1. RLA WITH NON-SCALING FFAG ARCS
V.S. Morozov, S.A. Bogacz, Y.R. Roblin
Thomas Jefferson National Accelerator Facility
K.B. Beard
Muons, Inc.
Muon Accelerator Program - Winter Meeting, March 2, 2011

2. RLA with Two-Pass FFAG Arcs
Alex Bogacz
RLA with FFAG Arcs
244 MeV
0.6 GeV/pass
3.6 GeV
0.9 GeV
146 m
79 m
2 GeV/pass
264 m
12.6 GeV
79 m
Two regular droplet arcs replaced by one two-pass FFAG arc
Simplified scheme
No need for a complicated switchyard
Non-linear and linear FFAG solutions with linear solution perhaps more preferable
Muon Accelerator Program - Winter Meeting, March 2, 2011

3. Two-Pass FFAG Arcs 300 60 simple closing of geometry
when using similar cells
 = 41.3 m
300
60
C = m
Muon Accelerator Program - Winter Meeting, March 2, 2011

4. Non-Linear FFAG: 1.2 GeV/c Linear Optics of Arc 1 Unit Cell
Combined-function bending magnets are used
1.2 GeV/c orbit goes through magnet centers
Linear optics controlled by quadrupole gradients in symmetric 3-magnet cell
Dispersion compensated in each 3-magnet cell
3-magnet cell
MAD-X (PTC)
Muon Accelerator Program - Winter Meeting, March 2, 2011

5. Non-Linear FFAG: 2.4 GeV/c Linear Optics of Arc 1 Unit Cell
Unit cell composed symmetrically of three 3-magnet cells
Off-center periodic orbit
Orbit offset and dispersion are compensated by symmetrically introducing sextupole and octupole field components in the center magnets of 3-magnet cells
symmetric unit cell
sextupole and octupole components
MAD-X (PTC)
Muon Accelerator Program - Winter Meeting, March 2, 2011

6. Cell Matching 1.2 GeV/c 2.4 GeV/c outward inward outward inward
Muon Accelerator Program - Winter Meeting, March 2, 2011

7. Non-Linear FFAG: Linear Optics of Arc 2 Unit Cell
Same concept as 1.2 GeV/c linear optics of Arc #1
1.8 GeV/c
3.0 GeV/c
Muon Accelerator Program - Winter Meeting, March 2, 2011

8. Matching of Non-Linear FFAG Arcs to Linac
Horizontal  functions of the higher momenta overfocused at the unit cell ends
Matching sections introduced in arcs to reduce  function values in linac
Muon Accelerator Program - Winter Meeting, March 2, 2011

9. Issues with Non-Linear FFAG Arcs
Small dynamic aperture and momentum acceptance
Compensation of non-linear effects is complicated
Matching to linac is difficult, the matching sections break the arcs’ superperiodicity
Hard to control the orbit lengths and therefore the difference in the times of flight of the two momenta
Combined function magnets with precise control of field components up to octupole
Muon Accelerator Program - Winter Meeting, March 2, 2011

10. Two-Pass Linear FFAG Arcs
Same concept as with the non-linear FFAG arcs
Droplet arcs composed of symmetric FFAG cells
Each cell has periodic solution for the orbit and the Twiss functions
For both energies, at the cell’s entrance and exit:
Offset and angle of the periodic orbit are zero
Alpha functions are zero
Dispersion and its slope are zero
Outward and inward bending cells are automatically matched
Muon Accelerator Program - Winter Meeting, March 2, 2011

11. Two-Pass Linear FFAG Arcs
Combined function magnets with dipole and quadrupole field components only
Much greater dynamic aperture expected than in the non-linear case
Easier to adjust the pass length and the time of flight for each energy
Easier to control the beta-function and dispersion values
Initial beta-function values chosen to simplify matching to linac
Much simpler practical implementation without non-linear fields
More elements are used in each unit cell to satisfy the diverse requirements and provide enough flexibility in the orbit control
Muon Accelerator Program - Winter Meeting, March 2, 2011

12. Linear FFAG: Linear Optics of Arc 1 Unit Cell
Initial conditions set; orbit, dispersion and -function slopes zero at the center
Path lengths adjusted to give time of flight difference of one period of RF
1.2 GeV/c
2.4 GeV/c
Muon Accelerator Program - Winter Meeting, March 2, 2011

13. Linear FFAG: Linear Optics of Arc 2 Unit Cell
Path lengths adjusted to give equal times of flight for the two momenta
1.8 GeV/c
3.0 GeV/c
Muon Accelerator Program - Winter Meeting, March 2, 2011

14. Multi-pass linac Optics 80 5
BETA_X&Y[m]
DISP_X&Y[m]
BETA_X
BETA_Y
DISP_X
DISP_Y
1.2 GeV
0.9 GeV
3.0 GeV
2.4 GeV
1.8 GeV
3.6 GeV
Arc 1
bx = 8 m by = 2 m
ax = 0 = ay
Arc 2
bx = 9 m by = 2 m
bx = 2 m by = 4 m
bx = 10 m by = 3 m
Alex Bogacz

15. Dynamic Aperture
Muon Accelerator Program - Winter Meeting, March 2, 2011

16. Tracking Bunch with p/p = 0
p = 2.4 GeV/c, xN = 300 m, yN = 300 m, z = 1 cm, x = 2 m, y = 4 m, particles, 1 turn
Muon Accelerator Program - Winter Meeting, March 2, 2011

17. Tracking Bunch with p/p = 0.01
Muon Accelerator Program - Winter Meeting, March 2, 2011

18. Tracking Bunch with p/p = 0.027
Muon Accelerator Program - Winter Meeting, March 2, 2011

19. Conclusions
Non-linear and linear NS FFAG schemes developed for muon RLA return arcs
Droplet arcs are composed of symmetric FFAG cells having
Periodic solution for the orbit and the Twiss functions
Orbit offset, dispersion and their slopes are zero at the cell’s entrance and exit for both energies
Automatic matching of the cells with each other and between the outward and inward bending cells from the optics and geometry points of view
The non-linear FFAG scheme has issues with dynamic aperture, momentum acceptance, orbit control and linac matching
The linear FFAG scheme
Promising dynamic aperture and momentum acceptance
The orbit length were adjusted to compensate for the time of flight difference
Simpler linac matching
Future plans
Sextupole compensation to improve the momentum acceptance
Study of the error sensitivity
Muon Accelerator Program - Winter Meeting, March 2, 2011