Synchrotron

1. Synchrotron • After the cyclotron, the next idea was to constrain the particles to a constant r and accelerate them with RF fields • Both the B field and the frequency (velocity) will increase • Oliphant (Australia) first developed the idea but it was classified • McMillan first published the idea, named it the synchrotron, and proposed to build one • Later Oliphant tried to build one in England but ran out of funds and graduate students • In the US, Berkeley (Bevatron) and Brookhaven (Cosmotron) raced to build one • BNL won

2. Bending • Bending in a synchrotron is provided by dipole magnets • The LHC circumference is ~27 km • Packing fraction of ~64% gives r~2.8 km • Thus B needed for p=7 TeV is ~8.3 T • The use of superconducting magnets using superfluid He at 1.8K are needed to reach this field • Final magnet current is 11850 A • Bending achieved by 1232 15-m dipoles

3. Bending • LHC dipoles

4. Bending

5. Strong Focusing • Modern accelerators are possible because of strong focusing • Simply a name given to alternating magnetic field gradients that now are provided by rotated quadrupoles • Invented by Courant, Livingston and Snyder from BNL • But actually patented several years earlier by Christofilos, a Greek elevator engineer! • Who went on to develop the first fusion machine at Livermore even though fusion was classified at the time • Also proposed ELF waves for communication with submarines

6. Strong Focusing • By rotating two quadrupoles through p/2 we produce a net focusing effect in the transverse direction

7. Strong Focusing • A good analogy comes from optics • Consider two lenses with focal lengths f1 and f2

8. Strong Focusing • In the case of quadrupoles, we define a strength k

9. Longitudinal Motion • In a synchrotron, the particle’s momentum is incremented on each turn by a precise voltage that will keep pace with the increasing magnetic field • The frequency is just 1/period

10. Longitudinal Motion • A synchronous particle is one that always arrives at the desired phase lag fs on the flank of the rising RF wave (particle A) • For this to occur the accelerating RF frequency must be an integer multiple of f • h is called the harmonic number • Chosen to make RF high in a convenient band for the cavity and electronics • h for the LHC is 35460, RF = 400 MHz • The accelerator has 35460 buckets in which a particle could be located and arrive synchronously

11. Longitudinal Motion • Phase stability is what keeps the beam together longitudinally

12. Longitudinal Motion • Phase stability is what keeps the beam together longitudinally • Early particles at N1 get a lower kick and arrive later next turn • Late particles at M1 get a higher kick and arrive earlier next turn

13. Longitudinal Motion • The non-synchronous particle will oscillate about the synchronous one • The longitudinal phase space looks like DE f

14. Transverse Motion • Beam enters the synchrotron as a bundle of trajectories spread about an ideal orbit • Unless corrected, the beam particles would naturally leave the beampipe • A restoring field is used that causes the beam to oscillate about the ideal orbit

15. Transverse Motion • Standard LHC lattice cell looks like

16. Transverse Motion • The previous structure is called FODO • Focus – Drift space – Defocus – Drift space • The envelope of oscillations follows a function called b(s) • b(s) has units of length but the units bear no direct relation to the beam size • The particles do not follow b(s) but rather oscillate within them in the form of a modified sinusoid

17. Transverse Motion • We wrote down an expression for the angular deflection of a particle through a quadrupole

18. Transverse Motion • In a class on accelerator physics we would proceed to solve these using matrix formalism (Twiss matrix) • Nonetheless you can see that Hill’s equations are reminiscent of harmonic motion except k depends on the position around the accelerator

19. Transverse Motion • Let k be a constant (like in the constant gradient machines like the Cosmotron and Bevatron

20. Transverse Motion • Again assuming k is constant • It’s important that Q not be an integer or simple fraction because otherwise the particle will repeat its path in the accelerator and see the same field imperfections • The b function in an LHC cell varies between 30 and 180 m • These will build up into resonances and blow-up the beam

21. Electron source Bending magnet Accelerating structure Pulse modulator Klystron or magnetron Treatment head Medical Linac • Block diagram

22. Medical Linac

23. Treatment Head

24. Important Accessories • Wedges • Dynamic wedges • Blocks • Multileaf Collimator (MLC) • Electronic Portal Imaging (EPID)

25. Electron Accelerators • Wedges • 3 or more fixed wedges • auto-wedge • dynamic wedge • Modify dose distribution angle

26. Multileaf Collimator (MLC) • Used to define any field shape for radiation beams • Several variations to the theme: • different leaf widths (1cm to 0.4cm) • replaces collimators or additional to normal collimators

27. Intensity Modulation MLC pattern 1 • Achieved using a Multi Leaf Collimator (MLC) • The field shape is altered step-by-step or dynamically while dose is delivered MLC pattern 2 MLC pattern 3 Intensity map

28. IMRT • Multiple individual fields, each of them intensity modulated in two dimensions Linac based IMRT

29. IMRT • Continuous rotation of a one dimensional fan beam which consists of many beamlets which can be turned on or off Tomotherapy

30. Binary MLC Ring detector at exit side Helical Scanning Components of Helical Tomotherapy

31. Cyclotron • The first circular accelerator was the cyclotron • Developed by Lawrence in 1931 (for $25) • Grad student Livingston built it for his thesis • About 4 inches in diameter

32. Cyclotron • Principle of operation • Particle acceleration is achieved using an RF field between “dees” with a constant magnetic field to guide the particles

33. Cyclotron • Principle of operation

34. Cyclotron • Why don’t the particles hit the pole pieces? • The fringe field (gradient) provides vertical and (less obviously) horizontal focusing

35. Cyclotron • TRIUMF in Canada has the world’s largest cyclotron

36. Cyclotron • TRIUMF

37. Cyclotron • NSCL cyclotron at Michigan State

38. Cyclotron

39. Betatron • Since electrons quickly become relativistic they could not be accelerated in cyclotrons • Kerst and Serber invented the betatron for this purpose (1940) • Principle of operation • Electrons are accelerated with induced electric fields produced by changing magnetic fields (Faraday’s law) • The magnetic field also served to guide the particles and its gradients provided focusing

40. Betatron • Principle of operation Steel r Coil <B> B0 Vacuum chamber Bguide = 1/2 Baverage

41. Betatron • Principle of operation

42. Synchrotron • The next idea was to constrain the particles to a constant r and accelerate them with RF fields • Both the B field and the frequency (velocity) will increase • Oliphant (Australia) first developed the idea but it was classified • McMillan scooped the idea, named it the synchrotron and proposed to build one • Later Oliphant tried to build one but ran out of funds and graduate students • In the US, Berkeley (Bevatron) and Brookhaven (Cosmotron) raced to build one • BNL won

43. Bending • Recall from our study of making momentum measurements • The LHC circumference is ~27 km • Packing fraction of ~64% gives r~2.8 km • Thus B needed for p=7 TeV is ~8.3 T • The use of superconducting magnets using superfluid He at 1.8K are needed to reach this field • Final magnet current is 11850 A • Bending achieved by 1232 15-m dipoles

44. Bending • LHC dipoles

45. Bending

46. Longitudinal Motion • Phase stability is what keeps the beam together longitudinally

47. Longitudinal Motion • The non-synchronous particle will oscillate about the synchronous one • The longitudinal phase space looks like DE f

48. Longitudinal Motion • In a synchrotron, the particle’s momentum must be incremented on each turn by a precise voltage that will keep pace with the increasing magnetic field • The frequency is just 1/period

49. Longitudinal Motion • A synchronous particle is one that always arrives at the desired phase lag fs on the flank of the rising RF wave (particle A) • For this to occur the accelerating RF frequency must be an integer multiple of f • h is called the harmonic number • Chosen to make RF high in a convenient band for the cavity and electronics • h for the LHC is 35460, RF = 400 MHz • The accelerator has 35460 buckets in which a particle could be located and arrive synchronously

50. Transverse Motion • Beam enters the synchrotron as a bundle of trajectories spread about an ideal orbit • Unless corrected, the beam particles would naturally leave the beampipe • A restoring field is used that causes the beam to oscillate about the ideal orbit