# Presentation: 845713

## Recent simulation study for MANX experiment

- K. Yonehara

- MCTF Meeting

- August 31, 2006

## Various momentum muons

- Can we see the cooling at the muon momentum below 0.25 GeV/c?

- MCTF Meeting

- August 31, 2006

## Set up geometry

-  = 1.6 m,  = 1.0
- r of beam pipe = 0.4 m
- r of reference orbit = 255 mm
- pinitial = 0.22, 0.25, 0.275, 0.3 GeV/c
- Total length
- 1.6 m (0.22 GeV/c), 2.4 m (0.25 GeV/c), 3.2 m (0.275 GeV/c)
-     4.0 m (0.3 GeV/c)
- 0.14 GeV/c < Final pfinal < 0.15 GeV/c
- Use LHe as absorber
- Momentum cut at the end of HCC (±0.15 ×pfinal)
- Field map is generated by using analytical formula.

**2.4 m**

- MCTF Meeting

- August 31, 2006

## Emittance evolutions in various p

- Initial / Final Cooling factor

- p=0.22 GeV/c, 71.13/50.88 = 1.40

**Matching**

**MANX**

- p=0.25 GeV/c, 75.29/48.53 = 1.55

- p=0.275 GeV/c, 85.02/45.61 = 1.86

- p=0.3 GeV/c, 85.42/41.49 = 2.06

**There is a coupling between transverse and longitudinal phase space in the matching.**

- Transverse emittance

- MCTF Meeting

- August 31, 2006

## Emittance evolution in various p

- Initial / Final Cooling factor

- p=0.22 GeV/c, 174.7/142.0 = 1.23

**Matching**

**MANX**

- p=0.25 GeV/c, 198.0/139.2 = 1.42

- p=0.275 GeV/c, 245.8/139.6 = 1.76

- p=0.3 GeV/c, 235.1/131.5 = 1.79

- Longitudinal emittance

- MCTF Meeting

- August 31, 2006

## Emittance evolution in various p

- Initial / Final Cooling factor

- p=0.22 GeV/c, 750.2/353.7 = 2.12

**Matching**

**MANX**

- p=0.25 GeV/c, 931.6/330.5 = 2.82

- p=0.275 GeV/c, 1427/280.7 = 5.08

- p=0.3 GeV/c, 1371/215.7 = 6.36

- 6D emittance

- MCTF Meeting

- August 31, 2006

## Summary

- We see the beam cooling at p = 0.22 ~ 0.3 GeV/c.
- There is no big difference between p = 0.275 GeV/c and p = 0.3 GeV/c.
- There is a coupling between the transverse and longitudinal phase spaces in the matching.

- MCTF Meeting

- August 31, 2006

## 6D phase space evolution

- ~ This study is for detector design. ~

- What is the required beam profile?

- MCTF Meeting

- August 31, 2006

## Test geometry

- pinitial = 0.3 GeV/c, pfinal = 0.17 GeV/c
- Beam size ± 0.12 m
-   = 1.6 m, = 1.0
- r of beam pipe = 0.5 m
- r of reference orbit = 0.255 m
- Total length = 3.2 m
- Matching length = 2.4 m
- 2 mm Al windows at both ends of MANX
- Field map is generated by a series of helical solenoids in TOSCA3d.

- MCTF Meeting

- August 31, 2006

## Upstream matching + MANX

**Upstream matching**

**2mm Thick Al Windows**

**MANX**

**Helical solenoid coil**

- MCTF Meeting

- August 31, 2006

## Emittance evolutions in various beams

- dp = 40 MeV/c, dpt = 60 MeV/c is chosen for further study.
- In this case, the cooling factor is 3.06.

- dp: standard deviation of total momentum
- dpt: standard deviation of transverse momentum

- 6D emittance

- Matching

- MANX

- MCTF Meeting

- August 31, 2006

## 6D Phase space evolution

- p = 0.27 to 0.34 (p = 0.07) [GeV/c]
- t = -5.8 to 9.0 (t = 14.8) [ns]
- x = -0.14 to 0.12 (x = 0.26) [m]
- y = -0.12 to 0.13 (y = 0.25) [m]
- px = -0.13 to 0.11 (px = 0.24) [GeV/c]
- py = -0.13 to 0.11 (py = 0.24) [GeV/c]

- Initial beam profile (z = 0.4 m)

- p = 0.15 to 0.21 (p = 0.06) [GeV/c]
- t = 21 to 37 (t = 16) [ns]
- x = -0.25 to -0.03 (x = 0.22) [m]
- y = -0.17 to 0.19 (y = 0.36) [m]
- px = -0.09 to 0.07 (px = 0.16) [GeV/c]
- py = -0.16 to -0.03 (py = 0.13) [GeV/c]

- Final beam profile (z = 6.4 m)

- total p

- t

- MCTF Meeting

- August 31, 2006

## 6D Phase space evolution

- x

- px

- y

- py

- MCTF Meeting

- August 31, 2006

## Note

- There is no big difference in the cooling performance at p = 0.3 and 0.275 GeV/c.
-     Therefore, the required p can be down
-     to p = 0.24 to 0.31 GeV/c.
- Larger transverse momentum deviation (px and py) makes a bigger 6D cooling factor.
- Bunch length can be shorter.
- The initial px and py have asymmetric structure.

- MCTF Meeting

- August 31, 2006

## Backup slides

-  Design matching section
-  Non-linear effect

- MCTF Meeting

- August 31, 2006

## Design matching section

- MCTF Meeting

- August 31, 2006

## Current matching design

-  3 m Matching section
-    (It needs 15 meters if a helix dipole
-     turns on adiabatically.)
-  2 mm Al window
-  4 m HCC
-  2 mm Al window
-  3 m Matching section
-    (It is not shown in schematic picture
-     and field plots.)

- Solenoid

- Dipole

- Matching

- HCC

- MCTF Meeting

- August 31, 2006

## Current matching design

- Quadrupole

- Matching

- HCC

- MCTF Meeting

- August 31, 2006

## Current matching design

- MCTF Meeting

- August 31, 2006

## Current matching design

- 85.52/43.69 = 1.96

- 199.3/137.2 = 1.45

- 1340/281.4 = 4.76

- Initial / Final 

**coupling**

- Matching

- MANX

- Matching

- MCTF Meeting

- August 31, 2006

## Non-linear motion inenergy loss process

- What is the difficulty to make a lower momentum HCC?

- MCTF Meeting

- August 31, 2006

## Non-linear effect in energy loss process (I)

-  The challenge here is how to build a lower momentum HCC.
-  A big difference between p=0.1 GeV/c and p=0.15 GeV/c (20 vs 600).
-   Dhat is the distance from theoretical Dhat+1st order energy loss correction.

**Cooling factor**

- MCTF Meeting

- August 31, 2006

## Non-linear effect in energy loss process (II)

- General definition

- Taylor expansion

- 1st order perturbation term

- 2nd order perturbation term

- 3rd order perturbation term

**B**

- *x*

- *p*

- *p*

- *x*

- MCTF Meeting

- August 31, 2006