1. 1 Muon Acceleration and FFAG Shinji Machida CCLRC/RAL/ASTeC NuFact06 Summer School August 20-21, 2006

2. 2 Content 1.Acceleration of muons Requirements Machine candidates 2.Evolution of FFAG 1950s Recent activities 3.FFAG as a muon accelerator 4.Design example of muon acceleration Reference (among others): –BNL-72369-2004, FNAL-TM-2259, LBNL-55478 –NuFactJ Design study report

3. 3 1 Acceleration of muons

4. 4 Requirement (1) Acceleration: as quick as possible –Life time of muon is ~2.2 us. –Example At momentum of 0.3 GeV/c Lorentz factor  ~3, Velocity  ~0.94. Flight path length ~2000 m –Lorentz factor helps once it is accelerated. Acceleration of muons

5. 5 Requirement (2) Acceptance: as large as possible –Muons are produced as secondary particles of protons –Cooling before acceleration if necessary Longitudinal emittance –dp/p ~ +-100% –dt or dx can be controlled by the width of primary proton: ~1 ns or 300 mm –dp/p * dx *  = 1000  mm at 0.3 GeV/c Transverse emittance –10 ~ 100  mm –30  mm normalized Acceleration of muons

6. 6 Machine candidate (1) Everyone knows modern high energy accelerator is synchrotron. Why not for muons? RCS (rapid cycling synchrotron) –Rapid (or fast) cycling means time required for acceleration from injection to extraction is short. –The most rapid cycling machine at the moment is ISIS at RAL, which has 50 Hz repetition rate. It still takes 10 ms to complete a whole cycle. ISISJ-PARC booster KEK-PS booster Fermilab booster AGS booster CPS booster Rep. rate50 Hz25 Hz20 Hz15 Hz~7.5 Hz1 Hz Acceleration of muons

7. 7 VRCS (Very rapid cycling synchrotron) In order to accelerate muons, repetition rate must be much faster. 4600 Hz design exists. (D.J.Summers, et.al.) Power supply and Eddy current are issues. dI/dt is too much. Acceleration of muons

8. 8 Machine candidate (2) If we cannot use AC (ramping) magnet, the alternative is to use only RF cavities. This is a linear accelerator. Linac (linear accelerator) –To accelerate muons to 20 GeV, the length becomes 4000 m with 5 MV/m accelerating cavity. Acceleration of muons

9. 9 Linac (continued) Linear collider assumes ~40 MV/m, why not for muons? –Muon emittance is much larger than electron emittance in linar collider. –To make acceptance larger, RF frequency must be relatively lower (200 MHz instead of 1.5 GHz) and field gradient is lower as well. Rule of thumb is that field gradient is proportional to square root of frequency. –Cost is another issue. Acceleration of muons

10. 10 Machine candidate (3) Synchrotron radiation is not a problem unlike electron. We can use bending arcs and reuse linac several times. RLA (recirculating linear accelerator) –Use 400 m linac with energy gain of 2 GeV 10 times, we can accelerate muons to 20 GeV. –Need 10 arcs to bend 10 different momentum separately because we give up ramping magnet. This machine looks like JLAB machine. Acceleration of muons

11. 11 RLA (continued) This was a baseline for muon acceleration until a few years ago. Switchyard becomes complex with more number of arcs and large muon emittance. Switchyard Acceleration of muons

12. 12 Machine candidate (4) Suppose if we can make orbit in bending arc less sensitive to momentum, the same arc can be used for different momentum. FFAG (fixed field alternating gradient) –Large field index in radial direction makes orbit shift small as a function of momentum. In accelerator terminology, dispersion function is small. –How small it should be? Beam size is something we can compare with. –Such an optics can be realized with high periodicity lattice. There is no clear separation of straight for acceleration and bending arc. Acceleration of muons

13. 13 FFAG (continued) Easy to understand with alternative bending. Alternative bending with finite field gradient gives alternative focusing. RF Acceleration of muons

14. 14 FFAG compared with others Cost effective. –Use RF cavity several times. Large acceptance. Machine is simple. –Fixed field magnet –No switchyard Accelerating gradient is relatively low or must be low. Acceleration of muons

15. 15 Acceleration of muons Summary Muons have to be accelerated as quick as possible against muon life time. Muon accelerator has to have large acceptance because a muon beam is produced as a secondary particle and emittance is huge. Several schemes are considered: VRCS, Linac, RLA, and FFAG. FFAG seems most feasible and cost effective. However, there is a problem to be solved (tomorrow I will mention). Requirement for muon collider is different. Although machine is similar, muon collider has to assume small emittance to increase luminosity. Acceleration of muons

16. 16 2 Evolution of FFAG

17. 17 Invention AG principle was invented in 1950s. –By Courant, Synder, Christofilos –Combination of convex (focusing) and concave (defocusing) elements makes net (strong) focusing. horizontal vertical FFAG principle was invented a few years later –By Ohkawa, Symon, Kolomenski Evolution of FFAG

18. 18 FFAG vs. ordinary AG synchrotron Fixed field (DC field) makes a machine simpler. –Cost of power supply for magnet is less. No synchronization between magnet and RF frequency. –Repetition rate is only determined by RF frequency change. –Repetition rate of o-AG is determined by ramping speed of magnet. Large momentum acceptance. –+-100% vs. +-1% Magnet size tends to be large. –Even it is small, orbit moves in horizontal direction. Evolution of FFAG

19. 19 MURA days (Midwest University Research Associate) In US, electron model was constructed at MURA. –Radial sector (400 keV) –Spiral sector (180 keV) –Two beam accelerator (collider) In Russia and Japan –Magnet design and fabrication. Evolution of FFAG

20. 20 Good old days at MURA Bohr Chandrasekhar 400 keV radial sector180 keV spiral sector 40 MeV two beam accelerator All are electron FFAG. Evolution of FFAG

21. 21 How does FFAG work? (field profile) Bending radius cannot be constant for all momentum. However, sharp rise of field makes orbit shift small. Focusing force can be constant if the field gradient increases with radius. Proposed field profile in radial direction is k >1 Bz(r) r Gradient of high p Gradient of low p Orbit of low p Orbit of high p Evolution of FFAG

22. 22 How does FFAG work? (transverse focusing) Alternating gradient can be realized by two ways. F(  ) has alternating sign. radial sector Add edge focusing. spiral sector Bz(r) r r + Evolution of FFAG

23. 23 How does FFAG work? (radial and spiral sector) machine center Radial sector consists of normal and reverse bends. Spiral sector use edge to have vertical focusing. Evolution of FFAG

24. 24 A way to change output energy Change k value by trim coils. Low momentum particle will reach the outer (extraction) orbit with low k. Bz(r) r k (high) k (low) injection radius extraction radius extraction momentum with high k. (Bz(r) h *r ex ) extraction momentum with low k. (Bz(r) l *r ex ) Evolution of FFAG

25. 25 “Two beam accelerator” Particles with the same charge can rotate in both directions. –Neighboring magnets have opposite sign. Colliding point Evolution of FFAG

26. 26 Three reasons to stop development Development is stopped in late 1960s because, 1.Magnet design was complicated. It was hard to get desired 3-D fields profile in practice. 2.No material for RF cavity. It requires high shunt impedance, high response time, and wide aperture. 3.Synchrotron was more compact and better choice for accelerator of high energy frontier. Evolution of FFAG

27. 27 Revival in late 1990s Technology becomes ready and enough reason to re-start development, 1.3-D calculation code such as TOSCA becomes available. Static fields can be modeled precisely. 2.RF cavity with Magnetic Alloy (FINEMET as an example) has most suitable properties for FFAG. 3.Growing demands for fast cycling, large acceptance, and high intensity in medium energy accelerator regime. Evolution of FFAG

28. 28 Magnet can be made with 3-D modeling code With an accuracy of 1%, 3-D design of magnet with complex shape becomes possible. Spiral shaped magnet for Kyoto-U FFAG (yoke with blue). Evolution of FFAG

29. 29 RF cavity with new material (MA)  QF remains constant at high RF magnetic RF (Brf) more than 2 kG Ferrite has larger value at low field, but drops rapidly. –RF field gradient is saturated. Magnetic Alloy also has High curie temperature ~570 deg. Thin tape (large core can be made) ~18  m Q is small (broadband) ~0.6 Evolution of FFAG

30. 30 Magnet for large acceptance From 1980s’, high intensity machine is demanded, not only high energy. Ordinary AG machine needs large aperture magnet to accommodate large emittance beam. Quad of J-PARC 3 GeV synchrotronMagnet of 150 MeV FFAG Evolution of FFAG

31. 31 First proton FFAG at KEK With all those new technology, proton FFAG (proof of principle) was constructed and a beam is accelerated in June 2000. Evolution of FFAG

32. 32 What we achieved from PoP FFAG Design procedure. –FFAG accelerator works as we expected. –3-D modeling of magnet is accurate enough. 1 ms acceleration (1 kHz operation) is possible. –MA cavity gives enough voltage. Enough acceptance in both longitudinal and transverse. Beam dynamics study –Multi-bucket acceleration –Acceleration with fixed frequency RF bucket –Resonance crossing, preliminary result Evolution of FFAG

33. 33 Evolution of FFAG summary FFAG is an old idea back to 1950s. FFAG concept was not fully appreciated because people wanted an accelerator for energy frontier. Technology was not ready yet. RF cavity with new material and 3D calculation tool make it possible to realize proton FFAG. Proof of principle machine demonstrates that FFAG machine works as it designed. Evolution of FFAG

34. 34 Exercise (1) Life time of a muon is 2.2  s. It becomes longer when it is accelerated and Lorentz boosted. Calculate what percentage of muons does survive when it is accelerated from 3 GeV/c to 20 GeV/c assuming two cases of average energy gain. One is 1 MeV/m and the other is 5 MeV/m. This exercise can be extended to more complex system. For example, assume there are two FFAGs, one from 3 GeV to 8 GeV, and the other from 8 to 20 GeV. Also assume the number of RF cavity is 5 times more in the bigger ring and RF cost is proportional to square of average energy gain. To make the cost of muons minimum, how we can choose the average energy gain (MeV/m) in the first and the second ring?

35. 35 Exercise (2) Explain how the two-beam accelerator, one beam rotates clockwise and the other does counter clockwise, becomes possible with FFAG lattice. Why not with other lattice, for example, an ordinary synchrotron. Colliding point

36. 36 Exercise (3) Consider non-scaling FFAG lattice consisting of focusing and defocusing quadrupole with strength k (+ for QF and - for QD). There is drift space in between and its distance is L. –Using thin lens approximation, show phase advance as a function of k and L. where and one turn matrix is written as –If phase advance per cell is limited between 60 degrees and 120 degrees, what is the maximum momentum ratio from injection to extraction?

37. 37 Exercise (4) Scaling FFAG has magnetic field shape as –Momentum compaction factor  c is defined as –Show momentum compaction factor of scaling FFAG. –RF bucket (half) height is where E is total energy, h is harmonic number,  is slippage factor defined as how much RF voltage is required to accelerate 10 to 20 GeV when h=20 and k=280.