1. Linac and RLAs – Overview of NF-IDS
Alex Bogacz
Mini-workshop on Low Energy Muon Acceleration, CNU, February 2-5 , 2010

2. Linac and RLAs - Goals IDS Goals:
0.6 GeV/pass
3.6 GeV
0.9 GeV
244 MeV
146 m
79 m
2 GeV/pass
264 m
12.6 GeV
IDS Goals:
Define beamlines/lattices for all components
Resolve physical interferences, beamline crossings etc
Error sensitivity analysis
End-to-end simulation (machine acceptance) OptiM vs ELEGANT
Component count and costing
Mini-workshop on Low Energy Muon Acceleration, CNU, February 2-5 , 2010

3. RLA Acceleration - Status
Presently completed lattices
Linear pre-accelerator – solenoid focusing
4.5 pass Dogbone RLA × 2 (RLA I + RLA II)
Optimized multi-pass linac optics (bisected - quad profile along the linac)
Droplet return arcs (4) matched to the linacs
Transfer lines between the components – injection chicanes
Droplet arcs crossing – Double achromat Optics design
Chromatic corrections with sextupoles at Spr/Rec junctions
Error analysis for the Arc lattices (proof-or-principle)
Magnet misalignment tolerance – DIMAD Monte Carlo Simulation
Focusing errors tolerance – betatron mismatch sensitivity
Piece-wise end-to-end simulation with OptiM (pre-accelerator + RLA I)
Mini-workshop on Low Energy Muon Acceleration, CNU, February 2-5 , 2010

4. Linear Pre-accelerator – 244 MeV to 909 MeV
6 short cryos
15 MV/m
8 medium cryos
17 MV/m
11 long cryos
1.1 Tesla solenoid
1.4 Tesla solenoid
2.4 Tesla solenoid
Transverse acceptance (normalized): (2.5)2eN = 30 mm rad
Longitudinal acceptance: (2.5)2 sDpsz/mmc = 150 mm
Mini-workshop on Low Energy Muon Acceleration, CNU, February 2-5 , 2010

5. ‘Soft-edge’ Solenoid
Non-zero aperture - correction due to the finite length of the edge :
It introduces axially symmetric edge focusing at each solenoid end:
Hard edge solenoid:
Mini-workshop on Low Energy Muon Acceleration, CNU, February 2-5 , 2010

6. ‘Soft-edge’ Solenoid – Nonlinear Effects
Nonlinear focusing term DF ~ O(r2) follows from the scalar potential:
Solenoid B-fields
Nonlinear focusing included in particle tracking
Mini-workshop on Low Energy Muon Acceleration, CNU, February 2-5 , 2010

7. Pre-accelerator Optics – soft vs hard solenoids
a = 19.5 cm
a = 0 cm
Mini-workshop on Low Energy Muon Acceleration, CNU, February 2-5 , 2010

8. Linac Optics – OptiM vs ELEGANT
a = 19.5 cm
a = 19.5 cm
Yves Roblin
Mini-workshop on Low Energy Muon Acceleration, CNU, February 2-5 , 2010

9. Linac Optics – OptiM vs Elegant
Transverse acceptance (normalized): (2.5)2eN = 30 mm rad
Longitudinal acceptance: (2.5)2 sDpsz/mmc = 150 mm
Yves Roblin
Mini-workshop on Low Energy Muon Acceleration, CNU, February 2-5 , 2010

10. Initial phase-space after the cooling channel at 220 MeV/c
Linac-RLA Acceptance
Initial phase-space after the cooling channel at 220 MeV/c
ISS/IDS
erms
A = (2.5)2 e
normalized emittance: ex/ey
mmrad
4.8 30
longitudinal emittance: el
(el = sDp sz/mmc)
momentum spread: sDp/p
bunch length: sz mm 24
0.07
165
150
0.17
412
bx,y = 2.74 m
ax,y =
bg = 2.08
Mini-workshop on Low Energy Muon Acceleration, CNU, February 2-5 , 2010

11. Introduction of synchrotron motion in the linac
Longitudinal acceptance: Dp/p=0.17 or Df =93 (200MHz)
Mini-workshop on Low Energy Muon Acceleration, CNU, February 2-5 , 2010

12. Linear Pre-accelerator – Longitudinal phase-space
Transverse acceptance (normalized): (2.5)2eN = 30 mm rad
Longitudinal acceptance: (2.5)2 sDpsz/mmc = 150 mm
Transport efficiency:
Mini-workshop on Low Energy Muon Acceleration, CNU, February 2-5 , 2010

13. Longitudinal phase-space tracking
OptiM tracking
Initial distribution
ELEGANT tracking
Preliminary
Yves Roblin
Mini-workshop on Low Energy Muon Acceleration, CNU, February 2-5 , 2010

14. Multi-pass Linac Optics – Bisected Linac
‘half pass’ , MeV
initial phase adv/cell 90 deg. scaling quads with energy
quad gradient
1-pass, MeV
mirror symmetric quads in the linac
quad gradient
Mini-workshop on Low Energy Muon Acceleration, CNU, February 2-5 , 2010

15. Multi-pass linac Optics – bisected linac
2-pass, MeV
minimized beta beating due to under focus
3-pass, MeV
Mini-workshop on Low Energy Muon Acceleration, CNU, February 2-5 , 2010

16. Injection/Extraction Chicanem+ m-
Mini-workshop on Low Energy Muon Acceleration, CNU, February 2-5 , 2010

17. Re-injection double-chicanem+ m-
0.9 GeV
1.5 GeV m-
Mini-workshop on Low Energy Muon Acceleration, CNU, February 2-5 , 2010

18. Pre-accelerator–Chicane–Linac Matching
Mini-workshop on Low Energy Muon Acceleration, CNU, February 2-5 , 2010

19. Pre-accelerator–Chicane–Linac Matching
Mini-workshop on Low Energy Muon Acceleration, CNU, February 2-5 , 2010

20. Injection-to–Linac – Chromatic Corrections
uncorrected
one family of sextupoles
two families of sextupoles
Dfxy = 1800
Dfxy = 1800
Dfxy = 1800
Dfxy = 1800
Mini-workshop on Low Energy Muon Acceleration, CNU, February 2-5 , 2010

21. Linac ½-to-Arc1 – Beta Match
E =1.2 GeV
Already matched ‘by design’
900 phase adv/cell maintained across the ‘junction’
No chromatic corrections needed
Mini-workshop on Low Energy Muon Acceleration, CNU, February 2-5 , 2010

22. Linac1-to-Arc2 – Chromatic Compensation
E =1.8 GeV
‘Matching quads’ are invoked
No 900 phase adv/cell maintained across the ‘junction’
Chromatic corrections needed – two pairs of sextupoles
Mini-workshop on Low Energy Muon Acceleration, CNU, February 2-5 , 2010

23. Linac1-to-Arc2 - Chromatic Corrections
initial
uncorrected
two families of sextupoles
Mini-workshop on Low Energy Muon Acceleration, CNU, February 2-5 , 2010

24. Mirror-symmetric ‘Droplet’ Arc – Optics
10 cells in
2 cells out
(bout = bin and aout = -ain , matched to the linacs)
transition
E =1.2 GeV
Mini-workshop on Low Energy Muon Acceleration, CNU, February 2-5 , 2010

25. ‘Droplet’ Arcs scaling – RLA I
Ei [GeV]
pi/p1
cell_out
cell_in
length [m]
Arc1
1.2 1
2×2 10
130
Arc2
1.8
3/2
2×3 15
172
Arc3
2.4 2
2×4 20
214
Arc4
3.0
5/2
2×5 25
256
Fixed dipole field: Bi =10.5 kGauss
Quadrupole strength scaled with momentum: Gi = × 0.4 kGauss/cm
Arc circumference increases by: (1+1+5) × 6 m = 42 m
Mini-workshop on Low Energy Muon Acceleration, CNU, February 2-5 , 2010

26. Mirror-symmetric ‘Droplet’ Arc – Optics
Arc1 (E =1.2 GeV)
10 cells in
2 cells out
2 cells out
Arc2 (E =1.8 GeV)
15 cells in
3 cells out
3 cells out
Mini-workshop on Low Energy Muon Acceleration, CNU, February 2-5 , 2010

27. Longitudinal Compression in the RLA
Adiabatic compression in the RLA - off-crest acceleration in the linac + non zero momentum compaction in the arcs (M56~6 m)
Mini-workshop on Low Energy Muon Acceleration, CNU, February 2-5 , 2010

28. ‘Droplet’ Arcs scaling – RLA II
Ei [GeV]
pi/p1
cell_out
cell_in
length [m]
Arc1
4.6 1
2×2 10
260
Arc2
6.6
3/2
2×3 15
344
Arc3
8.6 2
2×4 20
428
Arc4
10.6
5/2
2×5 25
512
Fixed dipole field: Bi = 40.3 kGauss
Quadrupole strength scaled with momentum: Gi = × 1.5 kGauss/cm
Arc circumference increases by: (1+1+5) × 12 m = 84 m
Mini-workshop on Low Energy Muon Acceleration, CNU, February 2-5 , 2010

29. RLA II - Linac Optics 1-pass, 4.6 -6.6 GeV
mirror symmetric quads in the linac
Quad gradient
length
Mini-workshop on Low Energy Muon Acceleration, CNU, February 2-5 , 2010

30. Focusing Error Tolerances – Quadrupole Spec
By design, one can tolerate Arc-to-Arc mismatch at the level of 1% (to be compensated by the dedicated matching quads).
For any given Arc and the following Linac one can evaluate: Fmin ≈1 m and
Thanks to well balanced, tight focusing in the Arcs and compact Spr/Rec optics the last number, 50 m, is factor of 6 smaller than the corresponding quantity for a typical CEBAF Arc-Linac segment.
This yields the required design specification for quadrupoles of 0.2%:
Mini-workshop on Low Energy Muon Acceleration, CNU, February 2-5 , 2010

31. Magnet Misalignment Errors
Lattice sensitivity to random misalignment errors via DIMAD Monte-Carlo assuming:
quadrupole misalignment errors (Gaussian):
F: sx = sy = 1 mm sx‘ = sy‘ = 0.8 ×10-3
D: sx = sy = 1 mm sx‘ = sy‘ = 1.47×10-3
(sx,y' = sx,y/L)
Arc 2
RMS Orbit Displacement [m]:
X: e-02
y: e-02
Orbit drifts at the level of ~3 cm can easily be corrected by pairs of hor/vert correctors (2 kGauss cm ) placed at every quad girder
Similar level of dipole misalignment errors had virtually no effect on random steering
Mini-workshop on Low Energy Muon Acceleration, CNU, February 2-5 , 2010

32. Summary Presently completed Lattices:
Pre-accelerator (244 MeV-0.9) + injection double chicane
RLA I ( GeV) and RLA II ( GeV)
4.5 pass linac
Droplet Arcs1-4
Chromaticity correction with sextupoles validated via tracking
Magnet error lattice sensitivity of Arc lattices
Magnet misalignment error analysis shows quite manageable level of orbit distortion for ~1 mm level of magnet misalignment error.
Great focusing errors tolerance for the presented lattice - 1% of Arc-to-Arc betatron mismatch limit sets the quadrupole field spec at 0.2%
Mini-workshop on Low Energy Muon Acceleration, CNU, February 2-5 , 2010

33. Summary – cont.
Piece-wise end-to-end simulation with OptiM/ELEGANT (transport codes)
Solenoid linac
Injection chicane
RLA I
Still to do…
End-to-end simulation with fringe fields (sol. & rf cav.)
Engineer individual active elements (magnets and RF cryo modules)
Element count and costing
Mini-workshop on Low Energy Muon Acceleration, CNU, February 2-5 , 2010