Muon Acceleration System

1
Muon Acceleration System

• Shinji Machida
• CCLRC/RAL/ASTeC
• 29 August, 2006
• http//hadron.kek.jp/machida/doc/nufact/
• ffag/machida_20060829.ppt pdf

2
Contents

• Motivations and code development
• Phase slip problem in RLA and Linac
• end to end simulation from Linac to FFAG
• Matching between machines

3
Motivations

• We now know that non-scaling FFAG has a problem
  of phase slip due to large transverse amplitude
• (30 pi mm rad or 30,000 pi mm mrad).
• How about the rest of accelerator complex?
• Is there similar problem in Linac and RLA?
• Is there any matching issue between machines?

FFAG2
Kinetic energy GeV
Kinetic energy GeV
FFAG1
RF phase/2Pi
RF phase/2Pi
4
Code for RLA and Linac Modeling

• Comments by Scott Berg on 21 July meeting.
• A code is slightly modified from the one for
  FFAG.
• No TaylorPolySeries. No paraxial approximation.
• Geometry is separated from orbit.
• Modeling of end fields.
• Time as an independent variable.
• Integration of kick and drift.

5
Code for RLA and Linac Parameters

• Bogacz, et. al., NuFact01
• Linac from 0.130 to 2.48 GeV
• RLA (Racetrack) from 2.48 to 20 GeV
• For end to end simulation, use only first 2
  turns to 11 GeV.

6
Benchmarktransverse

• Beta functions in a linac part of RLA.
• Approximation Arc is nothing but M56.

1st pass
2nd pass
beta function m
path length10 m
4th pass
3rd pass
7
Benchmarklongitudinal

• Synchronous phase of each pass.

2nd linac of 4th turn
1st linac of 4th turn
2nd linac of 3rd turn
1st linac of 3rd turn
Momentum GeV/c
2nd linac of 2nd turn
1st linac of 2nd turn
2nd linac of 1st turn
1st linac of 1st turn
Phase/2Pi
8
RLA on crest
Bunch shape of exit
Momentum GeV/c
ex,y0 pi mm
Phase/2Pi
ex,y30 pi mm
dp/p vs. ex,y
ex,y45 pi mm
9
RLA off crest and M56
Bunch shape of exit
Momentum GeV/c
ex,y0 pi mm
Phase/2Pi
ex,y30 pi mm
dp/p vs. M56
ex,y45 pi mm
10
RLA RF phase and M56
Phase slip effects becomes invisible with some
combination of RF and M56.
RF phase23 deg.
RF phase11.5 deg.
RF phase30 deg.
11
RLA summary

• (As we knew,) two knobs in RLA, namely RF phase
  and M56 (phase slip factor in arc), mix phase
  slip.
• Phase slip problem is less serious.

12
Linac chromaticity

• Bare tune per cell (0.224, 0.224).
• Finite chromaticity makes a tune shift due to
  dp/p.

Beam loss vs. dp/p for small transverse
amplitude (0.001 pi mm).
13
Linac phase slip due to transverse amplitude

• There are synchrotron oscillations only in low
  momentum side.
• 35 pi mm particle is ok, but 40 pi mm particle is
  out.

3
0 pi mm
35 pi mm
40 pi mm
2
Kinetic energy GeV
1
Synchrotron osc.
0
RF phase/2Pi
14
end to end simulationaccelerator complex
assumed

• Linac
• Study II, simplified.
• 0.13 to 2.48 GeV
• RLA
• Part of Study II
• Racetrack with 2 turns
• 2.48 to 11 GeV
• FFAG
• Study IIa
• 11 to 20 GeV

15
end to end simulationlongitudinal phase space

• Transverse emittance 0.001 pi mm
• Transverse emittance 30. pi mm

3
12
22
Kinetic energy GeV
10
2
0
RF phase/2Pi
3
12
22
Kinetic energy GeV
0
10
2
16
end to end simulationevolution of emittance
and beam loss

• Initial parameters
• 0.07, 0.20/b2pi
• 30 pi mm
• Waterbag distribution

FFAG
FFAG
RLA
RLA
Linac
Linac
17
Summary

• A code is modified to simulate Linac and RLA as
  well as FFAG.
• Phase slip problem can be cured in RLA with RF
  phase and M56.
• Phase slip problem becomes visible beyond 35 pi
  mm in Linac.
• end to end simulation is started.
• Tails of distribution created in Linac remain in
  FFAG.
• Cure of the problem in RLA is not necessarily
  good enough for FFAG.
• Need more study to optimize the overall
  performance.