Berkeley Lab Generic Presentation

1
Parametric Resonance Ionization Cooling of Muons
Alex Bogacz in collaboration with Kevin Beard,
Slava Derbenev and Rol Johnson?
Jefferson Laboratory ? Muons Inc.
7-th International Workshop on Neutrino
Factories and Superbeams, LNF Frascati, June 21,
2005
2
Overview

• Final transverse ionization cooling - Parametric
  resonance enhancement
• Resonant transport channels - lattice prototypes
• quadrupole based
• solenoid based
• Transverse beam dynamics in the cooling channel
  tracking studies
• soft-edge solenoid
• linear transfer matrix
• nonlinear corrections (in tracking)
• thin ideal absorber model
• Chromatic aberrations - compensation of the
  detuning effects with RF
• tracking studies

3
Transverse parametric resonance cooling

• Transport channel (between consecutive absorbers)
  designed to replenish large angular component,
  x, sector of the phase-space, mined by
  ionization cooling process.
• Parametric resonance in an oscillating system -
  perturbing frequency is equal to the harmonic of
  the characteristic (resonant) frequency of the
  system, e.g half-integer resonance
• Normal elliptical motion of a particles
  transverse coordinate in phase space becomes
  hyperbolic resulting beam emittance has a wide
  spread in x and narrow spread in x sector of
  the phase-space where ionization cooling is most
  effective

4
Transfer matrix of a periodic resonant lattice

• Symplectic transfer matrix, M(s), for a beamline
  (in x or y)

• Lattice period can be designed in such a way that
  sin ? 0 ? ? n? , n 1, 2.

• Coordinate and angle are uncoupled - resulting
  beam emittance has a wide spread in x and
  narrow spread in x.

x x const
5
Symmetrized double cell (Dfx 3p Dfy)
6
Angular shearing of the transverse phase-space
7
4-cell resonant channel

• Uniform triplet lattice resonantly perturbed by a
  singlet
• Absorber placed half way between triplets

8
Solenoid cell (Dfx p Dfy)
c1 Lcm130 BkG32.4
Aperturecm10 c2 Lcm80
BkG-34.1 Aperturecm10
9
soft-edge solenoid model

• Zero aperture solenoid - ideal linear solenoid
  transfer matrix

10
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

11
soft-edge solenoid nonlinear effects

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

12
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

13
Thin absorber with re-acceleration

• Ionization cooling due to energy loss (-Dp) in a
  thin absorber followed by immediate
  re-acceleration (Dp) can be described as
• The corresponding canonical transfer matrix can
  be written as

14
Final cooling initial beam parameters
p 287 MeV/c
after helical cooling channel erms
normalized emittance ex/ey mm?mrad 30
longitudinal emittance el (el sDp sz/mmc) momentum spread sDp/p bunch length sz mm mm 0.8 0.01 30
15
Solenoid cell, with absorber 6D tracking
each absorber Dp/p 0.05 4 cm Be Dp 14 MeV/c
detuning effect - the momentum-dependent
betatron frequency causes off- momentum particles
to be out of resonance with the focusing lattice
16
Solenoid cell, with absorber and RF 6D tracking
each absorber Dp/p 0.05 4 cm Be Dp 14 MeV/c
by choosing suitable synchrotron motion
parameters, the resonance condition can be
maintained
synchrotron phase advance of 2p/8 per cell two
RF cavities at zero-crossing (cavity gradient
17.3 MeV/m at 400 MHz)
17
Chromatic aberration compensation with RF cells
1-4top plots NO RF, bottom plots with the RF
18
Chromatic aberration compensation with RF cells
5-8 top plots NO RF, bottom plots with the RF
19
Solenoid cell G4BL view
20
Summary

• Present status
• Prototype PIC lattices - quadrupole and solenoid
  channels
• Lattices with absorbers studied via transfer
  matrix code
• Beam dynamics studies vie multi-particle tracking
• Building and testing G4BL tools
• Chromatic aberration compensation with
  synchrotron motion
• Proof-of-principle transport code tracking
  (solenoid triplet channel)
• Future work
• G4beamline simulation of a qudrupole/solenoid
  channel with absorbers
• G4beamline simulation with absorbers followed by
  RF cavities - include multiple scattering and
  energy straggling effects
• Emittance calculation - implementation of ecalc9