Accelerator Magnets

1. Accelerator Magnets Peter Ostroumov With significant contribution from Dr. Alexander Plastun November 20, 2018

2. Content • Room temperature magnets • Types • Application • Requirements • Power supplies • Design of magnets • Superconducting magnets • Super ferric • Ironless P. Ostroumov, Lecture 26 RT Magnets

3. Charged particle in magnetic field • Lorentz force in magnetic field • Magnetic rigidity of particles P. Ostroumov, Lecture 26 RT Magnets

4. Ampere law • Magnetic field of current I in vacuum P. Ostroumov, Lecture 26 RT Magnets

5. Units P. Ostroumov, Lecture 26 RT Magnets

6. Magnitude of magnetic field • FRIB • SC solenoids up to 8 T • SC magnets (with iron) ~2.2 T • RT quads, dipoles ~1.7 T P. Ostroumov, Lecture 26 RT Magnets

7. Types of magnets • Dipoles • Quadrupoles • Sextupoles • Octupoles • Correctors: small dipole magnets • Septum magnets • Kickers • Solenoids • Undulators/wigglers • Combined function magnets P. Ostroumov, Lecture 26 RT Magnets

8. There are several types of magnets found in synchrotrons and transfer lines – based on technology P. Ostroumov, Lecture 26 RT Magnets

9. Optics analogy P. Ostroumov, Lecture 26 RT Magnets

10. Dipole • The dipole magnet has two poles, a constant field and steers a particle beam. Using the right hand rule, the positive dipole steer the rotating beam toward the left. N S P. Ostroumov, Lecture 26 RT Magnets

11. Quadrupole • The quadrupole magnet has four poles. The field varies linearly with the distance from the magnet center. It focuses the beam along one plane while defocusing the beam along the orthogonal plane. An F or focusing quadrupole focuses the particle beam along the horizontal plane. P. Ostroumov, Lecture 26 RT Magnets

12. Sextupole • The Sextupole Magnet has six poles. The field varies quadratically with the distance from the magnet center. It’s purpose is to affect the beam at the edges, much like an optical lens which corrects chromatic aberration. An F sextupole will steer the particle beam toward the center of the ring. Note that the sextupole also steers along the 60 and 120 degree lines. P. Ostroumov, Lecture 26 RT Magnets

13. In synchrotrons/transfer lines magnets the B field as seen from the beam is usually expressed as a series of multipoles • R is the aperture radius • n=1, dipole • n=2, quadrupole • n=3, sextupole • n=4, octupole P. Ostroumov, Lecture 26 RT Magnets

14. Each multipole term corresponds to a magnetic flux distribution, which can be added up P. Ostroumov, Lecture 26 RT Magnets

15. The field profile in the horizontal plane follows a polynomial expansion P. Ostroumov, Lecture 26 RT Magnets

16. Injection into synchrotron • See Y. Hao lecture on synchrotrons Bumped beam P. Ostroumov, Lecture 26 RT Magnets

17. Septum magnet • Due to limited space for the coil, septum magnets operate at low field, small kick on beam orbit P. Ostroumov, Lecture 26 RT Magnets

18. Injection/extraction from synchrotron, Lambertson magnet • Field strength in Lambertson magnet is higher than in septum • Frequently Lambertson magnet is used in combination with septum magnet • Septum – small angle, provides more distance to circulating orbit at the location of Lambertson magnet • Apply Lambertson magnet after the septum • Cons: there is a stray magnetic field effecting the circulating beam, should be included into beam dynamic calculations • See Y. Hao lecture on synchrotrons P. Ostroumov, Lecture 26 RT Magnets

19. Magnet design • Yoke design • Provide higher field at lower coil currents • Reduce weight of the yoke • Use proper steel • Reduce yoke saturation effects • Hysteresis and Magnet Cycling • Reduce fringe field effects • Reduce eddy currents if needed • Improve field uniformity / linearity • Create simple mechanical design (easy to manufacture, assembly and align on axis) • Coil design • Provide high current density • Provide sufficient cooling of the coils, water flow calculations/simulations • Use proper wire cross-section • Design of the current and water supply and returns • Evaluate inductance and stored energy P. Ostroumov, Lecture 26 RT Magnets

20. Magnets DC AC Non-Laminated Yoke Permanent Magnet Laminated Yoke to avoid eddy currents P. Ostroumov, Lecture 26 RT Magnets

21. Lamination, Eddy current in AC magnets • Lamination is applied to minimize magnetic flux that reduces electric current in AC magnets • Heat is ~I2R • Laminated magnets are used in all synchrotrons P. Ostroumov, Lecture 26 RT Magnets

22. Yoke design P. Ostroumov, Lecture 26 RT Magnets

23. Ampere’s Law for a dipole magnet How much current and how many turns do we need to create the desired B-field? YOKE I – coil current N – number of turns TIP COIL COIL GAP g TIP YOKE P. Ostroumov, Lecture 26 RT Magnets

24. Material properties in CST (Computer Simulation Technology) CST has a material library: BH-curve μH-curve μ >> 1 Typical range A lot of materials are already imported, but you can create your own material. Nonlinear material properties are supported. Hysteresis is not supported! P. Ostroumov, Lecture 26 RT Magnets

25. CST model of dipole magnet Real magnet geometry is more complicated, details are important. Simulations are used for magnet design to get accurate result. Solution of nonlinear problem iteratively converges. Geometry of the yoke is created from scratch, from drawings or imported as a 3D CAD model. Yoke COIL Poisson’s equation for magnetostatics: COIL Sector dipole magnet 3D tetrahedral mesh P. Ostroumov, Lecture 26 RT Magnets

26. Simulation results H=B/μ B μ B P. Ostroumov, Lecture 26 RT Magnets

27. Good Field Region In a simple case: - field at the beam trajectory. If one includes the fringe field effects: GOOD FIELD REGION s – path of a particle P. Ostroumov, Lecture 26 RT Magnets

28. Saturation effects – different distribution at high currents In a mid-plane B0 [T] Current [A] Near the pole tip Saturated edges P. Ostroumov, Lecture 26 RT Magnets

29. Field corrections 1. Tip profile (Rogowskiprofile) 2. Shims (cyclotron magnet) 3. Trim coils (sector cyclotron) P. Ostroumov, Lecture 26 RT Magnets

30. Coil design P. Ostroumov, Lecture 26 RT Magnets

31. Coil parameters Coil power P: Current density j = I/a: Air-cooled coils: < 2 A/mm2 ρ – conductor material resistivity [Ωm] l – average turn length Water-cooled coils: < 10 A/mm2 Na=fA f – coil packing fraction ≈ 0.5-0.9 Conductor net cross-sectional area a [m2] for copper, ρ ≈ 1.86 × 10−8 Ω m at T = 40◦ C P. Ostroumov, Lecture 26 RT Magnets

32. Types of coils P. Ostroumov, Lecture 26 RT Magnets

33. These are the most common types of resistive dipoles P. Ostroumov, Lecture 26 RT Magnets

34. Example of coil cross-section - electrical joints 9 X 12 = 108 turns Coil cross-section Current supply Pancake coils Isolation 6 parallel circuits per each coil water return Current return 181.8 mm water supply P. Ostroumov, Lecture 26 RT Magnets

35. Current carrying wires in magnetic field • Currents with the same charge travelling in the same direction attract. • Currents with opposite charge travelling in the same direction repel. • Currents with the same charge travelling in the opposite direction repel. • Currents with the opposite charge travelling in the opposite direction attract. • The forces are not very high in room temperature coils and can be stabilized with a cable structure itself • In superconducting magnets these forces become large and should be taken into account in the SC magnet design P. Ostroumov, Lecture 26 RT Magnets

36. Cooling calculation (example) Initial data: - Reynolds number, defines the flow regime. If Re < 2300 – laminar flow, Re > 2900 – turbulent flow. - turbulent flow regime is needed for efficient cooling - water flow velocity, should not exceed 3 m/s to avoid channel erosion - kinematic viscosity of water - cooling channel diameter Calculation: GOAL: To find the proper number of circuits and wire size, which satisfy the requirements (pressure drop, temperature rise and water flow). - friction factor - pressure drop per each circuit - water temperature rise - water flow per each circuit P. Ostroumov, Lecture 26 RT Magnets

37. Cooling characteristics Usually the only parameter, which can be varied in a cooling system is waterflow (by a valve). ΔP can not exceed the available pressure, provided by the pump P. Ostroumov, Lecture 26 RT Magnets

38. Magnet power supplies • DC power supplies • High current, low voltage • Up to ~kA, Up to ~100 V • AC power supplies • Sine-wave • Programmable • Several kA and kV Separator for Capture Reactions (SECAR) Power supplies Magnets, quadrupoles P. Ostroumov, Lecture 26 RT Magnets

39. Permanent magnets Hysteresis loop BR – remanence, residual field at zero current! HC - coercive field It is desirable that the material have a high remanence for the maximum possible flux density in a circuit. Another goal is a high coercive field HC, so that the permanent magnet will not be easily demagnetized. The maximum product (BH)max is therefore a good figure of merit. Magnetic materials for yokes are called soft, materials for PM are called hard. Alexander Plastun

40. Permanent magnets Alexander Plastun

41. Ampere’s Law for PM PM - load line in plot Alexander Plastun

42. Permanent Magnets for Accelerators Halbach PMQs PM Undulator Hybrid PMQ ITEP PMQ Alexander Plastun

43. Undulator magnets • Electrons radiate light in the magnetic field P. Ostroumov, Lecture 26 RT Magnets

44. References Applied Electromagnetism: Magnet and RF-Cavity Design, USPAS Course by Mau Lopes and Jeremiah Holzbauer, Fermilab http://uspas.fnal.gov/materials/16Austin/austin-magnets.shtml 2) Iron Dominated Electromagnets Design, Fabrication, Assembly and Measurements, SLAC-R-754, by Jack Tanabe http://www.slac.stanford.edu/cgi-wrap/getdoc/slac-r-754.pdf 3) Field Computation for Accelerator Magnets, Stephan Russenschuck, WILEY-VCH Verlag GmbH & Co. KGaA https://onlinelibrary-wiley-com.proxy2.cl.msu.edu/doi/book/10.1002/9783527635467 4) Superconducting magnets http://etodesco.web.cern.ch/etodesco/uspas/uspas.html P. Ostroumov, Lecture 26 RT Magnets