1. Scaling VFFAG eRHIC Design Progress Report 4 July 15, 2013Stephen Brooks, eRHIC FFAG meeting1

2. Last time: Found FODO lattices rated for 9.4 and 9.5GeV – Extrapolation suggests both allow orbit excursions of less than 7cm (k=30m^-1) with <10^-6 losses But this is without alignment errors – Location relative to resonances understood 9.5GeV/80% packing factor lattice became baseline for scaling VFFAG arc magnet design Synchrotron radiation ~10MW to first order July 15, 2013Stephen Brooks, eRHIC FFAG meeting2

3. I. Macroparticle Weighting July 15, 2013Stephen Brooks, eRHIC FFAG meeting3

4. Greater accuracy for tail losses July 15, 2013Stephen Brooks, eRHIC FFAG meeting4 Generate macroparticles roughly uniformly as a function of normalised radius out to >10  Weights are w = f(r)/g(r) where: – f(r) is desired real phase space density function – g(r) is density of generated macroparticles Details available in the note on distributions: http://stephenbrooks.org/ral/report/2013- 9/4ddist.pdf http://stephenbrooks.org/ral/report/2013- 9/4ddist.pdf

5. Comparison: 9.5GeV FODO lattice July 15, 2013Stephen Brooks, eRHIC FFAG meeting5

6. Zoom: ‘resonance’ features remain July 15, 2013Stephen Brooks, eRHIC FFAG meeting6

7. Comparison: 8GeV FODO lattice July 15, 2013Stephen Brooks, eRHIC FFAG meeting7

8. Comparison: 9.4GeV FODO lattice July 15, 2013Stephen Brooks, eRHIC FFAG meeting8

9. Comparison: 10GeV FODO lattice July 15, 2013Stephen Brooks, eRHIC FFAG meeting9

10. II. Error Studies of FODO Lattice July 15, 2013Stephen Brooks, eRHIC FFAG meeting10

11. Tracking with translational errors Random offsets were generated for each magnet in 500 cells (then reused) Error in each axis a normal distribution with mean 0 and standard deviation  – RMS 3D distance offset = sqrt(3)  ~ 1.73  – 99% single axis offset ~ 2.58  – 99% 3D distance offset ~ 3.37  Tracked 2 turns at 1.2GeV, disrupted beam July 15, 2013Stephen Brooks, eRHIC FFAG meeting11

12. Beam loss vs. error sigma July 15, 2013Stephen Brooks, eRHIC FFAG meeting12

13. Loss vs. k and  for 9.5GeV lattice July 15, 2013Stephen Brooks, eRHIC FFAG meeting13

14.  =100um transmission July 15, 2013Stephen Brooks, eRHIC FFAG meeting14

15.  =100um beam centroid July 15, 2013Stephen Brooks, eRHIC FFAG meeting15

16.  =100um norm. RMS emittances July 15, 2013Stephen Brooks, eRHIC FFAG meeting16

17.  =10um transmission July 15, 2013Stephen Brooks, eRHIC FFAG meeting17

18.  =10um beam centroid July 15, 2013Stephen Brooks, eRHIC FFAG meeting18

19.  =10um norm. RMS emittances July 15, 2013Stephen Brooks, eRHIC FFAG meeting19

20.  =2.5um transmission July 15, 2013Stephen Brooks, eRHIC FFAG meeting20

21.  =2.5um beam centroid July 15, 2013Stephen Brooks, eRHIC FFAG meeting21

22.  =2.5um norm. RMS emittances July 15, 2013Stephen Brooks, eRHIC FFAG meeting22

23.  =1um transmission July 15, 2013Stephen Brooks, eRHIC FFAG meeting23

24.  =1um beam centroid July 15, 2013Stephen Brooks, eRHIC FFAG meeting24

25.  =1um norm. RMS emittances July 15, 2013Stephen Brooks, eRHIC FFAG meeting25

26.  =0 transmission July 15, 2013Stephen Brooks, eRHIC FFAG meeting26

27.  =0 beam centroid July 15, 2013Stephen Brooks, eRHIC FFAG meeting27

28.  =0 norm. RMS emittances July 15, 2013Stephen Brooks, eRHIC FFAG meeting28

29. III. Synchrotron Radiation Losses July 15, 2013Stephen Brooks, eRHIC FFAG meeting29

30. Compensation-free designs FFAG arcs transmit a continuum of energies so don’t strictly speaking need compensation of synchrotron energy losses – All examples given for “9.5GeV” FODO lattice – Assumed FFAG straights radiate same rate as arcs Constraints: – My FFAG arcs won’t transmit beam below 1.2GeV – Assumed ring linac won’t transmit below 100MeV July 15, 2013Stephen Brooks, eRHIC FFAG meeting30

31. Schematic changes July 15, 2013Stephen Brooks, eRHIC FFAG meeting31 Before Source, 10?MeV dump 100MeV ERL 1.1GeV ERL Compensation RF After ~200MeV linac 1.xGeV ERL 100MeV ERL?

32. 9-pass 10GeV (worst) July 15, 2013Stephen Brooks, eRHIC FFAG meeting32

33. 9-pass 9GeV July 15, 2013Stephen Brooks, eRHIC FFAG meeting33

34. 6-pass 10GeV July 15, 2013Stephen Brooks, eRHIC FFAG meeting34

35. 6-pass 9GeV (<10MW) July 15, 2013Stephen Brooks, eRHIC FFAG meeting35

36. 6-pass 9GeV to 13.5GeV, 6.1mA July 15, 2013Stephen Brooks, eRHIC FFAG meeting36

37. 6-pass 9GeV to 14.9GeV, 3.3mA July 15, 2013Stephen Brooks, eRHIC FFAG meeting37

38. This may or may not be practical? July 15, 2013Stephen Brooks, eRHIC FFAG meeting38 Source, dump Overdrive mode 197MeV linac 1.474GeV not quite ERL 100MeV ERL RF

39. 4-pass 10GeV (~10MW, long linac) July 15, 2013Stephen Brooks, eRHIC FFAG meeting39

40. IV. VFFAG Options Comparison July 15, 2013Stephen Brooks, eRHIC FFAG meeting40

41. FFAG type Synchrotron radiation Dynamic aperture / error tolerance Time of flight Energy range / multiple rings Vertical (nonlinear) scaling ** # 10MW at 9- 10GeV Not impossible but difficult 1-beta effect only Infinite / one ring Vertical linear nonscaling * ## Potentially to 20GeV 50mA Better? Unknown but better than horizontal FFAG Probably factor 3x / two rings for 10GeV, three rings for 20-30 Vertical nonlinear nonscaling *** ### Potentially to 20GeV 50mA Also bad? At least as good as linear nonscaling VFFAG Horizontal linear nonscaling * ## 20GeV OKLinear magnetsProblematicTwo/three rings Non-FFAG20GeV OKPresumably goodEach ring exactToo many rings July 15, 2013Stephen Brooks, eRHIC FFAG meeting41 *, **, *** indicate complexity of magnets and correction #, ##, ### indicate conceptual difficulty

42. V. Future Work July 15, 2013Stephen Brooks, eRHIC FFAG meeting42

43. Next steps (if scaling VFFAG) Develop “straight” cell for full ring lattice Work with magnet and FFAG splitter designers Decide on RF/linac energies Open issues: – Emittance growth from SR photon emission – Coherent synchrotron radation? “End-to-end” tracking of full ring – Eventually track with fieldmaps from magnet July 15, 2013Stephen Brooks, eRHIC FFAG meeting43

44. Next steps (if non-scaling VFFAG) Try linear field NS-VFFAG first (“Davidtron”) – Much less synchrotron radiation – Expect better dynamic aperture – Easier to build (correct and understand!) magnets – Will likely need a cascade of rings 1-3, 3-10 etc. Develop quadrupole field models for Muon1 and/or VFFAG tracker code Try to search and understand lattice space July 15, 2013Stephen Brooks, eRHIC FFAG meeting44