Berkeley Lab Generic Presentation

1
RLA for Muon Collider with non-scaling FFAGs
Dejan Trbojevic, Alex Bogacz Popovic Milorad and
Ronald Johnston
2
RLA for Muons

• Introduction
• Present design of the muon RLAs you have heard
  the talk an hour ago
• What is the non-scaling FFAG?
• Goals
• Try to make four or five times in muon energy by
  either a race track or dog-bone acceleration with
  a single arc (2.5-10 GeV or 10-40 GeV).
• New concept linac with fixed betatron function
  during all energy passes.
• 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.

3
Racetrack vs Dogbone RLA (both m and m-
species )
From Alex Bogacz presentation at the previous
LEMC
DE

• better orbit separation at linacs 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

4
FODO vs Triplet focusing - flat focusing' linac
profile
Bob Palmer
From Alex Bogacz presentation at the previous
LEMC
Triplet
1-pass, 3-5 GeV
256.82 meters
phase adv. drops much faster in the horizontal
plane
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What is the non-scaling FFAG?

• Orbit offsets are proportional to the dispersion
  function
• Dx Dx dp/p
• To reduce the orbit offsets to -6 cm range, for
  momentum range of dp/p - 60 the dispersion
  function Dx has to be of the order of
• Dx 6 cm / 0.6 10 cm
• The size and dependence of the dispersion
  function is best presented in the normalized
  space and by the H function
• ? Dx /??x and ? Dx ??x ?x Dx ??x
• with H H ?2 ?2

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Basic properties of the NS-FFAG
A . Particle orbits
B. Lattice
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Basic properties of the NS-FFAG
Muon acceleration

• Concept introduced 1999 at Montauk meeting
  Trbojevic, Courant, Garren) using the light
  source lattice with small emittance minimized H
  function

• Extremely strong
• focusing with small
• dispersion function.
• large energy acceptance.
• - tunes variation
• very small orbit offsets
• - small magnets

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Design of the arcs from the densely populated
FODO cells for the 2.5 -gt 10 GeV muons
N142 cells L1.9 m LBD0.9 m LQF0.6 m For the
dp/p-60 BBD1.64 T BQF -1.09 T GF20.8
T/m GD-10.2 T/m For the dp/p 0, -75 BBD3.62
T BQF -2.98 T GF37.0 T/m GD-23.0 T/m
r42.94 m
85.9 m
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Design of the arcs from the densely populated
FODO cells for the 2.5 -gt 10 GeV muons
N142 cells L1.9 m LBD0.9 m LQF0.6 m For the
dp/p-60 BBD1.64 T BQF -1.09 T GF20.8
T/m GD-10.2 T/m For the dp/p 0, -75 BBD3.62
T BQF -2.98 T GF37.0 T/m GD-23.0 T/m
r42.94 m
85.9 m
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Arc cells for two different lattices
FODO cell for the central energy at the top 10 GeV
FODO cell for the -60
1.9 m
x max81 mm
0.3 m
x min -16 mm
0.9 m
x max62 mm
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Matching cell arc to linac
The matching cell length is L3 1.9 m 5.7 m
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Matching cell with arcs without linac
Orbits from 2.5 10 GeV Through the matching
cells and arcs
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Time of flight correction preliminary chicanes
design
Details of the orbits Through the matching cells
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New concept of the linac triplets with cavities
20 cavities each 25 MV/m 0.250 GeV per one
pass
2q
- q
-q
10 GeV
2.5 GeV
7.2 mm
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New concept of the linac Betatron Function
dependence on energy
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New concept of the linac Tunes per Linac cell
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New concept of the linac triplets with cavities
Cavity
Cavity
2q
-q
-q
7.2 mm
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Matching cell with linac arc to linac
Orbits magnified 100 times From 2.5 GeV- 10GeV
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20 cells linac
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New Concept Multipass Linac with racetrack FFAG
Chicane
20 Cavities
Chicane
Non-scaling FFAG arc
Non-scaling FFAG arc
Chicane
Chicane
20 Cavities
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New Concept Multipass Linac with fixed betatron
functions
Longer linac
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New Concept Multipass Linac with fixed betatron
functions
Details of the orbits with Chicanes
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Path length difference from the arc cell
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Details of the Chicane
CAVITY
TRIPLET
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Details of the chicane calculations
Lo /Lcos q
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Conclusions

• It looks like a combination of the non-scaling
  FFAG with linac is possible this could reduce
  present number of arcs.
• New concept of the multiple pass linac with
  stable betatron function has been introduced for
  the first time!!
• 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
  (Polymorhic Tracking Code).
• There is a possibility to increass energy gain to
  5 times as it had been done in the eRHIC example.
• Thanks to Muon Inc. for the support