1. ‘Multi-pass-Droplet’ Experiment
Kevin Beard, Alex Bogacz, Vasiliy Morozov, Yves Roblin
Discussion
Why?
Why multi-pass arcs? Recent development of Dogbone RLAs Alex 15 min.
Proof-of-principle optics for a two-pass arc Vasiliy 15 min.
Scaled super-cell test with electrons Yves 25 min.
Discussion All 20 min.
How?
What?
????

2. Recent development of Dogbone RLAs
Why multi-pass arcs?
Recent development of Dogbone RLAs
Alex Bogacz

3. A Decade of Muon RLAs
Racetrack RLA – NF Study I (2000) (Bogacz/Lebedev)
Switchyard (single bend, horizontal)
Individual energy return Arcs for recirculation
Dogbone RLA – NF Study II (2005) (Bogacz)
Better separation of passes
Compact arcs, saving on beamlines
Simultaneous acceleration of both charge species
Increasing number of passes (ISS/IDS-NF):
Bi-sected linac Optics (2006) (Bogacz)
Ramped linac quads (2007) (Johnson)
Reducing number of return Arcs – Multi-pass Arcs (IDS-NF):
Non-scaling FFAG arcs with sextupoles (2008) (Trbojevic/Bogacz/Wang)
Linear Non-scaling FFAG arcs (2010) (Morozov)
Arcs based on combined function magnets (2011) (Morozov)

4. Racetrack vs ‘Dogbone’ RLA
DE/2 DE DE
2.5 DE
the droplets can be reduced in size according to the required energy
better orbit separation at linac’s end ~ energy difference between consecutive passes (2DE)
allows both charges to traverse the Linac in the same direction (more uniform focusing profile)
both charge signs can be made to follow a Figure-8 path (suppression of depolarization effects) 4

5. Dogbone RLA – IDS
244 MeV
900 MeV
0.9 GeV
3.6 GeV
86 m
0.6 GeV/pass

6. Pre-Linac and RLA I to RLA II …
244 MeV
3 GeV
900 MeV
1.8 GeV
1.2 GeV
3.6 GeV
2.4 GeV 6

7. Injection/Extraction Chicane
FODO lattice:
900/900 (h/v) betatron phase adv. per cell 7

8. Droplet Arcs
top view
1.2 GeV
2.4 GeV
side view
1.2 GeV
 1 m
2.4 GeV

9. Mirror-symmetric ‘Droplet’ Arc – Optics
(bout = bin and aout = -ain , matched to the linacs) 20 3 -3
BETA_X&Y[m]
DISP_X&Y[m]
BETA_X
BETA_Y
DISP_X
DISP_Y
disp. sup. cells out
2 empty transition cells
2 empty transition cells
disp. sup. cells out
10 cells in
2 vertical steps
2 vertical steps

10. Switchyard - Arc 1 and 3
1.2 GeV
2.4 GeV
1.2 GeV

11. Switchyard - Arc 1 and 3
1.2 GeV
2.4 GeV
1.2 GeV

12. Multi-pass Linac Optics – Bi-sected Linac
‘half pass’ , MeV
initial phase adv/cell 90 deg. scaling quads with energy 15 5
BETA_X&Y[m]
DISP_X&Y[m]
BETA_X
BETA_Y
DISP_X
DISP_Y
6 meter 90 deg. FODO cells
17 MV/m RF, 2 cell cavities
quad gradient
1-pass, MeV
mirror symmetric quads in the linac 15 5
BETA_X&Y[m]
DISP_X&Y[m]
BETA_X
BETA_Y
DISP_X
DISP_Y
quad gradient

13. Multi-pass bi-sected linac Optics 30 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 4
Arc 3
Arc 2
Arc 1
bx = 3.2 m by = 6.0 m
ax = ay =1.5
bx,y → bx,y
axy → - axy
bx = 6.3 m by = 7.9 m
ax = ay =1.3
bx = 7.9 m by = 8.7 m
ax = ay =1.3
bx = 13.0 m by = 14.4 m
ax = ay =1.5
quad grad.
length

14. ‘Fixed’ vs ‘Pulsed’ linac Optics (8-pass)
100 5
BETA_X&Y[m]
DISP_X&Y[m]
BETA_X
BETA_Y
DISP_X
DISP_Y
Fixed
100 5
BETA_X&Y[m]
DISP_X&Y[m]
BETA_X
BETA_Y
DISP_X
DISP_Y
Pulsed

15. ‘Dogbone’ RLA with 2-pass Arcs

16. A Decade of Muon RLAs
Racetrack RLA – NF Study I (2000) (Bogacz/Lebedev)
Switchyard (single bend, horizontal)
Individual energy return Arcs for recirculation
Dogbone RLA – NF Study II (2005) (Bogacz)
Better separation of passes
Compact arcs, saving on beamlines
Simultaneous acceleration of both charge species
Increasing number of passes (ISS/IDS-NF):
Bi-sected linac Optics (2006) (Bogacz)
Ramped linac quads (2007) (Johnson)
Reducing number of return Arcs – Multi-pass Arcs (IDS-NF):
Non-scaling FFAG arcs with sextupoles (2008) (Trbojevic/Bogacz/Wang)
Linear Non-scaling FFAG arcs (2010) (Morozov)
Arcs based on combined function magnets (2011) (Morozov)

17. 2-pass ‘Droplet’ Arc
Dipole and quadrupole field components of the remaining magnets adjusted so that at both momenta
Each super-cell has periodic solutions for the orbit and the Twiss functions
At the cell’s entrance and exit, periodic orbit offset, dispersion and their slopes are all zero B
1 .7 Tesla G
28 Tesla/m
Vasiliy Morozov
* Trajectories are shown to scale

18. Proof-of-principle optics for a two-pass arc
Vasiliy Morozov

19. RLA with Two-Pass 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 or potentially more regular droplet arcs replaced by one multi-pass arc
Simplified scheme
No need for a complicated switchyard
Compactness
More efficient use of RF by maximizing the number of passes
Potentially cheaper
Potential for other applications 19

20. Schematic Layout of a Two-Pass FFAG Arc
simple closing of geometry
when using similar cells
 = 41.3 m
300
60
C = m 20

21. Non-Linear FFAG: 1.2 GeV/c Linear Optics of 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
in + out + in = in
MAD-X (PTC) 21

22. Non-Linear FFAG: 2.4 GeV/c Linear Optics of 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) 22

23. Cell Matching
1.2 GeV/c
2.4 GeV/c
outward
inward
outward
inward 23

24. Issues with Non-Linear FFAG Arcs
Small dynamic aperture and momentum acceptance
Compensation of non-linear effects is complicated
Matching to linac is difficult
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 24

25. 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 25

26. 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 26

27. Linear FFAG: Linear Optics of 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 27

28. Dynamic Aperture 28

29. Design Based on Linear Combined-Function Magnets
Same concept as the linear FFAG design
Linear combined-function magnets
Droplet arc composed of symmetric super cells
Each super-cell has periodic solutions for the orbit and the Twiss functions
At the cell’s entrance and exit, periodic orbit offset, dispersion and their slopes are all zero
Two cells bending in the same or opposite directions automatically matched at both momenta
First few magnets of the super cell have dipole field component only, serving as spreader/recombiner
Both dipole and quadrupole field components of the remaining magnets used as parameters to meet the constraints
Synchronization with linac accomplished using path-length adjusting chicanes and/or vertical beam bypasses 29

30. Advantages of New Arc Design
All the advantages of a linear FFAG at a greater compactness
Alternating in-out-in or out-in-out pattern no longer required
Variation of the bending angles increases the number of available parameters and reduces the number of magnets required
Reduced orbit excursion
Spreader/recombiner incorporated into the arc design
Large dynamic aperture and momentum acceptance expected
Simple linear combined-function magnet design 30

31. Arc Layout
Still simple closing of arc geometry when using similar super cells
1.2 / 2.4 GeV/c arc design used as an illustration can be scaled/optimized for other momenta preserving the factor of 2 momentum ratio of the two passes
60
300
C = m B
1 .7 Tesla G
28 Tesla/m 31

32. Super-Cell Optics for P2 / P1 = 2
2xP 32

33. Droplet Arc Spreader/Recombiner
First few magnets of the super cell have dipole field component only, serving as Spreader/Recombiner
* Trajectories are shown to scale 33

34. Two 2-Pass Arc Switchyard
Lower momentum arc is the most challenging because of the highest momentum ratio; have a solution but still plenty of room for optimization
* Trajectories are shown to scale 34

35. Future Studies and Optimization Paths
Lower momentum ratio
In case of a race-track design or in the inner droplet super cells, quadrupole field component can be used in the super-cell’s first magnets
Introduce sextupole component in the spreader/recombiner to control orbit deviation
Study the possibility of more than two passes
Study sextupole compensation of chromatic effects
Study error sensitivity
Tracking using realistic field maps 35

36. Scaled super-cell test with electrons
Yves Roblin

37. goal of the project
Validate the concept of combined function magnet return arcs
Demonstrate feasibility, establish leadership
The scaled down test is a fertile ground for beam physics:
Dynamic aperture,
Effect of non linearities,
Tunability,
Envelope control,
Exploring the range of momenta that can be transported
Etc..etc.. 37

38. Closed orbit in cell
20cm aperture 38

39. scope
Build a fully functional half-cell (first phase) and eventually a full arc using electrons rather than muons.
Use this arc to characterize and demonstrate the concept for the MAP program
Great teaching tool. Can partner with local universities (ODU Beam physics program) 39

40. feasibility
Electron is 206 times lighter than muon. We only need a few MeV to 10’s of MeV to carry out the tests. Canonical 2.4 GeV/c lattice requires 11.6 MeV/c electrons.
Real arc will have superconducting magnets. We can build small normal conducting magnets in house to test the concept (more about this later)
We have the expertise with electron beams and can deliver the needed beam
We have the room at JLAB (see next slides) for testing a half cell, maybe even a full cell and later a full arc. 40

41. Testing a Half-Cell with Electrons
Cell with 12 combined function magnets bending a total of 30 degrees.
Each magnet is a dipole+quad+sextupole.
L=50cm, aperture=20cm
Need instrumentation between each magnet
(beam position monitors and
means of measuring beam profile at some locations)
Low current is adequate.
5 to 40 MeV/c of electron beam is good 41

42. Footprint of the apparatus
Full cell
Add a 3-4 meters behind it for a dump and maybe diagnostics. (like the 0L07 dump).
About 8x3 meters on floor for the half cell. 42

43. Possible Locations at Jefferson Lab
Where 0L07 spectrometer is.
In a Hall after setting up CEBAF in energy recovery mode to get a
Low energy beam. Good option if one want to test a bigger device.
In the test lab !! Using the injector group test gun along with
a cavity to bring beam to 5 MeV. Maybe some paperwork
involved.. 43

44. Magnet specifications
Aperture of 20 cm, length of 50 cm.
The real thing will have to provide around 1.8 Tesla.
Our prototype only needs to put out 1.8/206 or about 87 Gauss.
These magnets can be easily (maybe??) made in house. 44

45. Printed Circuit design(cont)
University of Maryland also designed printed circuit dipoles for their low energy ring. Martin Reiser group. Detailed paper on how to build them.
And it works..
Phys. Rev. ST Accel. Beams 3, (2000) 45

46. Printed Circuit design
That’s a quad !
Front
Back 46

47. Full scaled down simulation of RLA with return arcs
Eventually two of these return arcs can be build.
A small recirculating linac would accelerate from
11.6 GeV to 46.4 GeV/c over several recirculations.
This would be a full scaled down test of the neutrino factory
and/or muon colliders. 47