# Presentation: 283550

## Design MANX experiment

- Katsuya Yonehara

- MANX magnet, Matching, and More

- NFMCC 2007, UCLA

- January 30, 2007

## Aim of the MANX experiment

- MANX is a proof-of-principle experiment.
- _Six dimensional helical cooling theory __(ref. PRSTAB 8,041002 (2005)_
- Demonstrate 6D cooling, Continuous emittance exchange, Exceptional cooling performance...
- MANX can be a prototype cooling magnet to R&D of cooling performance for muon colliders
- MANX can be applied for a short length precooler.
- Synchrotron motion and transverse and longitudinal coupling with the beta function in HCC.
- Non-linear effects associated with the higher order  EM field components and energy loss process.

- NFMCC 2007, UCLA

- January 30, 2007

## Particle motion in Helical Magnet

**Blue: Beam envelope**

**Red: Reference orbit**

**Magnet Center**

- Repulsive force

- Attractive force

**Both terms have opposite signs.**

*Combined function magnet (invisible in this picture)*
- 	Solenoid + Helical dipole + Helical Quadrupole

**Dispersive component makes longer **
**path length for higher momentum **
**particle and shorter path length for **
**lower momentum particle.**

- NFMCC 2007, UCLA

- January 30, 2007

## Overview of MANX channel

- Use Liquid He absorber
- No RF cavity
- Length of cooling channel: 3.2 m
- Length of matching section: 2.4 m
- Helical pitch : 1.0
- Helical orbit radius: 25 cm
- Helical period: 1.6 m
- Transverse cooling: ~150 %
- Longitudinal cooling: ~120 %
- 6D cooling: ~200 %

- NFMCC 2007, UCLA

- January 30, 2007

## Design practical helical cooling magnet

- Siberian snake type magnet
- Consists of 4 layers of helix dipole to produce
-    tapered helical dipole fields.
- Maximum field is ~7 T (coil diameter: 1.0 m)

- Use helical solenoid coil
- Consists of 73 single coils (no tilt).
- Maximum field is ~5 T (coil diameter: 0.5 m)
- Flexible field configuration

- See Mike Lamm’s talk

**Large bore channel**
**(conventional)**

**Small bore channel**
**(helical solenoid)**

- NFMCC 2007, UCLA

- January 30, 2007

## Helical field maps in TOSCA

- Small bore magnet (helical solenoid)

- Large bore magnet (conventional)

- Design with = 2.0 m and  = 0.8

- Design with = 1.6 m and  = 1.0.

- NFMCC 2007, UCLA

- January 30, 2007

## Natural quadrupole component in small bore magnet system (helical solenoid)

- Negative field gradient is produced in helical
-   solenoid coils.
- The required helical quadrupole component is
-    changed by (helical pitch).
- The strength of the quadrupole component can
-    be adjusted by the solenoid coil diameter.

-  = 1.0 m, p = 300 MeV/c

- NFMCC 2007, UCLA

- January 30, 2007

## Matching design

- Connect the straight beam section to the helical beam section.
- Need to induce
- Helical pitch (=p/pz)
- Helical radius *a*

*a*

- NFMCC 2007, UCLA

- January 30, 2007

## Adiabatic method

- Matching section

- Helical section

- Matching section

- Helical section

- Use atan to make smooth tapered field.
- Clearly see a smooth tracking.
- This channel is needed 10~15 meters.

- NFMCC 2007, UCLA

- January 30, 2007

## Can we make a shorter matching section?

- Repulsive central force

- Attractive central force

- Equilibrium orbit (ref orbit)

- Transverse b field produces transverse p kick.
- Solenoid bz field stabilizes orbit.

**and ** are the coefficients.

- NFMCC 2007, UCLA

- January 30, 2007

## Shorter matching and HCC field map

- HCC
- (4 meters)

- Upstream M
- (4 meters)

- Downstream M
- (4 meters)

- b0: Amplitude of initial helical dipole magnet
- :  Ramping rate

- Use linear function for first trial

- Adjust solenoid strength to connect
- to a proper helical orbit.

- NFMCC 2007, UCLA

- January 30, 2007

## Beam size (rms): ± 60 mm
 p/p (rms): ± 40/300 MeV/c
x’ and y’ (rms): ± 0.4
(Acceptance study has not been done yet.)

Obtained cooling factor: ~200%

- Simulation study

- Beam size (rms): ± 60 mm
-  p/p (rms): ± 40/300 MeV/c
- x’ and y’ (rms): ± 0.4
- (Acceptance study has not been done yet.)
- Obtained cooling factor: ~200%

- Initial beam profile

- NFMCC 2007, UCLA

- January 30, 2007

## Discussion of simulation result

- Good cooling performance is preserved in the helical solenoid coil magnet.
- Longitudinal betatron oscillation makes complicated emittance evolutions.
- Optimize matching magnet
- Fine tune Twiss parameters
- Optimize MANX magnet
- Obtain the best cooling performance.

- NFMCC 2007, UCLA

- January 30, 2007

## Possible beam line in Fermilab site

- Candidates
- Linac (0.4 GeV proton) See Andreas Jansson’s talk.
- Low yield, narrow space
- Meson Test area (120 GeV proton) Ask B. Abrams.
- Need energy absorber to reduce momentum.
- Parasitic design with the ILC detector group
- pbar accumulator ring (8 GeV)
- Obtain good quality beam, sufficiently high intensity
- One of the most preferable place
- MiniBooNe (8 GeV)
- Need muon capturing element

- NFMCC 2007, UCLA

- January 30, 2007

## Preliminary optics design in MTA

**Uses BNL D2 quads         “Almost” fits in MTA**

**Decay channel**

**180****o ****dispersion **
**free bend**

**Diagnostic sections**

**HCC**

- See Andreas Jansson’s talk

- NFMCC 2007, UCLA

- January 30, 2007

## Spectrometer design

- 6D phase space (or emittance exchange) measurements at HCC entrance/exit are the minimum requirement to verify the cooling theory.
- Single particle tracking measurement vs beam measurement
- Cost, reliability, precision, beam transport, etc...
- Fermilab AD now consider rastering a pencil beam.
- The hardest part of the spectrometer design is how to determine the longitudinal phase space.
- Time structure measurement?
- HCC is a kind of spectrometer itself. Therefore, we can determine the momentum by tracking the particle in HCC.
- Other interesting parameter is the feature of isochronous. This can be done by measuring ToF between upstream and downstream spectrometers.
- PID?

- NFMCC 2007, UCLA

- January 30, 2007

## Conclusions

- Big inflation in magnet design
- Found the simple solution for matching
- Need fine tuning
- Beam line design in progress
- Spectrometer design in progress

- NFMCC 2007, UCLA

- January 30, 2007

## Collaborators list

*Muons, Inc.*
- 	       B. Abrams, M. Alsharo’a, M.A. Cummings, R. Johnson,
-                        S. Kahn, M. Kuchnir, T. Roberts
*JLab*
- 	       K. Beard, A. Bogacz, S. Derbenev
*IIT*
- 	       D. Kaplan
*Fermilab Technical Division*
- 	       N. Andreev, V.V. Kashikhin, V.S. Kashikhin, M. Lamm,
-                        I. Novitski, V. Yarba, A. Zlobin
*Fermilab Accelerator Division*
- 	       C. Ankenbrandt, D. Broemmelsiek, M. Hu, A. Jansson,
- 	       M. Popovic, V. Shiltzsev

- And many useful comments & suggestions
- from Muon Collider Task Force people

- NFMCC 2007, UCLA

- January 30, 2007

## Appendix

- Show isochronous feature in HCC

- NFMCC 2007, UCLA

- January 30, 2007

## t vs Ptotal

- t vs Ptotal
- MANX Z=0 m

- t vs Ptotal
- Z=1 m

- ptotal= 0.937 /m

- t= 1.001 /m

- Fractions from initial

- t vs Ptotal
- Z=2 m

- ptotal= 0.829 /2m

- t= 1.002 /2m

- ptotal= 0.762 /3m

- t= 1.003 /3m

- t vs Ptotal
- Z=3 m

- ptotal= 0.735 /4m

- t= 1.005 /4m

- t vs Ptotal
- Z=4 m

- Bin size 0.2 ns

- Momentum compaction factor  = 0.34
-                                                       t-2 = 0.72

- NFMCC 2007, UCLA

- January 30, 2007