Berkeley Lab Generic Presentation

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Beam Dynamics of Low Energy Muon Acceleration
Alex Bogacz Jefferson Lab
7-th International Workshop on Neutrino
Factories and Superbeams, LNF Frascati, June 24,
2005
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Overview

• FFAG acceleration below 5 GeV not cost effective
• Dogbone RLA (3.5-pass) scheme based on 200MHz
  SRF
• Pre-accelerator (273 MeV/c 1.5 GeV) based on
  solenoid focusing
• Main Linac (1 GeV/pass) based on triplet focusing
  
• Three droplet arcs with horizontal multi-pass
  separation
• Longitudinal phase-space compression in the arcs
  (M45 and off-crest RF)
• M45 and off-crest RF linac acceleration
• Large (?2) transverse acceptance
• Lattices linear optics, tracking studies,
  emittance preservation
• multi-pass linac optics
• tracking studies

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Muon Acceleration Complex

• Linear pre-accelerator (273 MeV/c 1.5 GeV)
• Dogbone 3.5-pass RLA (1.5 5 GeV)
• 5 10 GeV FFAG
• 10 20 GeV FFAG

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Dogbone RLA (3.5-pass) scheme

• Linear pre-accelerator (273 MeV/c 1.5 GeV) -
  solenoid focusing
• Main Linac (1 GeV/pass) - triplet focusing
• Single magnet horizontal multi-pass separation
• 3 Arcs based on the same strength of bending
  magnets ( 1 Tesla)

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Initial beam emittance/acceptance
after the cooling channel at 273 MeV/c
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Beam Parameters
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Pre-accelerator Longitudinal dynamics
longitudinal acceptance, bucket height
energy profile along the linac
Dp/p?0.17or Df ?93 (200MHz)
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Pre-accelerator Longitudinal acceptance
Phase space contours initial, half-way through
and at the end of acceleration contours defined
for particles at 2.5s (95 of particles contained
inside)
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Linear Pre-accelerator Longitudinal dynamics,
tracking
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soft-edge solenoid model

• Zero aperture solenoid - ideal linear solenoid
  transfer matrix

Larmour wave number
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soft-edge solenoid edge effect

• Non-zero aperture - correction due to the finite
  length of the edge
• It decreases the solenoid total focusing via
  the effective length of
• It introduces axially symmetric edge focusing at
  each solenoid end
• axially symmetric quadrupole

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soft-edge solenoid nonlinear effects

• Nonlinear focusing term DF O(r2) follows from
  the scalar potential
• Scalar potential in a solenoid
• Solenoid B-fields

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soft-edge solenoid nonlinear effects

• In tracking simulations the first nonlinear
  focusing term, DF O(r2) is also included
• Nonliner focusing at r 20 cm for 1 m long
  solenoid with 25 cm aperture radius

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Linear Pre-accelerator transverse emittance
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Main Linac - multi-pass Optics

• Focusing compromise strategy
• focusing optimized for the half-pass (1.5-2 GeV)
  - 900 phase advance per cell
• Uniform focusing restored in the second half of
  the first full-pass (2.5-3 GeV)

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Main Linac - Multi-pass Optics (lower passes)
1.5-2 GeV
2-3 GeV
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Main Linac - Multi-pass Optics (higher passes )
3-4 GeV
4-5 GeV
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Main Linac - Multi-pass phase advance slip
2-3 GeV
3-4 GeV
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Main Linac - the half-pass (1.5-2 GeV)
longitudinal tracking
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Main Linac - transverse emittance (tracking)
the half-pass 1.5-2 GeV
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Arc Optics - beam transport choices

• Principle of uniform focusing periodicity (900)
  cancellation of chromatic effects
• Single dipole (horizontal) separation of
  multi-pass beams in RLA
• No need to maintain achromatic Spreaders/Recombine
  rs
• Compact Spreaders/Recombiners minimized
  emittance dilution
• SC dipoles and quads (triplets) in RLA (1 Tesla
  dipoles/1 Tesla quads)
• Requirement of high periodicity and smooth
  transition between different kinds of optics,
  linac-spreader-arc-recombiner-linac

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Droplet return (600 out - 3000 in - 600 out)

• arc footprint

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Droplet arc Optics building blocks

• inward and outward cells, missing dipole cell

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Chromatic properties of the periodic cell

• Dp/p?0.07

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Droplet Arc Optics (Spreader and Transition) -
Arc 1
Quads Lcm GkG/cm D 68 -0.32 F 125 0.32
Dipoles Lcm BkG 150 7.8
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Arc 1 Longitudinal dynamics (tracking)
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Arc 1 Transverse emittance (tracking)
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Arc 2 Optics
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Summary

• Lattice for 3.5-pass, 5 GeV, RLA based on 200MHz
  SRF - linear optics
• Pre-accelerator, three styles of cryo-modules
• Proof-of-principle Arc optics lattice - further
  longitudinal compression in the Arcs, with M56
  3 m
• multi-pass linac optics
• compact Spr/Rec
• matched periodicity (betatron phase advance per
  cell) between linacs and Arcs
• Future work
• Emittance preservation scheme - nonlinear
  corrections in the Arcs
• Chromatic corrections in the Arcs to effectively
  restore longitudinal space linearity (via three
  families of sextupoles)
• Emittance preservation checked independently by
  ICOOL