# Presentation: 208105

## Design Helical Cooling Channelwith ICOOL and G4BL

**Design Helical Cooling Channel****with ICOOL and G4BL**

**K. Yonehara**

**MC meeting, Berkeley CA**

**Feb. 15, 2005**

**Slide 1**

## Contents

**Contents**

**Introduction of HCC**
**Simulation study**
**Compare ICOOL and G4BL**
**Design HCC **
**Effective dispersion factor**
**Find optimum parameter**
**Summary**

**Slide 2**

**MC meeting, Berkeley CA**

- Feb. 15, 2005

## Collaborators

**Collaborators**

**D. M. Kaplan**
- Illinois Institute of Technology, Chicago, IL

**Slide 3**

**M. Alsharo’a, 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

- MC meeting, Berkeley CA

- Feb. 15, 2005

## Introduction (I)

**Introduction (I)**

**Slide 4**

-  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**

**MC meeting, Berkeley CA**

**Feb. 15, 2005**

## Introduction (II)

**Introduction (II)**

**Slide 5**

-  Now we can analyze the beam dynamics in the simulations
- and develop the channel for applying to a muon collider.

**MC meeting, Berkeley CA**

**Feb. 15, 2005**

- Pre-cooling channel MANX
- &
- Cooling channel

## Introduction (III)Helix coil

**Introduction (III)****Helix coil**

**Slide 6**

**Spin rotator coil for AGS**

- MC meeting, Berkeley CA

- Feb. 15, 2005

## Introduction (IV)HCC Layout

**Introduction (IV)****HCC Layout**

**Slide 7**

- MC meeting, Berkeley CA

- Feb. 15, 2005

- Magnet (Helical + Solenoid)

- Reference orbit

- +

## Introduction (V)Helical orbit

**Introduction (V)****Helical orbit**

**Slide 8**

- MC meeting, Berkeley CA

- Feb. 15, 2005

## Simulation study

**Simulation study**

**Slide 9**

- MC meeting, Berkeley CA

- Feb. 15, 2005

- Effective dispersion

- Optimum beam momentum

- Comparison between ICOOL and G4BL

## ICOOL and G4BLSpecifications

**ICOOL and G4BL****Specifications**

**ICOOL**
**Fortran**
**Based on Geant3**
**Tested many times by many people**
**Easy to learn**

**G4BL**
**C++**
**Based on Geant4**
**Flexible**
**Easy to develop**

**Slide 10**

- MC meeting, Berkeley CA

- Feb. 15, 2005

## ICOOL and G4BLexample beam tracking

**G4BL**

**ICOOL and G4BL****example beam tracking**

**Slide 11**

- Reference orbit

- Particle orbit

- x

- y

**ICOOL**

**HCC**
**Length: 10 m**
**Period:  1 m**
**Radius: 0.65 m**

- z

- MC meeting, Berkeley CA

- Feb. 15, 2005

## ICOOL and G4BLSimulation parameters

**ICOOL and G4BL****Simulation parameters**

**Slide 12**

| Parameters | Value in simulation for + | Unit |
| --- | --- | --- |
| Beam momentum, p | 200 | MeV/c |
| Solenoid field | -5.45 | T |
| Helix period | 1.0 |  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 (14.8 in G4BL) | MeV/m |

- MC meeting, Berkeley CA

- Feb. 15, 2005

## ICOOL and G4BLFirst result

**Slide 13**

**These plots include**
**  ****all particles.**

**ICOOL and G4BL****First result**

- MC meeting, Berkeley CA

- Feb. 15, 2005

## ICOOLParticle motion in HCC, No absorber

**ICOOL****Particle motion in HCC, No absorber**

**Slide 14**

***dr vs p******r***

***z vs dr***

**Reference orbit**

**Start point**

- MC meeting, Berkeley CA

- Feb. 15, 2005

## ICOOLParticle motion in HCC, With absorber

***z vs p******r***

***z vs dr***

**Slide 15**

***z, dt vs dE***

**Particle direction**

- MC meeting, Berkeley CA

- Feb. 15, 2005

**ICOOL****Particle motion in HCC, With absorber**

## Simulation studyDesign HCC

**Simulation study****Design HCC**

**Slide 16**

- MC meeting, Berkeley CA

- Feb. 15, 2005

- Effective dispersion factor

- Find optimum parameter

## Simulation studyEffective dispersion factor

**Simulation study****Effective dispersion factor**

***D******eff****** = D******lattice***

***D******lattice****** = ***

***a***

***p***

***dp***

***da***

**Slide 17**

- MC meeting, Berkeley CA

- Feb. 15, 2005

## Simulation studyEstimate Deloss

|  p
(MeV/c) |  |
| --- | --- |
| 150 | -0.483 |
| 200 | -0.265 |
| 250 | -0.138 |
| 374 | 0.0 |

**Simulation study****Estimate *****D******eloss***

**Slide 18**

- MC meeting, Berkeley CA

- Feb. 15, 2005

## Simulation studyAnalysis of simulation results

**Simulation study****Analysis of simulation results**

***Use quadratic function***
***for curve fitting:***
***Easy to extract the peak***
***position***

**Slide 19**

***Merit factor***
***= cooling facter ***
***Transmission efficiency***

**+**

- MC meeting, Berkeley CA

- Feb. 15, 2005

## Simulation studyAnalyzed result

|  p (MeV/c) | Peak position
(fitting curve) | Distance 
from 374 MeV/c | Estimated 
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 |

**Slide 20**

- MC meeting, Berkeley CA

- Feb. 15, 2005

## Simulation studyConclusion of effective dispersion 

**Simulation study****Conclusion of effective dispersion **

- The additional dispersion factor caused by the energy loss effect can predict 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.

**Slide 21**

- MC meeting, Berkeley CA

- Feb. 15, 2005

## Simulation studyFind optimum momentum

**Simulation study****Find optimum momentum**

**Slide 22**

- MC meeting, Berkeley CA

- Feb. 15, 2005

## Simulation studyAcceptance 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 |

**Slide 23**

- MC meeting, Berkeley CA

- Feb. 15, 2005

## Simulation studyConsideration of low momentum problem

**Simulation study****Consideration of low momentum problem**

- HCC momentum acceptance is 25 % of reference particle momentum. The lower momentum particle can be out of the acceptance because of its large energy loss rate.
- Cooling decrement rate gets bigger at lower momentum particle because of its larger energy loss rate.
- So the optimum momentum is around 250 MeV/c.

**Slide 24**

- MC meeting, Berkeley CA

- Feb. 15, 2005

## Summary

**Summary**

- ICOOL and G4BL return the consistent values each other.
- The particle motion in HCC can be studied in the simulation. We will investigate non-linear effect.
- The effective dispersion factor can be significant in the big acceptance HCC.
- The matching problem should be solved.

**Slide 25**

- MC meeting, Berkeley CA

- Feb. 15, 2005

## Future plan

**Future plan**

- HCC has a very strong magnetic field.

**Slide 26**

- MC meeting, Berkeley CA

- Feb. 15, 2005

- A pre-cooler (ex. MANX) shows very high cooling factor.

- We can provide narrower beam into HCC.

- We can reduce the field strength.

- HCC becomes more realistic device!!