RLA WITH NON-SCALING FFAG ARCS

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 0.9 GeV 244 MeV 146 m 79 m 79 m 0.6 GeV/pass 3.6 GeV 264 m 12.6 GeV 2 GeV/pass • 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 simple closing of geometry when using similar cells  = 41.3 m 300 60 C = 302.4 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 sextupole and octupole components symmetric unit cell 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 5 5 80 80 BETA_X&Y[m] BETA_X&Y[m] DISP_X&Y[m] DISP_X&Y[m] 0 0 0 0 0 0 BETA_X BETA_X BETA_Y BETA_Y DISP_X DISP_X DISP_Y DISP_Y 355.552 355.552 Arc 1 bx = 2 m by = 4 m ax = 0 = ay Arc 2 bx = 9 m by = 2 m ax = 0 = ay Arc 1 bx = 8 m by = 2 m ax = 0 = ay Arc 2 bx = 10 m by = 3 m ax = 0 = ay 3.0 GeV 0.9 GeV 1.2 GeV 1.8 GeV 2.4 GeV 3.6 GeV 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, 3000 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