# Presentation: 304144

## Bunched-Beam Phase Rotation

- David Neuffer
**Fermilab**

## Outline

**Introduction**
**“****High-frequency” Buncher and ******** Rotation**
- Concept
- 1-D, 3-D simulations
**Continuing Studies ...**
- Variations
**Matching, Optimization ******** Study 3**
**Match to Palmer cooling section**
**Obtains up to ~0.27 ********/p**
**Variations (shorter, ...) ******** cost performance optimum**

## 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 ****(********+****, ********-****) ****!!**

## Adiabatic Buncher overview

- Want **rf phase to be zero **for reference energies as beam travels down buncher
- Spacing must be N rf              rf increases (rf frequency decreases)
**Match to**** ********rf****= ~1.5m** at end:
**Gradually increase rf gradient **
- 	(linear or quadratic ramp):

- Example: ******rf**** : **0.901.5m

## Adiabatic 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

##  Rotation

**At end of buncher, change rf to ****decelerate high-energy bunches, accelerate low energy bunches**
- With central reference particle at zero phase,                                 set ******rf ****a bit less than bunch spacing**
- 	(increase rf frequency)
**Places low/high energy bunches at accelerating/decelerating phases**
- Can use **fixed frequency **(requires fast rotation)   or
- Change frequency along channel to maintain phasing         **“Vernier” rotation –A. Van Ginneken **

## “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()

## First ICOOL Simulations

**ICOOL Simulations**
**Include Transverse motion + realistic initial distributions**
**Initial beam – Study II target production **
**Transverse focusing - **
**20 T****(Target)**** ******** 1.25T solenoid**
**1.25 T focusing throughout (********x**** = 10cm)**
**Buncher + ********E rotation**
**Use parameters approximating 1-D simulation;**
**Initial transport into Study 2 Cooling channel**
**Accepts only ********T**** =0.12 rms; ~40% loss by scraping**
**Up to ~0.2 ******** obtained **
**Better with matched cooling ? ********T**** =0.20 rms;**

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

## Key Parameters

- General
- Muon capture momentum (200MeV/c?) 280MeV/c?
- Baseline rf frequency (200MHz)
**Drift**
- Length **L****D**
**Buncher** –  Length (**L****B**)
- Gradient, ramp **V****B**   (linear OK)
- Final Rf frequency (LD + LB) (1/) = ******RF**
**Phase Rotator**-Length (**L********R**)
- Vernier, offset : **N********R**, ******V**
- Rf gradient **V********R**** **
- Match into cooling channel, Accelerator

## Implementation in ICOOL

- Define 2 reference particles: P1, P2
**ACCEL** option 10
**N** –wavelengths between ref particles
- V(z) = A +Bz +Cz2
- Long. Mode
- Phase model 0 or 1
- 0 at t1 (part**REFP **model 3 or 4icle 1)
- 1 at (t1 + t2)/2
- 3 –constant velocity
- 4 –energy loss + reference energy gain in cavities

- SREGION         !  RF
- 0.50  1    1e-2
- 1  0.   0.30
- ACCEL
-   10. 0. 0. 0. 5.05   1. 30. 15 0 0  0. 0. 0. 0. 0
- VAC
- NONE
-    0. 0. 0. 0. 0.   0. 0. 0. 0. 0.

## New Cooling Channel

- 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 was unmatched
- Transverse match
- B=Const.  B sinusoidal
- Gallardo, Fernow & Palmer

## Palmer Dec. 2003 scenario

- Drift –110.7m
- Bunch -51m
- (1/) =0.0079
- -E Rotate – **52m**
- P1=280 , P2=154 ******V = ****18.032**
- Match and cool (100m)
- P0 =214 MeV/c
- 0.75 m cells, 0.02m LiH

## Simulation results

- (Palmer, Gallardo, Fernow,...
- 0.25 /p in 30  mm acceptance

## How many rf frequencies?

- Example has new frequency every rf cavity
- Elvira and Keuss explored how many different rf cavities were needed, using Geant4
- 60 initially
- 20 OK
- 10 also OK, but slightly worse performance
- Need to go through this exercise for present scenario

**Only 20 frequencies**
**and voltages.**
**(20 equidistant**
**linacs made of 3 cells)**

## 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**

## “Latest” short buncher

- Drift – 20m
- Bunch – 20m
-  Vrf = 0 to 15 MV/m ( 2/3)
- P1 at 205.037, P2=130.94
- N = 5.0
- Rotate – 20m
- N = 5.05
- Vrf = 15 MV/m ( 2/3)
- Palmer Cooler up to 100m

**60m**

**40m**

**95m**

## Simulation results

- ICOOL results
- 0.12 /p within 0.3 cm acceptance
- Bunch train ~12 bunches long  (16m)
- (but not 8 bunches ...)

## 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 **

## Comment on costs

## Hardware/Cost (Shelter Island Now)

**Rf requirements:**
**Buncher:** ~300~210 MHz; 0.14.8MV/m (60m)
- (~10 frequencies; ~10MHz intervals)
****** ****Rotator:** ~210200 MHz; 10MV/m (~10m)
**Transverse focussing**
**160m ****B=1.25T** solenoidal focusing;**R=0.30m** transport

-  2002 cost estimate
- (**Rf  =30M$** (Moretti); **magnets =40M$**(M. Green);  conv. fac.,misc. **20M****$**)
- 		**( ?? 100M$ )**
**NOW – ****Rotator ******** up to 50m, rf at least 40M$ (?) more**
**Transverse Focusing at 2T, ****R =0.25m, 200+ m long**
**Need better/updated cost estimate; cost/performance optimization**
**	****see Palmer’s talk****	**** **

## Summary

- High-frequency Buncher and E Rotator simpler and **cheaper** (?) than induction linac system
- Performance better (?) than study 2,
_**And**_
**System will capture both signs (********+****, ********-****) !**
**	****(Twice as good ?)**
- Method could be baseline capture and phase-energy rotation for **any**** **neutrino factory ...
**To do:****	**
- Optimizations, Best Scenario, cost/performance ...

## ~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

## 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... **

## Hardware For Adiabatic Buncher

- Transverse focussing (currently)
**B=1.25T** solenoidal focusing
**R=0.30m** transport for beam
**Rf requirements:**
**Buncher:** ~300~210 MHz; 0.14.8MV/m (60m)
- (initially 1 cavity every 1m; reduces frequency in 2-4MHZ steps; 1-D and GEANT4 simulations indicate ~10 frequencies are sufficient (~10MHz intervals)
****** ****Rotator:** 210200 MHz; 10MV/m (~10m)

## Rf Cost Estimate (Moretti)

| Frequency | Cavity length | Cavity Cost  | Rf Power | Total |
| --- | --- | --- | --- | --- |
| 300MHz | 0.5 m | 225 k$ | 225 k$ | 450k$ |
| 290 | 1 | 450 | 350 | 800 |
| 280 | 2 | 900 | 700 | 1600 |
| 270 | 2 | 900 | 1000 | 1900 |
| 260 | 2 | 900 | 1000 | 1900 |
| 250 | 2 | 900 | 1000 | 1900 |
| 240 | 2 | 900 | 1000 | 1900 |
| 230 | 3 | 1200 | 1500 | 2700 |
| 220 | 4 | 1400 | 1500 | 2900 |
| 210 | 5 | 1800 | 2000 | 3800 |
| 200 | 10 | 3800 | 4200 | 8000 |
|  | 33.5m | 13375 | 14475 | 27850k$ |

## Transport requirements

- Baseline example has 1.25 T solenoid for entire transport (drift + buncher + rf rotation) (~170m)
- Uncooled -beam requires 30cm radius transport **(100m drift with 30cm IR – 1.25T**)
- In simulations, solenoid coils are wrapped outside rf cavities.                                       ******(~70m 1.25T magnet with 65cm IR)**
- FODO (quad) transport could also be used ...

## Cost of magnets (M. Green)

- 100m drift: **11.9 M$** (based on study 2)
- Buncher and phase rotation: **26 M$** (study 2)
- Cryosystem: 1.5M$; Power supplies 0.5M$
- Total Magnet System : **40M$ **
**(D. Summers says he can do Al solenoids for ~10 M$)**
**Would quad-focusing be cheaper ?**

## $$ Cost Savings ??

- High Frequency -E Rotation replaces Study 2:
- Decay length (20m, 5M$)
- Induction Linacs + minicool (350m, 320M$)
- Buncher (50m, 70M$)
- Replaces with:
- Drift (100m)
- Buncher (60m)
- Rf Rotator (10m)
- Rf cost =30M$; magnet cost =40M$  Conv. Fac. 10M$ Misc. 10M$ ......
- Back of the envelope:
- 		**(400M$  ******** ?? 100M$ )**