1. Method of beam extraction from a synchrotron by the instrumentality of multilayer Cu-Fe shield Bondarenko Alexey

2. Classic method of beam extraction from a synchrotron

3. Type of septum-magnets Lambertson septum. Magnetic field is perpendicular to septum sheet which consists of ferromagnetic material (typically iron). Pulse septum. Magnetic field is parallel to septum sheet which consists of high-conductivity material (typically copper).

4. Method of beam extraction by the instrumentality of magnetic shield

5. Main idea: Perturbation of pulse external magnetic field by multilayer Cu-Fe shield can be significantly reduced

6. Field perturbation vs. external magnetic field

7. Necessary condition of minimal field perturbation In optimal case :   (t) is a flux through a shield wall per unit of length

8. Shielding equation A – vector potential  – average conductivity    – tensor of average relative permeability   –  permeability of free space ║ and ┴ are parallel and perpendicular to layers. h Cu – thickness of copper layers h Fe – thickness of iron layers

9. Estimation of  0 (t) In the neighborhood of   r – penetration depth of magnetic field

10. Magnetic field penetration into planar wall in case of linear rise of external field B s – saturation field H 0 – external field

11. Estimation of B 0 (t)

12. Numerical simulation of magnetic field penetration into shield wall The flux flowing through the multilayer copper–iron shield wall per unit of length depending on time and rise rate of external magnetic field.

13. Numerical simulation of field perturbation vs. rise rate of external magnetic field elliptical Cu-Fe shield: outer half-axes 11 and 17 mm, external magnetic field increase linearly from 0 to 0.5 T

14. Measurement of magnetic field perturbation by Cu-Fe shield Magnetic shield consists of 12 iron and 12 copper layers. Thickness of iron layer is 0.08 mm, thickness of copper layer is 0.1 mm.

15. — search coil — Cu-Fe shield — dipole

16. Measurement of optimal rise rate of external magnetic field

17. Maximum of magnetic field perturbation vs. rise rate of external magnetic field B 0 – field at 0.45 ms since the dipole is activated. Optimal rise rate of external magnetic field is 0.108 T per 0.45 ms

18. Measurement of  (B) in case of B<1.1 Т channel 1 – voltage on coil, channel 3 – voltage on shunt (R sh =0.4 Ω ) Parameters of toroidal coil: Average radius of core is 37,5 mm Effective area is 193 mm 2 Coil is 113 turns

19. Measurement of  (B) in case of 2.3 T<B<2.9 T channel 1 – signal from current sensor ACS754SCB-200 channel 2 – signal from capacitance integrator (R=102.8 kΩ, С=0.195 µF ) Parameters of toroidal coil: Average radius of core is 20,5 mm Effective area is 33 mm 2 Test coil is 40 turns Current coil is 188 turns

20. Magnetic permeability vs. magnetic induction was measurement

21. The distribution of the field perturbation near the magnetic shield in the dipole centre x is the distance to the shield centre and t is the time since the dipole is activated measurementsnumerical simulations

22. The distribution of the field perturbation near the magnetic shield (40 mm from the dipole centre) x is the distance to the shield centre and t is the time since the dipole is activated measurementsnumerical simulations

23. The distribution of the field perturbation near the magnetic shield (55 mm from the dipole centre) x is the distance to the shield centre and t is the time since the dipole is activated measurementsnumerical simulations

24. Project of 2.2 GeV booster Lattes functions of a booster half-ring Parameters of extraction kicker: Voltage 50 kV Distance between plates 27 mm Angle 1.7 mrad

25. Project of extraction chicane vertical rms beam size is about 0.4 mm horizontal rms beam size is 2.6 mm β x =10 m β y =20 m Trajectory shift by kicker 20 mm

26. Field perturbation by Cu-Fe shield y - the distance to the shield centre  B – field perturbation

27. K0K0 K 0 leads to orbit shift

28. K1K1 Betatron frequencies shift

29. K2K2 1)sextupole resonances 3  y =2  2  x +  y =2  2)additional chromatism, maximum dispersion in chicane D≈5cm

30. Field perturbation by vacuum chambers Time of field rise is 1.5 ms. In case of cylindrical vacuum chamber field perturbation is minimal because: Walls of cylindrical vacuum chamber can be made thinner. Field perturbation in cylindrical vacuum chamber by homogenous magnetic field is homogenous. Higher multipoles are results of image the vacuum chamber in magnet gap.

31. Comparison with other extraction system from booster HIGS Booster in Duke University, 1.2 GeV, vertical extraction, Lambertson septum K0K0 K1K1 K2K2 00.02 m -1 4 m -2 Booster of SPEAR Storage Ring in Stanford Synchrotron Radiation Laboratory, 3.5 GeV, horizontal extraction, pulse Lambertson septum. K0K0 K1K1 K2K2 0.2 mrad0.005 m -1 ? Project of extraction system 2.2 GeV. K0K0 K1K1 K2K2 0.3 mrad0.01 m -1 5 m -2

32. Numerical simulation of beam extraction Beam loss in % depends on betatron phase incursion per one turn

33. Conclusion It was shown that in case of external magnetic field linear rise the rate of magnetic flux penetration into multilayer copper-iron shield wall is constant. This effect can be used for minimization of magnetic field perturbation by multilayer copper-iron shield. The prototype of multilayer copper-iron shield was made. Measurement and numerical simulation of magnetic field perturbation by shield were performed. The measurement confirms correctness of method and model which are used for simulation of field perturbation. The numerical simulation and analytical estimation of beam dynamics under the influence of field perturbation by multi- layer Cu-Fe shield prove possibility of using the magnetic shield for extraction from synchrotron.

34. Particle coordinates transformation per one turn

35. Calculation of field perturbation by vacuum chambers using image method.

36. Field perturbation in vacuum chambers y – the distance to the centre of vacuum chamber diameter is 110 mm, thickness is 1mm, located at in first and second dipole diameter is 75 mm, thickness is 1,5 mm, located at in third and fourth dipole

37. K 0 by vacuum chambers

38. K 1 by vacuum chambers