# Presentation: 681632

## Bunched-Beam Phase Rotation-Variation and 0ptimization

- David Neuffer,
- A. Poklonskiy
**Fermilab**

## 0utline

**Introduction**
**Study 2AP******** ???**
**“****High-frequency” Buncher and ******** Rotation**
**Study 2A scenario, Obtains up to ~0.2 ********/p**
**Variations**
**Shorter rotator (52m ******** 26m), fewer rf frequencies**
**Short bunch train (< ~20m)**
**Optimization ....**
**Muon Collider scenarios**
**Gas filled cavities **
**Higher gradients?**
**Cooling in buncher and rotator**
**Polarization ??**

## Study2AP June 2004 scenario

- Drift –110.7m
- Bunch -51m
- V(1/) =0.0079
- 12 rf freq., **110MV**
- 330 MHz  230MHz
- -E Rotate – **54m –**** ****(416MV total)**
**15 rf freq. 230******** 202 MHz**
- P1=280 , P2=154 ******N****V**** = ****18.032**
- Match and cool (80m)
- 0.75 m cells, 0.02m LiH
- “Realistic” fields, components

## Shorter bunch Rotator

**Drift** –123.7m (a bit longer)
**Bunch** -51m
- V’ = 3(z/LB) + 3 (z/LB)2 MV/m
- (1/) =0.0079
******-E Rotate** – **26m –**
**12 MV/m **(× 2/3)
- P1=280 , P2=154 ******V = ****18.1**
- (Also P1=219 , P2=154,            ******V = ****13.06)**
**Match and cool** (100m)
- V’ = 15 MV/m (× 2/3)
- P0 =214 MeV/c
- 0.75 m cells, 0.02m LiH
- Obtain ~0.22 /p

## Short bunch train option

- Drift (20m), Bunch–20m **(100 MV)**
-  Vrf = 0 to 15 MV/m ( 2/3)
- P1 at 205.037, P2=130.94
- N = 5.0
- Rotate – 20m (200MV)
- N = 5.05
- Vrf = 15 MV/m ( 2/3)
- Palmer Cooler up to 100m
- Match into ring cooler
- ICOOL results
**0.12 ********/p **within 0.3 cm
- Could match into ring cooler (C~40m) (~20m train)

**60m**

**40m**

**95m**

## FFAG/ μ+-μ- Collider –influenced:

**Example I**** (250 MeV)**** ****100MHz**
**Uses ~90m drift + 100m 200********100 MHz rf (5MV/m)**
**Captures ****250********200 MeV**** ********’s into 250 MeV bunches with ****±80 MeV**** widths**
** **
**Example II**** (125 MeV) ****50MHz**
**Uses ~60m drift + 90m 100********50 MHz rf (<3MV/m) ~180MV total**
**Captures ****125********100 MeV**** ********’s into 125 MeV bunches with ****±****40 MeV**** widths**

## Advantages of high-pressure cavities 

-  **high gradient rf**
- In magnetic fields B=1.75T, or more ...
- With beam
- Change cavity frf by 
- Can Integrate cooling with capture
- Capture and phase-energy rotation + cooling
- Can get high-gradient at low frequencies (30, 50, 100 MHz ???)
- Beam manipulations
- Polarization

**Research can be funded...**

## Simplest Modification

**Cool here**

**Add gas** + higher gradient to obtain **cooling within rotator**
- ~300MeV energy loss in cooling region
- Rotator is 51m;
- Need ~6MeV/m H2 Energy loss
- 9MeV/m if cavities occupy 2/3
- ~30% Liquid H2 density
- 100atm, 90oK gas
- Alternating Solenoid lattice in rotator
- 21MV/m rf
- Lattice changes
- Try shorter system ...

## Polarization for μ+-μ- Colliders

- Start with short proton bunch on target < ~1ns
- Before π⇒μ+ν decay, use low-frequency rf to make π-beam more monochromatic
- ~50MV in ~5m?
- Drift to decay (~10m?)
- Higher energy μ’s pol. +
- Lower energy μ’s pol. –
- 1⁄4 Phase-Energy rotation
- ~10m
- Rebunch at ~2× frequency
- +’s in one bunch
- -’s in other bunch
**~50 ******** 100MHz ??**

- +

- +

**-**

**-**

## Some initial simulations (K. Paul)

- Initial beam from MARS
- 5m from target - 76% π
- 200MHz rf, 50 MV/m
- 5m from target then 2m rf

## Summary

- High-frequency Buncher and E Rotator (ν-Factory)
**Variations (see ****Poklonskiy****),**
**Shorter systems ??**
- Lower Frequency (fewer bunches).
**Gas-filled rf cavities**
**Higher gradient??**
**Cool in buncher rotator**
- Polarization ...  ???
**To do:****	**
- Optimizations, Best Scenario, cost/performance ...
- Consider applications besides ν-Factory: μ+-μ- collider, low-energy muon source

## Meeting Status