1. Muon acceleration by RLA using non-scaling FFAG
Dejan Trbojevic
Dejan Trbojevic FFAG’08 Workshop, Manchester, 15:00, September 2, 2008

2. RLA for Muons Introduction: Problems: Goals:
Present design of the muon RLA’s
Problems:
Matching of the circular non-scaling FFAG to the straight linac.
Time of flight adjustments for each pass.
Goals:
Try to make four or five times in muon energy by either a race track or dog-bone acceleration with a single arc ( GeV or GeV).
Match the betatron and dispersion functions from the arc to the linac.
Design a chicane to adjust the time of flight for different energy passes.
Dejan Trbojevic FFAG’08 Workshop, Manchester, 15:00, September 2, 2008

3. Few references for Mike Craddock:
D. Trbojevic E.D. Courant, and A. Garren,
September 30, 1999, Montauk, Long Island
High Energy Muon Collider Workshop
Lee Teng:
1956 Non-scaling FFAG proposal
at the conference
A year later a book Conference Proceedings came out:
D. Trbojevic, E.D. Courant, and A. Garren,
“FFAG lattice without opposite bends” , AIP Conf. Proc.
August 17, Volume 530, pp
Dejan Trbojevic FFAG’08 Workshop, Manchester, 15:00, September 2, 2008

4. ‘Racetrack’ vs ‘Dogbone’ RLA (both m+ and m- species )
From Alex Bogacz presentation at the previous LEMC: m- m+ m- m+ m- DE m+
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
the droplets can be reduced in size according to the required energy
both charge signs can be made to follow a Figure-8 path (suppression of depolarization effects) Chuck Ankenbrandt
DE/2 m+ m- m+ m-
Dejan Trbojevic FFAG’08 Workshop, Manchester, 15:00, September 2, 2008

5. FODO vs Triplet focusing - ‘flat focusing' linac profile*
Bob Palmer*
From Alex Bogacz presentation at the previous LEMC:
Triplet
1-pass, 3-5 GeV
meters
phase adv. drops much faster in the horizontal plane
Dejan Trbojevic FFAG’08 Workshop, Manchester, 15:00, September 2, 2008

6. Design of the arcs – from the densely populated FODO cells for the 2
Design of the arcs – from the densely populated FODO cells for the 2.5 -> 10 GeV muons
N=142 cells
L=1.9 m
LBD=0.9 m
LQF=0.6 m
For the:
dp/p=+-60%
BBD=1.64 T
BQF =-1.09 T
GF=20.8 T/m
GD=-10.2 T/m
r=42.94 m
85.9 m
Dejan Trbojevic FFAG’08 Workshop, Manchester, 15:00, September 2, 2008

7. Arc cells for two different lattices
FODO cell for the dp/p=+-60 % -> GeV
x max=69 mm
x min= -34 mm
1.9 m
0.3 m
0.9 m
Dejan Trbojevic FFAG’08 Workshop, Manchester, 15:00, September 2, 2008

8. Arc cells for two different lattices
FODO cell for the dp/p=+-60 % -> GeV
Dejan Trbojevic FFAG’08 Workshop, Manchester, 15:00, September 2, 2008

9. Matching cell – geometrical constraint - arc to linac
The matching cell length
is: L=3 * 1.9 m = 5.7 m
Dejan Trbojevic FFAG’08 Workshop, Manchester, 15:00, September 2, 2008

10. Matching cell to the non-scaling FFAG arcs
Dejan Trbojevic FFAG’08 Workshop, Manchester, 15:00, September 2, 2008

11. Non scaling FFA arcs with matching cells without linac
Orbits from 2.5 – 10 GeV
through the matching cells and arcs:
Dejan Trbojevic FFAG’08 Workshop, Manchester, 15:00, September 2, 2008

12. Non scaling FFA arcs with matching cells without linac
Betatron Functions from 2.5 – 10 GeV
through the matching cells and arcs:
Dejan Trbojevic FFAG’08 Workshop, Manchester, 15:00, September 2, 2008

13. Non scaling FFA arcs with matching cells without linac
Dispersion from 2.5 – 10 GeV
through the matching cells and arcs:
Dejan Trbojevic FFAG’08 Workshop, Manchester, 15:00, September 2, 2008

14. The linac – Betatron Function dependence on energy
Dejan Trbojevic FFAG’08 Workshop, Manchester, 15:00, September 2, 2008

15. Matching cell with linac – arc to linac
Orbits magnified 100 times
From 2.5 GeV- 10GeV
Dejan Trbojevic FFAG’08 Workshop, Manchester, 15:00, September 2, 2008

16. Multipass Linac - racetrack FFAG
Chicane
20 Cavities
Chicane
Non-scaling FFAG arc
Non-scaling FFAG arc
Chicane
20 Cavities
Chicane
Dejan Trbojevic FFAG’08 Workshop, Manchester, 15:00, September 2, 2008

17. 20 cells linac
Dejan Trbojevic FFAG’08 Workshop, Manchester, 15:00, September 2, 2008

18. Multipass Linac with combined function triplets
Details of the orbits with
Chicanes:
Dejan Trbojevic FFAG’08 Workshop, Manchester, 15:00, September 2, 2008

19. Path length difference from the arc cell dp/p=(0,-80%)
Dejan Trbojevic FFAG’08 Workshop, Manchester, 15:00, September 2, 2008

20. Path length difference from the arc cell
(Ds=0.55m for arc)
Dejan Trbojevic FFAG’08 Workshop, Manchester, 15:00, September 2, 2008

21. Details of the chicane calculations:Lo q
-2q L
Lo /L=cos q
Dejan Trbojevic FFAG’08 Workshop, Manchester, 15:00, September 2, 2008

22. Details of the Chicane CAVITY TRIPLET
Dejan Trbojevic FFAG’08 Workshop, Manchester, 15:00, September 2, 2008

23. New approach: What do we need to came from a remainder by Yoshimaru Mori yesterday: IEEE Transactions on Nuclear Science, Vol. NS-30, No. 4, August 1983
Dejan Trbojevic FFAG’08 Workshop, Manchester, 15:00, September 2, 2008

24. New matching cell Input parameters are:
xmax and xmin from the arc NS-FFAG
pmax, po, and pmin, Dx, bx, by,
Unknowns: BD , BF , Ffo , Fdo , and lo
rfmax
ffo
rfo
amax
fdo
amin
rfmin
ffo lo
fdo
umax
xmax
rdmin
umin
fdo
xmin
rdo
fdo
rdmax
To be matched to the input
parameters of the linac: bx, by, ax,ay
Dejan Trbojevic FFAG’08 Workshop, Manchester, 15:00, September 2, 2008

25. Matching Cell - @ zero dispersion end
amax
amin lo
rdmin
umax
fdmin
rdo
umin
fdo
rdmax
fdmax
Dejan Trbojevic FFAG’08 Workshop, Manchester, 15:00, September 2, 2008

26. Matching Cell @ entrancew
Ffmax
rfmax j
rfmax
Ffo
amax
rfo
Ffo- Ffmax
amin
Ffmin
Ffo- Ffmax= Fdo- Fdmax lo
rfmin
Ffmin- Ffo
Ffmin- Ffo= Fdmin- Fdo
umax
pmin
xmax
umin
umax=amax+lo tan(Ffo-Ffmax) po
xmin
umin=amin+lo tan(Ffmin-Ffo)
pmax
Dejan Trbojevic FFAG’08 Workshop, Manchester, 15:00, September 2, 2008

27. Mike Craddock’s approach:
rfmax
ffo
xd+=0
rfo
Xd+
fdo
xd-=0
Xd-
rfmin
ffo lo
fdo
umax
xfp+
rdmin
high p+
umin
fdo
xfp-
rdo po
fdo
low p-
F/2
rdmax
Dejan Trbojevic FFAG’08 Workshop, Manchester, 15:00, September 2, 2008

28. p>pcent orbits matched to linac -> zero dispersion for each momentum
p=pmax
p=pcent
Dejan Trbojevic FFAG’08 Workshop, Manchester, 15:00, September 2, 2008

29. orbits almost matched to linac -> zero dispersion for each momentum
10 GeV
2.5 GeV
Dejan Trbojevic FFAG’08 Workshop, Manchester, 15:00, September 2, 2008

30. Thanks to Muon Inc. for the support
Conclusions:
It looks like a combination of the non-scaling FFAG with linac is possible this could reduce present number of arcs.
Multiple pass linac by the triplet combined function dipoles cells.
Time of flight adjustments is necessary due to 0.6 m delay for the lowest energy pass through the arc. A details of chicane design has to be studied.
Initial matching between the two arcs and linac could be improved.
The simulation of acceleration with many particles is already set-up by the PTC (Polymorphic Tracking Code).
Thanks to Muon Inc. for the support
Dejan Trbojevic FFAG’08 Workshop, Manchester, 15:00, September 2, 2008