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

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Introduction

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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

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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

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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

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ICOOL and G4BLHelix coil

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Spin rotator coil

ICOOL and G4BLHelical orbit

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G4BL

ICOOL and G4BLLayout of HCC

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Reference orbit

Particle orbit

xy

ICOOL

HCCLength: 10 mPeriod: 1 mRadius: 0.65 m

z

ICOOL and G4BLSimulation parameters

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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

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•These plots include all particles.

ICOOL and G4BLFirst result

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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

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dr vs pr z vs drReference orbit

Start point

Beam dynamicsWith GH2 absorber

z vs pr z vs dr

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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.

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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.

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Low momentum problemEffective dispersion factor

Deff = Dlattice + Deloss

Dlattice =

Deloss =

ap

dp

da

dE/ds

pdp

d(dE/ds)

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p

(MeV/c)

150 -0.483

200 -0.265

250 -0.138

374 0.0

Deloss

Low momentum problemEstimate Deloss

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Low momentum problemAnalysis of simulation results

Use quadratic functionfor curve fitting:Easy to extract the peakposition

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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

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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.

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Low momentum problemEvolution of emittances

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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

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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).

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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

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No offset

With offset

+

+

12

3 4 5

1

2

3

45

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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

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• 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

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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.

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