Method of beam extraction from a synchrotron by the instrumentality of multilayer Cu-Fe shield

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 multilayerCu-Feshieldcan be significantly reduced

6. Field perturbation vs. external magnetic field

7. Necessarycondition of minimal field perturbation f0(t) is a flux through a shield wall per unit of length In optimal case:

8. Shielding equation A – vector potential<s> – averageconductivity<m> – tensor of average relative permeability m0 –permeability of free space ║and ┴are parallel and perpendicular to layers. hCu – thickness of copper layershFe – thickness of iron layers

9. Estimation of f0(t) In the neighborhood of j=0: Dr – penetration depth of magnetic field

10. Magnetic field penetration into planar wall in case of linear rise of external field Bs – saturation field H0 – external field

11. Estimation of B0(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. — dipole — Cu-Fe shield — search coil

16. Measurement of optimal rise rate of external magnetic field

17. Maximum of magnetic field perturbation vs. rise rate of external magnetic field Optimal rise rate ofexternal magnetic field is 0.108 Tper 0.45 ms B0 – field at 0.45ms since the dipole is activated .

18. Measurement ofm(B) incase ofB<1.1Т Parameters oftoroidal coil: Average radius of core is 37,5 mm Effective area is 193mm2 Coil is 113 turns channel 1 – voltageon coil, channel 3 – voltage on shunt (Rsh=0.4 Ω )

19. Measurement ofm(B) in case of 2.3 T<B<2.9 T Parameters oftoroidal coil: Average radius of core is 20,5 mm Effective area is 33 mm2 Testcoil is40 turns Currentcoil is 188 turns channel 1– signal from current sensor ACS754SCB-200 channel 2 – signal fromcapacitance integrator (R=102.8 kΩ, С=0.195 µF )

20. Magneticpermeability 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 measurements numerical 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 isthe time since the dipole is activated measurements numerical simulations

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

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

25. Project of extractionchicane • vertical rms beam size is about 0.4 mm • horizontal rms beam size is 2.6 mm • βx=10 m • βy=20 m • Trajectory shift by kicker 20 mm

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

27. K0 K0 leads to orbitshift

28. K1 Betatron frequencies shift

29. K2 1) sextupole resonances 3my=2p ; 2mx+my =2p • 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 areresults of image the vacuum chamber in magnet gap.

31. Comparison with other extraction system from booster Project of extraction system 2.2 GeV. HIGS BoosterinDuke University, 1.2 GeV, vertical extraction, Lambertson septum Booster of SPEAR Storage Ring in Stanford Synchrotron Radiation Laboratory, 3.5 GeV, horizontal extraction, pulse Lambertson septum.

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 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 y – the distance to the centre of vacuum chamber

37. K0 by vacuum chambers

38. K1 by vacuum chambers