Neil Marks; ASTeC, CI.‘AC Magnets’; CI School A.C. Magnet Systems Neil Marks, ASTeC, Cockcroft Institute, Daresbury, Warrington WA4 4AD, Tel: (44) (0) Fax: (44) (0)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Neil Marks; ASTeC, CI.‘AC Magnets’; CI School 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, > 10,000 >1,000 at B=1.8 T ,100 >160

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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