1. 1 Fixed Field Alternating Gradient (FFAG) Accelerator Part I Shinji Machida ASTeC/RAL 3rd March, 2008 The Cockcroft Institute Lecture Course

2. 2 Part I (Monday, 3rd March 2008) Accelerators in various fields –Three major uses of particle accelerators –Remark: particle and beam –Remark: stable and unstable particles –Why high energy frontier was synchrotron? –Why synchrotron light source was synchrotron? –Is a synchrotron for high beam power? –Beam power of accelerator –Future of high beam power accelerator. Evolution of accelerators –Different kinds of accelerator (1) linear accelerator –Different kinds of accelerator (2) conventional cyclotron (1) (2) –Different kinds of accelerator (3) betatron –Different kinds of accelerator (4) Thomas Azimuthal Varying Field cyclotron (1) (2) –Different kinds of accelerator (5) synchrocyclotron –Different kinds of accelerator (6) weak focusing synchrotron –Different kinds of accelerator (7) strong focusing (alternating gradient) synchrotron –Different kinds of accelerator (8) Fixed Field Alternating Gradient (FFAG) synchrotron –Different kinds of accelerator (9) AVF cyclotron –Different kinds of accelerator (1) summary –Accelerator for high beam power (1) beam power of accelerator –Accelerator for high beam power (2) future of high beam –Accelerator for high beam power (3) fixed or pulse B field –Accelerator for high beam power (4) weak or strong focusing –Accelerator for high beam power (5) possibility of high energy –Accelerator for high beam power (6) other considerations FFAG and early developments –FFAG basics (1) alternating gradient –FFAG basics (2) remark: alternating gradient and strong focusing –FFAG basics (3) constant tune –FFAG basics (4) cardinal conditions of a FFAG –FFAG basics (5) field profile –FFAG basics (6) simple case –FFAG basics (7) a way to realize AG –FFAG basics (8) another way (1) (2) –FFAG basics (9) comparison –MURA (1) birth –MURA (2) photo of MURA machines –MURA (3) remarkable outcome in accelerator physics –MURA (4) collider –MURA (5) closure New era of FFAG –PoP machine at KEK (1) aim –PoP machine at KEK (2) components –Gradient magnet (1) FDF triplet –Gradient magnet (2) modeling with 3D code –rf cavity (1) requirements –rf cavity (2) ferrite loaded cavity –rf cavity (3) magnetic Alloy cavity –rf cavity (4) core make by Magnetic Alloy –rf cavity (5) shunt impedance –Optics design (1) simplified model –Optics design (2) lattice functions –Optics design (3) when F and D are separated –Optics design (4) lattice functions –Optics design (5) modeling of spiral sector –Optics design (6) lattice functions –Commissioning (1) beam signal –Commissioning (2) tune measurement –Commissioning (3) synchrotron tune and beam position –Commissioning (4) remark Part II (Monday, 10th March 2008) FFAG developments in UK Applications Research subjects

3. 3 Accelerators in various fields

4. 4 Three major uses of particle accelerators Synchrotron light source ESRF, DIAMOND Brightness of light Ultimate goal is a beam as a point source. (or zero emittance.) Beam optics development. –Lattice –Stabilities High power source , K, factory, Neutron source Energy carried by a beam Large emittance to avoid multi particle effects High energy frontier LHC, ILC Energy of each particle Always a driving force of accelerator development. Small emittance is preferred. Accelerators in various fields (1)

5. 5 Remark: Particle and beam A beam is a group of particles confined in the small volume in 6-D phase space. Our machine is a “beam” accelerator, not a “particle” accelerator. –“particle” acceleration mechanism in the universe. –Laser driven acceleration: from a particle accelerator to a beam accelerator. Accelerators in various fields (2)

6. 6 Remark: Stable and unstable particles Accelerators used to accelerate stable (or long life) particles such as proton and electron. New challenge is to accelerate unstable (or short life) particles. For example, acceleration of muons. –Muon collider: high energy frontier –Neutrino factory: high power (intensity) source Accelerators in various fields (3)

7. 7 Why high energy frontier machine has been always a synchrotron? Repetitive use of rf cavities to increase energy. –Must be a circular type. –Linac is not efficient. Relatively small magnets. –Number of magnets tends to be large. –Cyclotron is out of question. High energy proton machine should be still a synchrotron (with superconducting magnet.) However –Synchrotron radiation from electron becomes significant and the next electron machine should be linear. Accelerators in various fields (4)

8. 8 Why synchrotron light source machine has been always a synchrotron? Repetitive use of rf cavities to maintain energy level. –Must be a circular type. –Need bending magnet to produce light Electron is ultra relativistic. –Cyclotron is out of question. However –Emittance blows up in a synchrotron even if emittance at the source is very small. –Deterioration of emittance suggests use of linac. –Instead of using rf cavities repetitively, use “rf energy” many time, which is Energy Recovery Linac (ERL). Accelerators in various fields (5)

9. 9 Is a synchrotron the best for high power source machine? First generation was cyclotron. –PSI (Swiss) and TRIUMF (Canada) have ~500 MeV cyclotron for meson production. Second generation was either synchrotron or linac plus storage ring. –ISIS (UK) uses 800 MeV proton synchrotron. –PSR (US) uses 800 MeV linac and storage ring. Trend is still the same. –J-PARC (Japan) is 3 GeV proton synchrotron under commissioning. –SNS (US) is 1 GeV linac and storage ring under commissioning. Accelerators in various fields (6)

10. 10 Beam power of accelerator Energy of each particle [GeV] Higher energy is preferable, but size should be moderate x Number of particle per beam [ppp] Enlarge aperture as much as possible x Repetition rate [Hz] Continuous operation is the best, but very high repetition is acceptable Low loss Keep accessibility Reliability Hardware failures cut integrated beam power Accelerators in various fields (7)

11. 11 Future of high beam power machine Type of accelerators depends on the needs of users, physics limitations, available technologies, and cost. –Physics limitations Synchrotron radiation Repulsive force among particles –Technical limitations(example) Maximum strength of magnets(6-10 T) Ramping rate of pulsed magnets (50 Hz) rf field gradient (50 kV/m in a few MHz) Modulation rate of rf frequency(1-10 kHz) Emittance from a source(1  mm mrad) High energy frontier machine (of electron) is now linac. Next generation synchrotron light source will be linac (or Energy Recovery Linac). What about high power beam accelerator? Accelerators in various fields (8)

12. 12 Evolution of accelerators

13. 13 Different kinds of accelerator (1) linear accelerator (linac) Sequence of rf accelerating structure –Cell length is proportional to –Synchrotron oscillations Evolution of accelerators (1)

14. 14 Different kinds of accelerator (2) conventional cyclotron (1) Repetitive use of rf acceleration. Energy is limited to about 12 MeV (Bethe and Rose) –Non-relativistic case –Relativistic case When B is constant,  varies. so that and so that and Evolution of accelerators (2)

15. 15 Different kinds of accelerator (2) conventional cyclotron (2) Focusing in both directions at the same time. –With field index, stability for horizontal and vertical requires When Bz decreases as radius. – F. Cole said If you went to graduate school in the 1940’s, this inequality was the end of the discussion of accelerator theory [1]. Evolution of accelerators (3)

16. 16 Different kinds of accelerator (3) betatron First use of pulsed magnet. –Ampere’s law –Equation of motion –Betatron principle Evolution of accelerators (4)

17. 17 Different kinds of accelerator (4) Thomas (or AVF) cyclotron (1) One way to overcome relativity –Increase B as orbit goes outward. –This makes vertical defocusing because field index n>0. Vertical focusing is obtained at the edge. –Sort of strong focusing. and n>0 vertical defocus n<0 vertical focus Evolution of accelerators (5)

18. 18 Different kinds of accelerator (4) Thomas (or AVF) cyclotron (2) Edge focusing y Bz xx – F. Cole said The problem with Thomas’ paper was that it was couched in very unfamiliar mathematics, … Nobody understood it at the time and it remained a mystery to most [1]. Evolution of accelerators (6)

19. 19 Different kinds of accelerator (5) synchrocyclotron Another way to overcome relativity –Modulate  as  increases. –Focusing in the both direction at the same time. –Only one momentum beam at a time. and p( ) t p t Only one beam exists at the same time. Many beam are accelerated simultaneously. Evolution of accelerators (7)

20. 20 Different kinds of accelerator (6) Weak focusing synchrotron The other way to overcome relativity. –Use pulsed magnet and frequency modulation. –Focusing in both directions at the same time. Cosmotron at BNL Evolution of accelerators (8)

21. 21 Different kinds of accelerator (7) strong focusing (alternating gradient) synchrotron Courant, Livingston, and Snyder invented alternating gradient focusing. –Beam size and therefore magnet size is considerably reduced. PS at CERN Evolution of accelerators (9)

22. 22 Different kinds of accelerator (8) fixed field alternating gradient (FFAG) Evolution of accelerators (10) What is advantage? –DC magnet is easier to operate. –Repetition rate can be high so the current become higher. –Beam current of synchrotron in early days was not enough. Price we have to pay –Larger magnets to accommodate orbit shift in horizontal direction. –Orbit shift can be minimized by using a high gradient magnet. Alternating gradient synchrotron can be operated with fixed field magnet ! –Synchrocyclotron with alternating gradient focusing or –AVF cyclotron with frequency modulation.

23. 23 Different kinds of accelerator (9) AVF cyclotron Proliferation in the 1960’s. –PSI cyclotron –TRIUMF –And many other small ones Evolution of accelerators (11) PSI cyclotron

24. 24 Different kinds of accelerator (10) summary Linac Push particles Cyclotron Repetitive use of linac Thomas cyclotron (only idea) Overcome relativistic effects by strong focusing (edge) Betatron Induction to push particles with pulsed magnets Synchrocyclotron Overcome relativistic effects by synchronized rf Synchrotron Overcome relativistic effects by pulsed magnet and synchronized rf AG synchrotron Reduce size of magnets by strong focusing (alternating gradient) FFAG Fixed magnet with strong focusing time AVF cyclotron Evolution of accelerators (12)

25. 25 Accelerator for high beam power (1) beam power of accelerator Energy of each particle [GeV] Higher energy is preferable, but size should be moderate x Number of particle per beam [ppp] Enlarge aperture as much as possible x Repetition rate [Hz] Continuous operation is the best, but very high repetition is acceptable Low loss Keep accessibility Reliability Hardware failures cut integrated beam power Evolution of accelerators (13)

26. 26 Accelerator for high beam power (2) future of high beam power machine Type of accelerators depends on the needs of users, physics limitations, available technologies, and cost. –Physics limitations Synchrotron radiation Repulsive force among particles –Technical limitations(example) Maximum strength of magnets(6-10 T) Ramping rate of pulsed magnets (50 Hz) rf field gradient (20 kV/m in a few MHz) Modulation rate of rf frequency(1-10 kHz) Emittance from a source(1  mm mrad) Evolution of accelerators (14)

27. 27 Accelerator for high beam power (3) fixed or pulsed B field Modulation of B field cannot be fast. e.g. 50 Hz of ISIS is the fastest. Modulation of freq. can be 1 kHz or more. Variable B (Fixed path) Fixed B (Variable path) Fixed frequencyBetatron e synchrotron Cyclotron Thomas cyclotron Microtron Variable frequencyp synchrotronSynchrocyclotron FFAG Evolution of accelerators (15) Energy of each particle [GeV] x Number of particle per beam [ppp] x Repetition rate [Hz]

28. 28 Accelerator for high beam power (4) weak or strong focusing Variable B (Fixed path) Fixed B (Variable path) Weak focusingWF synchrotron Betatron Cyclotron Synchrocyclotron Microtron Strong focusingSF synchrotronFFAG Thomas cyclotron Strong focusing can accommodate a higher number of particles with limited aperture. Evolution of accelerators (16) Energy of each particle [GeV] x Number of particle per beam [ppp] x Repetition rate [Hz]

29. 29 Accelerator for high beam power (5) possibility of high energy Variable B (Fixed path) Fixed B (Variable path) Weak focusingWF synchrotron Betatron Cyclotron Synchrocyclotron Microtron Strong focusingSF synchrotronFFAG Thomas cyclotron Because of larger orbit shift, higher energy (>1GeV) cyclotron is not realistic. Evolution of accelerators (17) Energy of each particle [GeV] x Number of particle per beam [ppp] x Repetition rate [Hz]

30. 30 Accelerator for high beam power (6) other considerations FFAG seem to be the best choice for a high beam power machine ! However, there are other considerations. –As a neutron source, large number of particles with less repetition (~10 Hz) is preferable. Need a storage ring if cyclotron (or linac) is a main accelerator. –Almost no development of FFAG until recently. No one wants to take a risk. Evolution of accelerators (18)

31. 31 FFAG and early developments EMMA is a little different from what I describe as FFAG here.

32. 32 FFAG basics (1) alternating gradient Use “Fixed Field” magnet like cyclotron. Gradient is determined by focusing condition, not by isochronism condition. Alternating gradient is a focusing scheme with both sign of gradient magnets, focusing and defocusing elements. horizontalvertical FFAG and early developments (1)

33. 33 FFAG basics (2) remark: alternating gradient and strong focusing Strong focusing weak focusing (-1<n<0) Thomas (AVF) cyclotron uses a combination of focusing (from the body) and defocusing (from the edge) elements to realize net focusing. Strong focusing synchrotron by Courant, Livingston and Snyder uses large gradient magnets with alternating sign. Alternating gradient is one way to realize strong focusing. –However, they are used in the same meaning. –There is even a FFAG without alternating gradient magnets ! FFAG and early developments (2)

34. 34 FFAG FFAG basics (3) constant tune Transverse tune has to be constant during acceleration. Same orbit Same focal length “cardinal condition” Conventional strong focusing synchrotron Qx Qy Tune diagram of 150 MeV FFAG Resonance in accelerator FFAG and early developments (3)

35. 35 FFAG basics (4) cardinal conditions of a FFAG Geometrical similarity   : average curvature  : local curvature : generalized azimuth Constancy of at corresponding orbit points Bz(r) r Gradient of high p Gradient of low p Orbit of low p Orbit of high p FFAG and early developments (4)

36. 36 FFAG basics (5) field profile Bz(r) r If the field profile has the shape of Cardinal condition is satisfied. FFAG and early developments (5)

37. 37 FFAG basics (6) simple case Radial sector type machine center Alternating magnet has opposite sign of bending. Bz(r) r r FFAG and early developments (6)

38. 38 FFAG basics (7) a way to realize AG Conventional strong focusing synchrotron Bending a beam in the same direction. focusingdefocusing FFAG Bending a beam in the opposite direction to change the sign. focusingdefocusing zz rr z r z r Bz FFAG and early developments (7)

39. 39 FFAG basics (8) another way (1) Radial sector type with edge focusing. machine center In practice, edge focusing is not strong enough. Bz(r) r r FFAG and early developments (8)

40. 40 FFAG basics (8) another way (1) Spiral sector type machine center Spiral angle gives stronger edge focusing. Bz(r) r FFAG and early developments (9)

41. 41 FFAG basics (9) comparison Thomas (AVF) cycFFAGStrong focus sync B fieldFixed Pulsed Strong focusBody and edgeAG or Body and edge Alternating Gradient TuneSmallLarge IsochronismYesNo RF freq.FixedVaried Duty100% (CW)LargeSmall Longitudinal focusing NoYes TuneChangeConstant FFAG and early developments (10)

42. 42 MURA (1) birth Birth of FFAG at Midwestern Universities Research Association (MURA) in 1950’s. Three inventors –Symon and Kerst in US –Ohkawa in Japan –Kolomensky in USSR They discussed FFAG as the main accelerator in Midwestern region of US. FFAG and early developments (11)

43. 43 MURA (2) Bohr Chandrasekhar 400 keV radial sector180 keV spiral sector 40 MeV two beam accelerator All are electron FFAGs. FFAG and early developments (12)

44. 44 MURA (3) remarkable outcome in accelerator physics Three Electron models were constructed. Accelerator physics issues Beam stacking. Hamiltonian theory of longitudinal motion. Useful colliding beams Storage ring Spiral sector geometry Lattice with zero dispersion and low beta section for colliding beams. Multiturn injection into a strong focusing lattice. First calculations of the effects of nonlinear forces in accelerators. First space charge calculations including effects of the beam surroundings. First experimental measurement of space charge effects. Theory of negative mass and other collective instabilities and correction systems. The use of digital computation in design of orbits, magnets and rf structures. Proof of the existence of chaos in digital computation Synchrotron radiation rings. [1] F. T. Cole, “A Memoir of the MURA years.” http://accelconf.web.cern.ch/AccelConf/c01/cy c2001/extra/Cole.pdf FFAG and early developments (13)

45. 45 MURA (4) collider Concept of a beam collider In one ring, a particle can rotate in both directions. Colliding point …… Head-On Accelerator. Another team of dealers in magnetic fields. Dr. Lawrence W. Jones of the University of Michigan and Tihiro Ohkawa of Tokyo University, told their colleagues about a new and cataclysmic kind of atom smasher. The most powerful one in operation at present is the Bevatron at Berkeley (6 billion electron volts), and a 25-Bev monster is under construction at Brookhaven National Laboratory on Long Island. These are rather puny little gadgets, think Jones and Ohkawa. The way to get real power is to force head-on collisions between high-speed particles. …… TIME, February 11, 1957 http://www.time.com/time/magazine/article/ 0,9171,809067-1,00.html FFAG and early developments (14)

46. 46 MURA (5) closure Closure of MURA because –Synchrotron turned out to be the best choice for high energy frontier machine. –Magnet fabrication was complicated. No tool to model 3D magnetic fields. –RF cavities was not matured enough for high repetition and high gradient with wide aperture. Activities in 1980’s –Design study at Argonne (US), Juelich (Germany), and KEK (Japan). FFAG and early developments (15)

47. 47 New era of FFAG

48. 48 PoP machine at KEK (1) aim Proof of principle (proton acceleration with rf cavity) machine was constructed in 2000. Demonstrate acceleration from 50 keV to 500 keV in 1 ms. New era of FFAG (1)

49. 49 PoP machine at KEK (2) components Everything except extraction channel. New era of FFAG (2)

50. 50 Gradient magnet (1) FDF triplet Instead of using F and D magnets separately, combine FDF together (triplet). Gradient is made by gap shape. New era of FFAG (3) high momentum

51. 51 Gradient magnet (2) modeling with 3D code OPERA3D(TOSCA) models a magnet with complex shape accurately, less than 1% accuracy. In this example, gradient is made by distributed currents, instead of shaping a gap. New era of FFAG (4)

52. 52 rf cavity (1) requirements rf cavity must be –Broad band Cover frequency modulation of, for example, 1.5 to 5 MHz. –High gradient Make fast acceleration possible. –Large aperture Especially in horizontal to accommodate orbit shift. New era of FFAG (5)

53. 53 rf cavity (2) ferrite loaded cavity is the air-cored inductance. depends on DC bias. B: magnetic flux density H: magnetic field New era of FFAG (6)

54. 54 rf cavity (3) Magnetic Alloy (instead of Ferrite) cavity Large permeability ~2000 at 5 MHz High shunt impedance (Efficient use of rf power) High curie temperature ~570 deg. Can sustain large rf power Thin tape ~18  m Any shape can be possible Q is small ~1 Do not need tuning of resonant frequency New era of FFAG (7)

55. 55 rf cavity (4) core made by Magnetic Alloy tape Wide aperture to accommodate orbit shift. New era of FFAG (8) Difficult to make a large ferrite core.

56. 56 rf cavity (5) shunt impedance (efficiency of a cavity) Frequency (MHz) In the range of operation, shunt impedance is not flat. However, tuning is still not necessary. New era of FFAG (9)

57. 57 Optics design (1) simplified model Edge focusing From the center of F to the center of drift New era of FFAG (10)

58. 58 Optics design (2) lattice functions New era of FFAG (11) With the approximation, synchrotron optics code such as MAD can calculate lattice functions (for fixed momentum).

59. 59 Optics design (3) when F and D are separated New era of FFAG (12) Edge focusing From the center of F to the center of D

60. 60 Optics design (4) lattice functions New era of FFAG (13) This example uses the identical magnet for F and D with opposite currents. A beam can rotate in either direction.

61. 61 Optics design (5) modeling of spiral sector New era of FFAG (14) Spiral optics is nothing special. Proper modeling of edge with only F magnet gives lattice functions. Edge focusing in MAD format

62. 62 Optics design (6) lattice functions New era of FFAG (15) One edge gives focusing and another edge gives defocusing. Lattice function is asymmetric.

63. 63 less charge Commissioning (1) beam signal New era of FFAG (16) more charge beam Beam position monitor tells total charge position time structure Frequency analysis gives tune. kHz

64. 64 Commissioning (2) tune measurement New era of FFAG (17) Keeping the total bending angle same, change the strength of F and D. F D Vertical focusing should be sensitive to F/D because of edge effects.

65. 65 Commissioning (3) synchrotron tune and beam position synchrotron oscillation frequencyradius position New era of FFAG (18) With acceleration, synchrotron oscillation frequency and radial position move.

66. 66 Commissioning (4) remark It is nice to have such a small and “homemade” accelerator. –Easy to operate but still have all aspects of accelerator. EMMA at Daresbury will be a gadget every one can play with ! New era of FFAG (19) EMMA PoP FFAG at KEK