1. EMMA: Pulsed magnets Kiril Marinov MaRS group, ASTeC, Daresbury Laboratory 1

2. 2. Outline  Septum magnet  Geometry and positioning  Modelling  Stray fields  Field quality  Kicker  Delay-line vs. inductive design  Modelling

3. 3. Septum – formulation of the problem  Movable septum, translation in one direction + rotation  Vacuum vessel geometry is fixed  Large bending angle – 70 o extraction, 65 o injection  Limited space available (w=10 cm)  The available space needs to be used efficiently.  Positioning and geometry need to be carefully optimized.

4. 4. Septum geometry w a Determine optimum values for w and a based on “real” injection/extraction data. Magnetic “steel” Coil Eddy-current screen

5. 5. Geometry II Simple shape: coaxial arcs and lines Rotation center Translation

6. 6. Hard edge model β δ α

7. 7. Thick septum with a small aperture Incoming beam parallel to the polygon side 17.14 mm away; w=102 mm, a=35mm c Advantage: Smaller field (current): smaller stray field Disadvantages Negative rotation angle Poor beam clearance C=2.5 mm Septum wall and wing too close to the vacuum vessel

8. 8. Thick septum with large aperture Incoming beam parallel to the polygon side 17.14 mm away; w=102 mm, a=70 mm Improved clearance C≈15 mm c Negative rotation angle, bigger in absolute value; Septum wall and wing too close to the vacuum vessel Larger pole area requires higher voltage; Using the largest possible magnet “that still fits in the box” is not the solution.

9. 9. “Thin” septum will “small” aperture Incoming beam parallel to the polygon side 17.14 mm away; w=80mm, a=35mm Positive rotation angle c Good beam clearance C>15 mm Longer wing can be used. Requires stronger field (current); stronger stray field Advantages: Disadvantage

10. 10. Vertical position The same incoming beam requires different “horizontal” position, rotation and magnetic field, depending on the septum “vertical” position.

11. 11. Results  200 injection/extraction scenarios considered for consistence with the septum geometry.  Both “phase-space painting” and “closed orbits” modes of operation B max =0.85 T 0<δ<7 o -7 <Translation<15 mm I max =16.5 kA L=0.19 μH V max =403 V

12. 12. Coil position

13. 13. Coil position II

14. 14. Field quality t=10 μs t=12.5 μs t=15 μs t=17.5 μs

15. 15. Eddy currents distribution Eddy currents Little or no current here

16. 16. Eddy currents distribution II Will go into the beam pipe, if necessary Beam pipe + wing  “box”; extra shielding

17. 17. Kickers Which type is suitable for EMMA? Kicker magnets Inductive magnets Delay-line magnets Easier to design and build. Faster, but structurally and electrically complex.

18. 18. Transmission-line model of a magnet Voltage source l h d ZL(ω)ZL(ω) Load impedance “Magnet” Distributed inductance L [H/m] and capacitance C [F/m].

19. 19. Transmission-line model: inductive magnet  Impedance 1) Inductive magnet  Suitable for EMMA ( ω l is small, fortunately…)  Limited to small ω l values.  “Ringing” (oscillations in the trailing edge of the current pulse).  E=0, no electric field in this magnet.

20. 20. Transmission-line model: delay-line magnet  Impedance  Impedance matching:  All frequencies “see” the same impedance: frequency independent behaviour; “high” frequency.  Travelling voltage-current wave (Z 0 is real); E and B are both non-zero!  Z 0 needs to be as low as possible:  E needs to be taken into account.

21. 21. Delay-line magnet: power supply Initial voltage distribution.  An impedance-matched line (PFN) is charged to a high voltage.  A voltage-current wave is then “launched” by closing the switch.

22. 22. Voltage evolution with time Time=1 Time=100 Time=250 Time=400 PFNMagnet PFN Magnet PFN Magnet

23. 23. Impedance  Voltage on the magnet is only a half of the source voltage.  Both forward and backward waves of equal amplitude.  Backward wave reflected upon reaching the open end of the circuit. w=58 mm, h=22 mm, D=26.5 mm R. B. Armenta et al, PAC’05 (2005) Ferrite

24. 24. Inductive kicker: window frame design Max length 100 mm Ferrite frame Shims are important.

25. 25. Kickers: geometry and ferrite material HV source connected here 70 ns current pulses! f=7 MHz Ferrite data: Type NiZn, Bs=0.35 T; Hc=400A/m, ρ=10 5 Ωm, f<100 MHz (“4E2”, page 142, Ferroxcube Data Handbook 2005) Ferrite material available B max =0.07 T

26. 26. Kickers: magnetizing coil Conductor spacing. Conductor cross- section. The shims are important.

27. 27. Role of the shims 0.2 % 0.2 % flux density variation in the presence of the shims.

28. 28. Role of the shims 12 % flux density variation in the absence of the shims. 12 %

29. 29. Vertical plane White areas B 0.075 T Saturation End effects

30. 30. Kicker: parameters