# Presentation: 538280

## Bunched-Beam Phase Rotation- Ring Coolers?  - FFAGs? 

- David Neuffer
**Fermilab**

## Outline

**Introduction**
**Study 2 scenario**
- Induction linac phase rotation + 200 MHz buncher
**“****High-frequency” Buncher and ******** Rotation**
- Concept
- 1-D, 3-D simulations
- Cost guesstimates ...
**Continuing Studies ...**
- Variations
- Matching, Optimization  Study 3
- For **FFAG ********-Factory** injection ??
- Lower frequencies, larger energy spreads ??

## Neutrino Factory Baseline Design 

- Feasible, but expensive
- Find ways to reduce costs ...

## Adiabatic buncher + Vernier  Rotation

**Drift ****(90m)**
** ********  ****decay;**
**	****beam develops  ******** correlation**
**Buncher**** ****(60m)**** ****(~333********200MHz)**** **
**Forms beam into string of bunches**
****** ****Rotation****(~10m)**** ****(~200MHz)**
**Lines bunches into equal energies**
**Cooler****(~100m long)**** ****(~200 MHz)**
**fixed frequency transverse cooling system**

**Replaces Induction Linacs with medium-frequency rf  (~200MHz) !**

## Longitudinal Motion (1-D simulations)

**Drift**

**Bunch**

******E rotate**

**Cool**

**System would capture both signs ****(********+****, ********-****) ****!!**

## Buncher overview

- Adiabatic buncher
**Set  T****0****, ******:
- 125 MeV/c,   0.01
- In buncher:
**Match to**** ********rf****=1.5m** at end:
- zero-phase with 1/ at integer intervals of  :
**Adiabatically increase rf gradient**:

******rf**** : **0.901.5m

## “Vernier”  Rotation

**At end of buncher, choose:**
- Fixed-energy particle T0
- Second reference bunch TN
- Vernier offset 
**Example:**
- T0 = 125 MeV
- Choose N= 10, =0.1
- T10 starts at 77.28 MeV
**Along rotator, keep reference particles at  (N + ********) ********rf**** spacing**
- 10 = 36° at =0.1
- Bunch centroids change:
**Use E****rf**** = 10MV/m; L****Rt****=8.74m**
- High gradient not needed ...
- Bunches rotate to ~equal energies.

******rf**** : **1.4851.517m in rotation;
- rf = ct/10 at end
**(********rf**** ******** 1.532m)**
- Nonlinearities cancel:
- T(1/)  ;   Sin()

## Key Parameters

- General
- Muon capture momentum (200MeV/c?) 400MeV/c?
- Baseline rf frequency (200MHz)
- Drift
- Length LD
- Buncher –  Length (LB)
- Gradient, ramp VB   (linear OK)
- Final Rf frequency (LD + LB) (1/) = RF
- Phase Rotator-Length (LB)
- Vernier offset : NB, V
- Rf gradient VR
- Cooling channel / Accelerator ???

## Next step: match into cooling channel !

- Need to design a new cooling channel, matched to bunched/rotated beam
- Do not (yet) have redesigned/matched cooling channel
**Use (for initial tries):**
- ICOOL beam from end of AVG simulations
**Study 2 cooling channel**
- Direct transfer of beam (no matching section)

## Results (~ICOOL)

- In first ~10m, 40% of ’s from buncher are lost,
********** ******** ****0.020m******** ************ ******** 0.012m**
- Remaining ’s continue down channel and are cooled and scraped, ********** ******** ~0.0022m, **similar to Study 2 simulation.
**Best energy, phase gives ~0.22  ********’s /24 GeV p**
- Study 2 baseline ICOOL results is ~0.23  ’s/p

**GeV**

**m**

## Caveats: Not properly matched 

**This is ****not**** the way to design a neutrino factory**
**Not properly matched in phase space**
**Cooling channel acceptance is too small ****	****	**** (add precooler ?)**
**Correlation factors “wrong” **
**“****Cooling” channel collimates as much as it cools ...**

## Shorter bunch train (for Ring Cooler ?)

- Ring Cooler requires shorter bunch train for single-turn injection – ~30m?
- 200MHz example
- –reduce drift to 20m (from 90)
- -reduce buncher to 20m
- Rotator is ~12m
- ~85% within <~30m
- Total rf voltage required is about the same (~200MV)
- RFOFO cooler wants **12m** bunch train !!!

**“****Long” Bunch**

**“****Short” Bunch**

** ********2 scale**

## “Match” into “cooling channel”

- Place beam output into  Study 2 cooling channel
- No “matching”
- Long bunch case accepts ~0.20 /p
- Short bunch case accepts ~0.145 /p
- (Study 2 example is 0.23 /p in these units)

## New Cooling Channel needed

- Need initial cooling channel
- (Cool T from 0.02m to 0.01m)
- Longitudinal cooling ?
- Examples
- Solenoidal precooler (Palmer)
- “Quad-channel” precooler
- 3-D precooler
- Match into precooler
- First try unmatched

## To do

**Move to more realistic models**
- Continuous changes in rf frequencies to stepped changes ...
- 3-D fields (not solenoid + sinusoidal rf)
**Match** into realistic cooling channels ...
- Estimate/Optimize  ** ****Cost**** **/performance

## Comment on costs

## Variations/ Optimizations ...

**Many possible variations and optimizations**
- But possible variations will be reduced after design/construction
**Shorter bunch trains ??**
**For ring Coolers ?**
**Other frequencies ??**
- 200 MHz(FNAL)  88 MHz ?? (CERN)  ??? ~44MHz
**Cost/performance optima** for neutrino factory (Study 3?)
**Collider ??** **both signs (********+****, ********-****) !**
**Graduate students (MSU) (Alexiy Poklonskiy, Pavel Snopok) will study these variations; optimizations; etc... **

## FFAG -Factory injection

- Baseline scenario is single bunch injection without -E rotation or bunch formation
- Capture is not matched to beam phase-space
- Capture is centered at higher energy than Study 2
- Requires very **low-frequency bucket **(~25 MHz or less)
- Rf Gradient is ~1 MV/m (or less)
- Can injection use buncher-rotator methods to improve acceptance, increase rf gradient ?

**Capture is ± 150MeV, **
** ****± 12 ns**

## Bunch sizes for various rf scenarios

| Case | Rf frequency | E (MeV)
(±) | z  (m)
(±) | 
(eV-s) |
| --- | --- | --- | --- | --- |
| JNF
(~300MeV)  | 5 MHz  ?? | 150 | 3.00 | 4.7
(~1.0m rms) |
| ~Study 2
(~125MeV) | 200MHz | 40 | 0.40 | 0.18 (~0.04m) |
| 250 MeV | 200MHz | 80 | 0.4 | 0.36 (~0.08m) |
| 125 MeV | 100MHz | 40 | 0.8 | 0.36 (~0.08m) |
| 250 MeV | 100MHz | 80 | 0.8 | 0.72 (~0.16m) |
| 125 MeV | 50MHz | 40 | 1.6 | 0.72 (~0.16m) |
| 250 MeV | 50MHz | 80 | 1.6 | 1.5 (~0.32m) |

## FFAG-influenced variation – 100MHz

- 100 MHz example
- 90m drift; 60m buncher, 40m rf rotation
- Capture centered at **250 MeV**
**Higher energy capture means shorter bunch train**
**Beam at 250MeV ****±**** 200MeV accepted into 100 MHz buncher**
**Bunch widths  < ****±****100 MeV**
- Uses ** ~ 400MV of rf **

## ~50 MHz variations

**Example I (250 MeV)**
- Uses ~90m drift + 100m 10050 MHz rf (<4MV/m) ~300MV total
- Captures 250200 MeV ’s into 250 MeV bunches with ±80 MeV widths
**Example II (125 MeV)**
- 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

## Summary

- High-frequency Buncher and E Rotator    simpler and **cheaper** than induction linac system
- Performance as good (or almost ...) as study 2,
_**But**_
**System will capture both signs (********+****, ********-****) !**
**	****(Twice as good ??)**
- Method could (?) be baseline capture and phase-energy rotation for **any**** **neutrino factory ... (FFAG)
**To do:**
- Complete simulations with **matched** cooling channel!
- Optimizations, Best FFAG Scenario, ...

## Last slide

## Compare with Study II (Capture + Cooling) 

**x:   –20 to 100m;  y: 0 to 400 MeV**

## ICOOL simulation –Buncher, , Cool 

## Study 2 system 

**Drift** to develop Energy- phase correlation
- Accelerate tail; decelerate head of beam (280m induction linacs (!))
**Bunch** at 200 MHz
- Inject into 200 MHz cooling system