in small accelerators revolution times can be << 1  s. iv) magnets are inductive  fast rise (fall) means (very) high voltage. B t

25. Neil Marks; ASTeC, CI.‘AC Magnets’; CI School 2013. 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): eg – Horizontal phase space at Q = ¼ integer: x x’ turn 1 – first injection turn 2turn 3 turn 4 – last injection septum 0 field deflect. field

26. Neil Marks; ASTeC, CI.‘AC Magnets’; CI School 2013. 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 injected beamnext injection after 1 damping time stored beam c) inject negative ions through a bending magnet and then ‘strip’ to produce a p after injection (H- to p only).

27. Neil Marks; ASTeC, CI.‘AC Magnets’; CI School 2013. Multi-turn extraction solution ‘Shave’ particles from edge of beam into an extraction channel whilst the beam is moved across the aperture: beam movement extraction channel 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. septum

28. Neil Marks; ASTeC, CI.‘AC Magnets’; CI School 2013. Magnet requirements Magnets required for injection and extraction systems. i) Kicker magnets: pulsed waveform; rapid rise or fall times (usually << 1  s); flat-top for uniform beam deflection. ii) Septum magnets: pulsed or d.c. 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

29. Neil Marks; ASTeC, CI.‘AC Magnets’; CI School 2013. 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.

30. Neil Marks; ASTeC, CI.‘AC Magnets’; CI School 2013. 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:

31. Neil Marks; ASTeC, CI.‘AC Magnets’; CI School 2013. Kickers - Distributed System Standard (CERN) delay line magnet and power supply:  Power Supply  Thyratron  Magnet  Resistor The power supply and interconnecting cables are matched to the surge impedance of the delay line magnet:

32. Neil Marks; ASTeC, CI.‘AC Magnets’; CI School 2013. Distributed System -mode of operation the first delay line is charged by the d.c. supply to a voltage :V; the thyratron triggers, a voltages wave: V/2 which propagates into magnet; this gives a current wave of V/( 2 Z ) propagating into the magnet; the circuit is terminated by pure resistorZ, to prevent reflection.

33. Neil Marks; ASTeC, CI.‘AC Magnets’; CI School 2013. Kickers – Lumped Systems. The magnet is (mainly) inductive - no added distributed capacitance; the magnet must be very close to the supply (minimises inductance). I = (V/R) (1 – exp (- R t /L) i.e. the same waveform as distributed power supply, lumped magnet systems..

34. Neil Marks; ASTeC, CI.‘AC Magnets’; CI School 2013. Improvement on above C The extra capacitor C improves the pulse substantially.

35. Neil Marks; ASTeC, CI.‘AC Magnets’; CI School 2013. Resulting Waveform Example calculated for the following parameters: mag inductance L = 1  H; rise timet = 0.2  s; resistorR = 10  ; trim capacitor C = 4,000 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. Performance:at t = 0.1  s, current amplitude = 0.777 of peak; at t = 0.2  s, current amplitude = 1.01 of peak. The maximum ‘overswing’ is 2.5%. This system is much simpler and cheaper than the distributed system.

36. Neil Marks; ASTeC, CI.‘AC Magnets’; CI School 2013. An EMMA kicker magnet – ferrite cored lumped system.

37. Neil Marks; ASTeC, CI.‘AC Magnets’; CI School 2013. EMMA Injection Kicker Magnet Waveform

38. Neil Marks; ASTeC, CI.‘AC Magnets’; CI School 2013. 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; 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

39. Neil Marks; ASTeC, CI.‘AC Magnets’; CI School 2013. 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.

40. Neil Marks; ASTeC, CI.‘AC Magnets’; CI School 2013. Comparison of the two types. Classical:Eddy current: Excitationd.c or low frequency pulse;pulse at > 10 kHz; Coilsingle turn includingsingle or multi-turn on front septum;backleg, room for large cross section; Coolingcomplex-water spiralsheat generated in in thermal contact with shield is conducted to septum;base plate; Yokeconventional steelhigh frequency material (ferrite or thin steel lams).

41. Neil Marks; ASTeC, CI.‘AC Magnets’; CI School 2013. Example Skin depth in material: resistivity  ; permeability  ; at frequency  is given by:d =  (2  /  µµ 0 ) Example: EMMA injection and extraction eddy current septa: Screen thickness (at beam height): 1 mm; " " (elsewhere) – up to10 mm; Excitation25 µs, half sinewave; Skin depth in copper at 20 kHz0.45 mm

42. Neil Marks; ASTeC, CI.‘AC Magnets’; CI School 2013. Location of EMMA septum magnets

43. Neil Marks; ASTeC, CI.‘AC Magnets’; CI School 2013. Design of the EMMA septum magnet Inner steel yoke is assembled from 0.1mm thick silicon steel laminations, insulated with 0.2  m coatings on each side.

44. Neil Marks; ASTeC, CI.‘AC Magnets’; CI School 2013. ‘Out of Vacuum’ designs. Benefits in locating the magnet outside the vacuum. But a (metallic) vessel has to be inserted inside the magnet -the use of an eddy current design (probably) impossible. eg the upgrade to the APS septum (2002): ‘The designs of the six septum magnets required for the APS facility have evolved since operation began in 1996. Improvements.. have provided better injection/extraction performance and extended the machine reliability...’ ‘Currently a new synchrotron extraction direct-drive septum with the core out of vacuum is being built to replace the existing, in-vacuum eddy- current-shielded magnet.’

45. Neil Marks; ASTeC, CI.‘AC Magnets’; CI School 2013. ‘New’ APS septum magnet. Synchrotron extraction septum conductor assembly partially installed in the laminated core.