Helical Cooling Channel Simulation with ICOOL and G4BL K. Yonehara Muon collider meeting, Miami Dec....
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Transcript of Helical Cooling Channel Simulation with ICOOL and G4BL K. Yonehara Muon collider meeting, Miami Dec....
Helical Cooling Channel Simulation with ICOOL and G4BL
K. Yonehara
Muon collider meeting, MiamiMuon collider meeting, MiamiDec. 13, 2004Dec. 13, 2004 Slide 1Slide 1
Contents
• Introduction• Simulation results
– ICOOL and G4BL
• Present interesting– Beam dynamics– Low momentum problem– Design RF cavity
• Summary/Next to do
Muon collider meeting, MiamiMuon collider meeting, MiamiDec. 13, 2004Dec. 13, 2004 Slide 2Slide 2
Introduction
Muon collider meeting, MiamiMuon collider meeting, MiamiDec. 13, 2004Dec. 13, 2004 Slide 3Slide 3
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
Introduction
Muon collider meeting, MiamiMuon collider meeting, MiamiDec. 13, 2004Dec. 13, 2004 Slide 4Slide 4
Now we can analyze the beam dynamics in the simulationsand develop the channel for applying to a muon collider.
Collaborators
D. M. KaplanIllinois Institute of Technology, Chicago, IL
Muon collider meeting, MiamiMuon collider meeting, MiamiDec. 13, 2004Dec. 13, 2004 Slide 5Slide 5
M. Alsharo’a, R. P. Johnson, P. Hanlet, K. Paul, T. J. RobertsMuons, Inc., Batavia, IL
K. Beard, A. Bogacz, Y. S. DerbenevJLab, Newport News, VA
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, MiamiMuon collider meeting, MiamiDec. 13, 2004Dec. 13, 2004 Slide 6Slide 6
ICOOL and G4BLHelix coil
Muon collider meeting, MiamiMuon collider meeting, MiamiDec. 13, 2004Dec. 13, 2004 Slide 7Slide 7
Spin rotator coil
ICOOL and G4BLHelical orbit
Muon collider meeting, MiamiMuon collider meeting, MiamiDec. 13, 2004Dec. 13, 2004 Slide 8Slide 8
G4BL
ICOOL and G4BLLayout of HCC
Muon collider meeting, MiamiMuon collider meeting, MiamiDec. 13, 2004Dec. 13, 2004 Slide 9Slide 9
Reference orbit
Particle orbit
xy
ICOOL
HCCLength: 10 mPeriod: 1 mRadius: 0.65 m
z
ICOOL and G4BLSimulation parameters
Muon collider meeting, MiamiMuon collider meeting, MiamiDec. 13, 2004Dec. 13, 2004 Slide 10Slide 10
Parameters Value in simulation for + 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 1.241.24 T
Helix quadrupole gradient -0.206-0.206 T/m
Helix orbit radius, a 0.159 m
Dispersion factor, D 1.7061.706
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, MiamiMuon collider meeting, MiamiDec. 13, 2004Dec. 13, 2004 Slide 11Slide 11
•These plots include all particles.
ICOOL and G4BLFirst result
Muon collider meeting, MiamiMuon collider meeting, MiamiDec. 13, 2004Dec. 13, 2004 Slide 12Slide 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 <10 %) with G4BL.
• This could be a proof test for both codes.
Beam dynamicsNo absorber
Muon collider meeting, MiamiMuon collider meeting, MiamiDec. 13, 2004Dec. 13, 2004 Slide 13Slide 13
dr vs pr z vs drReference orbit
Start point
Beam dynamicsWith GH2 absorber
z vs pr z vs dr
Muon collider meeting, MiamiMuon collider meeting, MiamiDec. 13, 2004Dec. 13, 2004 Slide 14Slide 14z, dt vs dE
Particle direction
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, MiamiMuon collider meeting, MiamiDec. 13, 2004Dec. 13, 2004 Slide 15Slide 15
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, MiamiMuon collider meeting, MiamiDec. 13, 2004Dec. 13, 2004 Slide 16Slide 16
Low momentum problemEffective dispersion factor
Deff = Dlattice + Deloss
Dlattice =
Deloss =
ap
dp
da
dE/ds
pdp
d(dE/ds)
Muon collider meeting, MiamiMuon collider meeting, MiamiDec. 13, 2004Dec. 13, 2004 Slide 17Slide 17
p
(MeV/c)
150 -0.483
200 -0.265
250 -0.138
374 0.0
Deloss
Low momentum problemEstimate Deloss
Muon collider meeting, MiamiMuon collider meeting, MiamiDec. 13, 2004Dec. 13, 2004 Slide 18Slide 18
Low momentum problemAnalysis of simulation results
Use quadratic functionfor curve fitting:Easy to extract the peakposition
Muon collider meeting, MiamiMuon collider meeting, MiamiDec. 13, 2004Dec. 13, 2004 Slide 19Slide 19
Merit factor= cooling facter Transmission efficiency
+
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, MiamiMuon collider meeting, MiamiDec. 13, 2004Dec. 13, 2004 Slide 20Slide 20
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, MiamiMuon collider meeting, MiamiDec. 13, 2004Dec. 13, 2004 Slide 21Slide 21
Low momentum problemEvolution of emittances
Muon collider meeting, MiamiMuon collider meeting, MiamiDec. 13, 2004Dec. 13, 2004 Slide 22Slide 22
Low momentum problemAcceptance and Equilibrium emittance
p (MeV/c)
Initial/Final
tran (mm rad)
Initial/Final
long (mm)
Initial/Final
6D (mm3)p/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, MiamiMuon collider meeting, MiamiDec. 13, 2004Dec. 13, 2004 Slide 23Slide 23
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, MiamiMuon collider meeting, MiamiDec. 13, 2004Dec. 13, 2004 Slide 24Slide 24
Design RF cavity
• Install bessel function type RF cavities in the simulation– Frequency
> 200, 400, 800, and 1600 MHz.– Location
> 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> We design a unique shape of RF cavities. We will
discuss them in future. Muon collider meeting, MiamiMuon collider meeting, MiamiDec. 13, 2004Dec. 13, 2004 Slide 25Slide 25
Design RF cavityOffset RF
Muon collider meeting, MiamiMuon collider meeting, MiamiDec. 13, 2004Dec. 13, 2004 Slide 26Slide 26
No offset
With offset
+
+
12
3 4 5
1
2
3
45
Muon collider meeting, MiamiMuon collider meeting, MiamiDec. 13, 2004Dec. 13, 2004 Slide 27Slide 27
Design RF cavityEvolution of emittance
frequency = 0.2 GHzCavity radius ~ 0.6 m
Design RF cavitySimulation result
p (MeV/c)Initial/Final
tran (mm rad)
Initial/Final
long (mm)
Initial/Final
6D (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, MiamiMuon collider meeting, MiamiDec. 13, 2004Dec. 13, 2004 Slide 28Slide 28
• 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.
Design RF cavitySummary
Muon collider meeting, MiamiMuon collider meeting, MiamiDec. 13, 2004Dec. 13, 2004 Slide 29Slide 29
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, MiamiMuon collider meeting, MiamiDec. 13, 2004Dec. 13, 2004 Slide 30Slide 30