Chromaticity correction and dynamic aperture in a FFAG

1
Chromaticity correction and dynamic aperture in a
FFAG

• Shinji Machida
• ASTeC/STFC/RAL
• 09 November, 2007
• http//www.astec.ac.uk/intbeams/users
• /machida/proc/FFAG2007/machida_20071109.pdf ppt

2
Contents

• Introduction (7 slides)
• Chromaticity correction for fast cycling machine
  (7)
• Chromaticity correction for slow cycling machine
  (5)

3
Introduction

4
Introduction (1)proposed neutrino factory
complex

• Linac 0.2 to 0.9 GeV
• Simple and straightforward.
• Costly.
• Large amplitude particles lag behind the correct
  phase (phase slip).
• Recirculating Linac (RLA) 0.9 to 12.6 GeV
• Cost effective way of using linac. Arc can
  compensate the phase slip.
• Is switchyard problem solved?
• Linear nonscaling FFAG 12.5 to 25 (or 50 GeV)
• Lower cost.
• The phase slip problem.
• Resonance crossing.

5
Introduction (2) Phase slip problem in a large
acceptance muon ring

• Large transverse amplitude particles take more
  time to complete one revolution.
• Above the limit, a particle gets into the
  deceleration phase.

horizontal and vertical
1.44 p mm
1.96 p mm
0
2.56 p mm
Single particle behavior in EMMA
6
Introduction (3) Phase slip problem in a large
acceptance muon ring
0.001 pi mm
30. pi mm
22
22

• End to end simulation shows deterioration of
  longitudinal emittance in a nonscaling FFAG.
• The phase slip problem determines
• Transition energy between RLA and FFAG.
• whether a cascade of FFAG is feasible.

FFAG
10
10
Kinetic energy GeV
RLA
2
2
Linac
0
0
RF phase/2Pi
RF phase/2Pi
7
Introduction (4) Resonance crossing in a slow
cycling proton or ion ring.

• Keil et. al.s medical machine.
• It is not sure if slow crossing of resonance doe
  not deteriorate beam quality.

8
Introduction (5) Resonance crossing in a slow
cycling proton or ion ring.

• rms orbit distortion due to alignment errors
  agrees with random walk model.

• Distortion for different acceleration rate.
• Circles are simulation results.
• Lines are random walk model.

Resonance regime
tracking
model
17 turns
local correction is the only measure.
9
Introduction (6) Resonance crossing in a slow
cycling proton or ion ring.

• Resonance behavior starts appearing when the
  acceleration rate is 4 or 5 time slower.

10
Introduction (7) chromaticity correction

• Linear nonscaling FFAG is a nice idea.
• However, finite chromaticity makes
• Phase slip problem in a large acceptance muon
  ring
• Resonance crossing in a slow cycling proton ring.
• Chromaticity correction may be needed.
• Scaling FFAG behaves better in that respect.

11
Chromaticity correction in a muon ring (1)

• It is possible to install multipole.
• Reduction of dynamic aperture is another concern.
• Way of installing multipole.
• Centre of multipole
• Maximum order of multipole

12
Chromaticity correction in a muon ring
(2)dynamic aperture in 100 turns

• Dynamic aperture at constant momentum

13
Chromaticity correction in a muon ring
(3)simulation results

• Chromaticity correction mitigates the phase slip
  problem.
• Muon beam with 30 p mm emittance is accelerated
  without beam loss.
• Even though dynamic aperture of 100 turns is only
  about 1 p mm while beam emittance is 30 p mm.

Linear lattice
Lattice with c.c
14
Chromaticity correction in a muon ring
(4)partial chromaticity correction

• Make a lattice with partial chromaticity
  correction.
• Only sextupole is installed.
• Dynamic aperture of 100 turns becomes larger.

Dynamic aperture of 100 turns
15
Chromaticity correction in a muon ring
(5)simulation results

• Sextupole mitigates the phase slip problem.
• Muon beam with 30 p mm emittance is accelerated
  without beam loss.
• Even though dynamic aperture of 100 turns does
  not give acceptance of 30 p mm.
• EMMA can simulate these results?

Linear lattice
Lattice with sextupole
16
Chromaticity correction in a muon ring
(6)dynamic aperture in 100 turns

• Aperture at constant momentum

Talk by Kelliher on mechanism behind
17
Chromaticity correction in a muon ring (7)price
we have to pay

• Orbit shift becomes as twice as much.
• Need a bigger aperture magnet.

• Time of flight range increases 50.
• Need a higher voltage.

• Exchange of transverse emittance.
• Can be cured by tune choice?

18
Chromaticity correction in a muon ring (8)summary

• Multipole can make the chromaticity of 10 to 20
  GeV muon ring zero.
• Although the dynamic aperture of 100 turns
  becomes even less than 1 p mm, muon emittance of
  30 p mm can survive for 17 turns.
• Sextupole only makse the chromaticity of 10 to 20
  GeV muon ring almost zero.
• Although the dynamic aperture of 100 turns
  becomes 10 to 20 p mm, muon emittance of 30 p mm
  can survive for 17 turns.
• Dynamic aperture gradually decreases as a
  function of turn number.
• Orbit excursion becomes twice as much.
• Voltage requirement is 50 more.
• There is a coupling between horizontal and
  vertical emittance.

19
Chromaticity correction in a slow cycling machine
(1)tune excursion

• Tune space with multipole
• w/ S. O. D. D
  w/ sextupole only

Use this setup
20
Chromaticity correction in a slow cycling machine
(2)evolution of emittance

• 10 to 20 GeV muon ring with slower acceleration
  (gt 17 turns)
• 50 turns total Hor.
  Ver.
• 200 turns total Hor.
  Ver.

21
Chromaticity correction in a slow cycling machine
(3)vertical phase space

• 10 to 20 GeV muon ring with slower acceleration
• 50 turns total
• 200 turns total

22
Chromaticity correction in a slow cycling machine
(4) scaling machine

• Scaling and scaling without higher order except Q
  and S.

23
Chromaticity correction in a slow cycling machine
(5) summary

• When the acceleration is 3 time slower, a lattice
  with partial correction has the maximum emittance
  growth.
• When the acceleration is 10 times slower,
  nonlinear nonscaling lattice gives a huge
  emittance growth due to smearing in the phase
  space.
• Is it due to non-adiabaticity?
• Scaling lattice without higher order multipole
  gives wide dynamic aperture only around small
  momentum.