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Helical Cooling Channel Simulation with ICOOL and G4BL

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helical cooling channel (HCC) with the high pressure gaseous ... Illinois Institute of Technology, Chicago, IL. Muon collider meeting, Miami. Dec. 13, 2004 ... – PowerPoint PPT presentation

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Title: Helical Cooling Channel Simulation with ICOOL and G4BL


1
Helical Cooling Channel Simulation with ICOOL and
G4BL
  • K. Yonehara

Muon collider meeting, Miami
Dec. 13, 2004
Slide 1
2
Contents
  • Introduction
  • Simulation results
  • ICOOL and G4BL
  • Present interesting
  • Beam dynamics
  • Low momentum problem
  • Design RF cavity
  • Summary/Next to do

Muon collider meeting, Miami
Dec. 13, 2004
Slide 2
3
Introduction
Analytical six-dimensional cooling demonstration
in the helical cooling channel (HCC) with the
high pressure gaseous hydrogen absorber has been
done (MuCoolNote0284).
We need to verify the new idea by a numerical
method.
ICOOL and G4BL
Muon collider meeting, Miami
Dec. 13, 2004
Slide 3
4
Introduction
Now we can analyze the beam dynamics in the
simulations and develop the channel for applying
to a muon collider.
Muon collider meeting, Miami
Dec. 13, 2004
Slide 4
5
Collaborators
  • D. M. Kaplan
  • Illinois Institute of Technology, Chicago, IL

M. Alsharoa, R. P. Johnson, P. Hanlet, K. Paul,
T. J. Roberts Muons, Inc., Batavia, IL
K. Beard, A. Bogacz, Y. S. Derbenev JLab, Newport
News, VA
Muon collider meeting, Miami
Dec. 13, 2004
Slide 5
6
ICOOL and G4BLSpecifications
  • ICOOL
  • Fortran
  • Based on Geant3
  • Tested many times by many people
  • Easy to learn
  • G4BL
  • C
  • Based on Geant4
  • Flexible
  • Easy to develop

Muon collider meeting, Miami
Dec. 13, 2004
Slide 6
7
ICOOL and G4BLHelix coil
Spin rotator coil
Muon collider meeting, Miami
Dec. 13, 2004
Slide 7
8
ICOOL and G4BLHelical orbit
Muon collider meeting, Miami
Dec. 13, 2004
Slide 8
9
ICOOL and G4BLLayout of HCC
G4BL
ICOOL
Reference orbit
z
HCC Length 10 m Period 1 m Radius 0.65 m
Particle orbit
y
x
Muon collider meeting, Miami
Dec. 13, 2004
Slide 9
10
ICOOL and G4BLSimulation parameters
Parameters Value in simulation for m Unit
Beam momentum, p 200 MeV/c
Solenoid field -5.45 T
Helix period 1.00 m
Helical magnet inner radius 0.65 m
Transverse field at beam center 1.24 T
Helix quadrupole gradient -0.206 T/m
Helix orbit radius, a 0.159 m
Dispersion factor, D 1.706
Accelerating RF field amplitude 33.0 (32.7 in G4BL) MV/m
Frequency 0.201 GHz
Absorber gas pressure 400 atm
Absorber energy loss rate 14.9 MeV/m
Muon collider meeting, Miami
Dec. 13, 2004
Slide 10
11
ICOOL and G4BLFirst result
  • These plots include
  • all particles.

Muon collider meeting, Miami
Dec. 13, 2004
Slide 11
12
ICOOL and G4BLSummary
  • We first observed the cooling effect of HCC in
    the simulations which is predicted by the
    analytical method.
  • The simulation result in ICOOL shows a good
    agreement (discrepancy lt10 ) with G4BL.
  • This could be a proof test for both codes.

Muon collider meeting, Miami
Dec. 13, 2004
Slide 12
13
Beam dynamicsNo absorber
dr vs pr
z vs dr
Start point
Reference orbit
Muon collider meeting, Miami
Dec. 13, 2004
Slide 13
14
Beam dynamicsWith GH2 absorber
z vs pr
z vs dr
Particle direction
z, dt vs dE
Muon collider meeting, Miami
Dec. 13, 2004
Slide 14
15
Beam dynamicsSummary
  • We just start considering this study. We will
    see more analysis results soon.
  • We observe a strong coupling between transverse
    and longitudinal motions.

Muon collider meeting, Miami
Dec. 13, 2004
Slide 15
16
Low momentum problemIntroduction
The design of helical cooling channel for a
lower momentum muon is practical since it can
significantly reduce the strength of helix and
solenoid fields. However, we never succeed to see
a nice cooling result in a lower momentum
region. We noticed that the dispersion factor
should be modified to take into account the
correction of the energy loss process. This
correction should be larger for a lower momentum
particle since the energy loss rate of it is
larger than that of a higher momentum particle.
Muon collider meeting, Miami
Dec. 13, 2004
Slide 16
17
Low momentum problemEffective dispersion factor
Deff Dlattice Deloss
p
da
Dlattice
a
dp
p
d(dE/ds)
Deloss
dp
dE/ds
Muon collider meeting, Miami
Dec. 13, 2004
Slide 17
18
Low momentum problemEstimate Deloss
p (MeV/c)
150 -0.483
200 -0.265
250 -0.138
374 0.0
Muon collider meeting, Miami
Dec. 13, 2004
Slide 18
19
Low momentum problemAnalysis of simulation
results
Use quadratic function for curve fitting Easy to
extract the peak position
Merit factor cooling facter Transmission
efficiency

Muon collider meeting, Miami
Dec. 13, 2004
Slide 19
20
Low momentum problemAnalyzed result
p (MeV/c) Peak position (fitting curve) Distance from 374 MeV/c Dispersion factor by energy loss Fraction between columns 4 5
374 0.229 0.0 0.0
250 0.0697 -0.160 -0.138 0.86
200 -0.0962 -0.326 -0.265 0.81
150 -0.321 -0.550 -0.483 0.88
Muon collider meeting, Miami
Dec. 13, 2004
Slide 20
21
Low momentum problemSummary (1)
  • The additional dispersion factor caused by the
    energy loss effect well reproduces the peak
    position in the merit factor curve.
  • However, we still see a small fraction in the
    effective dispersion factor. This could be caused
    by another dispersion effect.

Muon collider meeting, Miami
Dec. 13, 2004
Slide 21
22
Low momentum problemEvolution of emittances
Muon collider meeting, Miami
Dec. 13, 2004
Slide 22
23
Low momentum problemAcceptance and Equilibrium
emittance
p (MeV/c) Initial/Final etran (mm rad) Initial/Final elong (mm) Initial/Final e6D (mm3) Dp/p
374 27.8/3.36 71.0/7.68 48900/57.4 120/374
250 22.5/1.96 73.9/2.72 32000/6.62 60/250
200 18.3/1.91 66.4/2.47 17500/5.15 55/200
150 14.3/2.98 48.3/5.86 8660/20.0 45/150
Muon collider meeting, Miami
Dec. 13, 2004
Slide 23
24
Low momentum problemSummary (2)
  • The acceptance of higher momentum beam is larger
    but the cooling decrement is smaller while the
    cooling decrement in lower momentum beam is
    larger but the acceptance is smaller.
  • So the optimum beam momentum seems to be 200
    250 MeV/c.
  • The optimum beam momentum can be changed by the
    absorber density (pressure).

Muon collider meeting, Miami
Dec. 13, 2004
Slide 24
25
Design RF cavity
  • Install bessel function type RF cavities in the
    simulation
  • Frequency
  • gt 200, 400, 800, and 1600 MHz.
  • Location
  • gt We tested two types of location of the center
    of RF cavities one is on an HCC axis (no offset)
    and the other is on a reference orbit (with
    offset).
  • Shape
  • gt We design a unique shape of RF cavities. We
    will discuss them in future.

Muon collider meeting, Miami
Dec. 13, 2004
Slide 25
26
Design RF cavityOffset RF
No offset

2
3
1
With offset

2
1
4
3
4
5
5
Muon collider meeting, Miami
Dec. 13, 2004
Slide 26
27
Design RF cavityEvolution of emittance
frequency 0.2 GHz Cavity radius 0.6 m
Muon collider meeting, Miami
Dec. 13, 2004
Slide 27
28
Design RF cavitySimulation result
p (MeV/c) Initial/Final etran (mm rad) Initial/Final elong (mm) Initial/Final e6D (mm3)
Uniform Ez 18.3/1.88 64.0/2.42 17200/4.83
With offset 18.9/1.57 74.1/4.54 20100/6.46
No offset 16.2/5.46 64.0/3.85 12800/41.1
Muon collider meeting, Miami
Dec. 13, 2004
Slide 28
29
Design RF cavity Summary
  • The RF cavities with offset works well.
  • However, we observe a less reduction of the
    longitudinal emittance by using the offset type
    RF cavities.
  • We need to improve the propagation of
    longitudinal beam cooling in HCC.

Muon collider meeting, Miami
Dec. 13, 2004
Slide 29
30
Summary/Next to do
  • The two simulations work pretty well.
  • We study beam dynamics in HCC.
  • We found the effective dispersion factor.
  • We design several type of RF cavities.
  • We figure out the matching problem.

Muon collider meeting, Miami
Dec. 13, 2004
Slide 30
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