AC Lattice Magnets: Design, Operation, and Power Supply Systems

1. A.C. Magnets (II) Neil Marks, CCLRC, Daresbury Laboratory, Warrington WA4 4AD. n.marks@dl.ac.uk

2. Philosophy • 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. Present an overview of the design and operation of power supply systems, both d.c. (for storage rings) and cycling (for cycling accelerators). • 4. Give a qualitative overview of injection and extraction techniques as used in circular machines. • 5. Present the standard designs for kicker and septum magnets and their associated power supplies.

3. Contents Contents • ‘Extension’ • Power supply systems – d.c. and a.c.; • Injection and extraction schemes; • Core Syllabus • Variations in design and construction for a.c. magnets; • Effects of eddy currents; • ‘Low frequency’ a.c. magnets • Coil transposition-eddy loss-hysteresis loss; • Properties and choice of steel; • Inductance in an a.c. magnet; • ‘Fast’ magnets; • Kicker magnets-lumped and distributed power supplies; • Septum magnets-active and passive septa;

4. 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  104A; • pulse voltages of many kV. Typical geometry:

5. Magnet & Power Supply • 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.

6. 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:

7. Mode of Operation • the first delay line is charged to V • by the d.c. supply; • the thyratron triggers, a voltages wave: V/2 propagates into magnet; • this gives a current wave of V/( 2 Z ) • propagating into the magnet; • the circuit is terminated by pure resistor Z, • to prevent reflection.

8. Physical assembly • Magnet: • Usually capacitance is introduced along the length of the magnet, which is split into many segments: ie it is a pseudo-distributed line

9. Physical assembly. • Power supply: • Can be: • a true ‘line’ (ie a long length of high voltage coaxial cable); • or a multi-segment lumped line. • These are referred to as ‘pulse forming networks’ (p.f.n.s) and are used extensively in ‘modulators’ for: • linacs; • radar installations.

10. Parameters • The value of impedance Z (and therefore the added distributed capacitance) is determined by the required rise time of current: • total magnet inductance = L; • capacitance added = C; • surge impedance Z0 = (L/C); • transit time (t) in magnet =  (LC); • so Z0 = L/t; • for a current pulse (I), V = 2 Z I ; = 2 I L / t . • The voltage (V/2) is the same as that required for a linear rise across a pure inductance of the same value – the distributed capacitance has not slowed the pulse down!

11. Suitability: • Strengths: • the most widely used system for high I and V applications; • highly suitable if power supply is remote from the magnet; • this system is capable of very high quality pulses; • other circuits can approach this in performance but not improve on it; • the volts do not reverse across the thyratron at the end of the pulse. • Problems: • the pulse voltage is only 1/2 of the line voltage; • the volts are on the magnet throughout the pulse; • the magnet is a complex piece of electrical & mechanical engineering; • the terminating resistor must have a very low inductance - problem!

12. Distributed power supply– lumped magnet I = (V/Z) (1 – exp (-Z t /L)

13. Example of such a kicker system • SNS facility (Brookhaven)– extraction kickers: • 14 kicker pulse power supplies & magnets; • operated at a 60 Hz • repetition rate; • kicks beam in 250 nS; • 750nS pulse flat top.

14. Extraction systems layout

15. Kicker p.f.n simulation model

16. Simulated current waveform

17. EEV Thyratron CX1925 EEV HV = 80kV Peak current 15 kA repetition 2 kHz Life time ~3 year

18. 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..

19. C Improvement on above The extra capacitor C improves the pulse substantially.

20. Resulting Waveform • Example calculated for the following parameters: mag inductance L = 1 mH; rise time t = 0.2 ms; resistor R = 10 W; 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 ms, current amplitude = 0.777 of peak; at t = 0.2 ms, current amplitude = 1.01 of peak. The maximum ‘overswing’ is 2.5%. This system is much simpler and cheaper than the distributed system.

21. 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

22. Multiple septa • These engineering problems can be partially overcome by using multiple septa magnets (the septa can get thicker as the beams diverge). • eg – KEK (3 GeV beam): • Operation: DC • Beam: H+ • Energy: 3.0 GeV • Field strength: 0.41067 T (SEPEX-1) • 0.75023 T (SEPEX-2) • 0.87418 T (SEPEX-3) • 1.00530 T (SEPEX-4) • Effective length: 0.9 m • Field flatness: +/- 0.1 %

23. ‘Opposite bend’ septa magnets • KEK also use ‘opposite bend’ septum magnets at 50 GeV:

24. 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.

25. Comparison of the two types. • Classical: Eddy current: • Excitation d.c or low frequency pulse; pulse at > 10 kHz; • Coil single turn including single or multi-turn on • front septum; backleg, room for • large cross section; • Cooling complex-water spirals heat generated in in thermal contact with shield is conducted to septum; base plate; • Yoke conventional steel high frequency material (ferrite or radio metal).

26. Example • Skin depth in material: resistivity r; • permeability m; • at frequency w • is given by: d = (2 r/wµµ0 ) • Example: SRS injection eddy current septum. • Screen thickness (at beam height): 1 mm; • " " (elsewhere) 10 mm; • Excitation 25 µs, • half sinewave; • Skin depth in copper at 20 kHz 0.45 mm

27. SPS fast extraction (450 GeV) The proposed extraction septum system will consist of six 3.2 m long magnets, operating at a field of about 1.1 T at 450 GeV. Peak field at 450 GeV/c: 1.078 T; Magnetic length 6 x 3.2 m; Kick at 450 GeV/c: 13.8mrad; Pulse duration: 250 ms; Septum thickness:`5 (Cu) + 1 (Fe) mm; Peak current at 450GeV/c 17.16 kA Peak voltage at 450 GeV/c: 3.40 kV; Type: eddy. Note: twin vacuum systems!

28. ‘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.’

29. ‘New’ APS septum magnet. Synchrotron extraction septum conductor assembly partially installed in the laminated core.