EMMA: Pulsed magnets

Kiril Marinov

MaRS group, ASTeC, Daresbury Laboratory

1

2. Outline

Septum magnet

Geometry and positioning

Modelling

Stray fields

Field quality

Kicker

Delay-line vs. inductive design

Modelling

3. Septum – formulation of the problem

Movable septum, translation in one direction + rotation

Vacuum vessel geometry is fixed

Large bending angle – 70o extraction , 65o injection

Limited space available (w=10 cm)

The available space needs to be used efficiently.

Positioning and geometry need to be carefully optimized.

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. Geometry II

Simple shape: coaxial arcs and lines

Rotation center

Translation

6. Hard edge model

β

δ

α

sinsin1 22

0

wc

EEEB

7. Thick septum with a small aperture

Incoming beam parallel to the polygon side 17.14 mm away;

w=102 mm, a=35mm

cAdvantage: 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. 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. “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. Vertical position

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

11. Results

200 injection/extraction scenarios considered for consistence with the septum geometry.

Both “phase-space painting” and “closed orbits” modes of operation

Bmax=0.85 T0<δ<7o

-7 <Translation<15 mmImax=16.5 kAL=0.19 μHVmax=403 V

12. Coil position

13. Coil position II

14. Field quality

t=10 μs t=12.5 μs

t=15 μst=17.5 μs

15. Eddy currents distribution

Eddy currents

Little or no current here

16. Eddy currents distribution II

Will go into the beam pipe, if necessary

Beam pipe + wing “box”; extra shielding

17. Kickers

Which type is suitable for EMMA?

Kicker magnets

Inductivemagnets

Delay-linemagnets

Easier to design and build.

Faster, but structurally and electrically complex.

18. Transmission-line model of a magnet

Voltage source l

hd

ZL(ω)Load

impedance

“Magnet”

Distributed inductance L [H/m] and capacitance C [F/m].

C

LZ 0

19. Transmission-line model: inductive magnet

Impedance )2exp(1

)2exp(1

0

0

0

0

0

iklZZZZ

iklZZZZ

ZZ

L

L

L

L

LCk

1) Inductive magnet 0LZ

115.0 lLCkl

70

109

mHL /3.3

pF/m C 340

ml 1.0

kliZZ tan0

...

31 2

2

lLC

LliZ

3105.7

Ll 3

Cl

Suitable for EMMA (ωl is small, fortunately…)

Limited to small ωl values.

“Ringing” (oscillations in the trailing edge of the current pulse).

E=0, no electric field in this magnet.

20. Transmission-line model: delay-line magnet

Impedance )2exp(1

)2exp(1

0

0

0

0

0

iklZZZZ

iklZZZZ

ZZ

L

L

L

L

LCk

Impedance matching: C

LZZL 0

0ZZ

All frequencies “see” the same impedance: frequency independent behaviour; “high” frequency.

Travelling voltage-current wave (Z0 is real); E and B are both non-zero!

h

d

ZHEE

Hc

eE

Bev

F

F

e

m

0

0

0

0 377

d

hZ

hI

dV

H

E0

Z0 needs to be as low as possible:

E needs to be taken into account.

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. Voltage evolution with timeTime=1 Time=100

Time=250 Time=400

PFN Magnet MagnetPFN

PFN Magnet PFN Magnet

23. Impedance

3.3 / , 340L H m C pF m

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.

0

0

2200 !

0.06

100

Bh LV kV

C

B T

Z

w=58 mm,

h=22 mm,

D=26.5 mm

R. B. Armenta et al, PAC’05 (2005)

0 12.5Z

Ferrite

24. Inductive kicker: window frame design

Max length 100 mm

Ferrite frame

Shims are important.

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=105 Ωm, f<100 MHz (“4E2”, page 142, Ferroxcube Data Handbook 2005)

Ferrite material available

B max=0.07 T

26. Kickers: magnetizing coil

Conductor spacing.

Conductor cross-section.

2 1I A

The shims are important.

27. Role of the shims

0.2 %

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

28. Role of the shims

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

12 %

29. Vertical plane

White areas B< 0.065 T or B> 0.075 T

Saturation

End effects

30. Kicker: parameters