# Presentation: 274543

## Front EndCapture/Phase Rotation& Cooling Studies 

- David Neuffer
- March 2008

## 0utline

- Introduction
** ****ν****-Factory Front end and cooling**
**ν****-Factory****→****μ****+****-****μ****-**** Collider**
- Capture and Φ-E rotation
**High Frequency**** ****buncher/rotation **
**Shorter versions  **
- Recent variation studies
**Target studies 8 GeV, 56 GeV**
**Better cooling**
**Quad cooling**
**Rotate/cool combination**
- Future studies
**Discretization**
**Snake FOFO**

**Neutrino factory**

## Solenoid lens capture

**Target is immersed in high field solenoid**
**Particles are trapped in Larmor orbits**
- B= 20T -> ~2T
- Particles with p < 0.3 BsolRsol/2=0.225GeV/c are trapped
- Focuses both + and – particles
- Drift, Bunch and phase-energy rotation

## Study2B June 2004 scenario (ISS)

**Drift –110.7m**
**Bunch -51m**
- (1/) =0.008
- 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
**Captures both **μ+ and μ-
**~0.2** ** ****μ****/(24 GeV p)**

## Features/Flaws of Study 2B Front End

**Fairly ****long**** system  ~300m long (217 in B/R) **
**Produces long trains of ~****200 MHz**** bunches**
- ~80m long (~50 bunches)
- Transverse cooling is ~21⁄2 in x and y, no longitudinal cooling
- Initial **Cooling is relatively weak ** ? -
**Requires rf within magnetic fields **
- in current lattice, rf design; 15 MV/m at B = ~2T, 200MHz
- MTA/MICE experiments to determine if practical
**For Collider ****(Palmer)**
- Select peak 21 bunches
- Recombine after cooling
- ~1/2 lost

**-40**

**60m**

**500 MeV/c**

## Shorter Bunch train example 

**Reduce drift, buncher, rotator to get shorter bunch train:**
- 217m  ⇒ **125m  **
**57m drift, 31.5m buncher, 36m rotator**
**Rf voltages up to 15MV/m (×2/3)**
- Obtains **~0.26 ****μ****/p****24** in ref. acceptance
**Slightly better ? **
** ****~0.24 ****μ****/p for Study 2B baseline**
- 80+ m bunchtrain reduced to < 50m
**Δ****n: 18 -> 10 **

**-30**

**40m**

**500MeV/c**

## Further iteration/optimization

**Match to 201.25 MHz cooling channel**
**Reoptimize phase, frequency**
- f = 201.25 MHz, φ = 30o,
**Obtain shorter bunch train **
**Choose ~best 12 bunches **
- ~ 21 bunch train for Collider at NB= 18 case
**	****~12 bunches (~18m)**
- ~0.2 μ/pref in best 12 bunches
- ~70%
- Densest bunches are ~twice as dense as NB = 18 case

## Details of ICOOL model (NB=10)

**Drift– 56.4m**
- B=2T
**Bunch- 31.5m**
- Pref,1=280MeV/c, Pref,2 =154 MeV/c, nrf = 10
-  Vrf 0 to 15MV/m (0.5m rf, 0.25m drift) cells
- 360 MHz  240MHz
******-E Rotate – ****36m –**
- Vrf = 15MV/m (0.5m rf, 0.25m drift) cells
******N****V**** = ****10.08 (240 -> 202 MHz)**
**Match and cool (80m)**
- Old ICOOL transverse match to ASOL (should redo)
- Pref= 220MeV/c, frf = 201.25 MHz
-  0.75 m cells, 0.02m **LiH,** 0.5m rf, 16.00MV/m, φrf =30°
- Better cooling possible (H2, stronger focussing)

## Simulations (NB=10)

**-30m**

**30m**

**500 MeV/c**

**0**

**Drift and**
**Bunch**

**s = 89****m**

**s = 1m**

**Rotate**

**s = 125****m**

**s = 219****m**

**Cool**

## Even Shorter Bunch train ~(2/3)2

**Reduce drift, buncher, rotator to get even shorter bunch train:**
- 217m  ⇒ **86m  **
**38m drift, 21m buncher, 27m rotator**
**Rf voltages 0-15MV/m, 15MV/m (×2/3)**
- Obtains **~0.23 ****μ****/p** in ref. acceptance
**Slightly worse than previous ?  **
- 80+ m bunchtrain reduced to < 30m
**18 bunch spacing dropped to 7**

**-20**

**30m**

**500MeV/c**

## Variation: -Factory Cooling Channel

**Cooling is limited: **
**LiH **absorber, β ≅ 0.8m
-   **from ~0.018 to ~0.0076m in ~80m **
**ε****eq ******** 0.006m**** **
**Could be improved **
**H****2 ****Absorber (120A)**** or smaller **β
-  ****  **~0.0055**
**ε****eq ******** 0.003m**
**~20% more in acceptance**
**Less beam in halo  **

**Before**

**After LiH cooling**

**+0.4m**

**After H****2**** cooling**

**-0.4m**

## Example: NB = 10, H2 cooling

**Example: N****B**** = 10, H****2 ****cooling**

**0**

**0.3**

**0.6**

**μ****/p**
**(24GeV)**

**μ****/p within acceptance**

**All ****μ****’s**

**Transverse emittance**

**ε****t,,N**
**(m)**

**1.5 ZM**

## Discussion

**Guess: Optimum is N****B ****≈ 10  **
- (for both collider and ν-Factory)
- As many μ/p as baseline in more compact bunch train
- Bunch train is ~1/2 that of Study 2B
**Develop as ****new baseline**** parameter****  **
- Shorter buncher/rotator may be  cheaper
- 215m -> 125m, cost × ~0.8 ??  .... (150->120)
- Better cooling is desirable
- H2 absorber and/or stronger focussing
**Assumed for these scenarios:**
- ~15 MV/m at B  2T and f  200MHz is practical
- Capture at ~150 to 300 MeV/c is optimal

## Variations

**Beam energy, bunch length, longitudinal acc.**
- Target variations
**Quad channel**
**Rotator + cooler **
**Tilted solenoid - Y. Alexhin**
**Rf/experiment comments**
**Discrete frequencies **
- More realistic geometries

## 8 GeV baseline 

**Consider 8 GeV initial beam**
- New beam from Mars simulation – C. Yoshikawa
- B=20T, Hg-jet target, 8-GeV p-beam~60cm long target region, ~MERITgeometry, 1 to 3 ns rms
**Express yield in “E-independent” units**
**Z = Zetta = 10****21**
- 0.2μ/(24GeV p)=1.042 Zμ/year-MW       (ZyM)
- (1021 μ/ MW-year) , where year is 2×107 s
- Study 2B  is ~0.885 ZyM  ... (or ZM =ZisMans ?)

## ZyM-ology – ICOOL results

**Place 8GeV in N****B****=10 lattice**
**LiH** lattice
- Yield is 1.293 ZM (εt <0.03,εL<.2)(1ns)
- (0.0814 μ/p)
**1.213 ZyM @(****ε****t ****<0.03,****ε****L****<.0.2)(3ns)**
**Compare w/ 24 GeV  N****B****=10**
- St2 ref. beam: 1.375 ZM (3ns)
- St2A ref. beam: 1.156 ZM
**This initial beam is ~12% “worse” than ST2 reference beam **
- but ~5% “better” than study 2A reference beam
**Change to H****2**** cooling (****~20% more ...****)**
- ~1.59 ZM (εt <0.03,εL<.2,1ns) 8GeV  (_[1.51@3ns](mailto:1.51@3ns)_ beam)
**~Sensitive to longitudinal acceptance:**
**~1.42 ZM**(εt <0.03,εL<.15,1ns)

## Is 7.5cm adequate?

**Mars simulation obtains:**
- 0.38 π/8GeV proton forward
- B=20T R=7.5cm
- 0.53 π/8GeV hit sides
**Increase radius to 10cm:**
- ~0.54 π/8GeV proton forward
- ~0.37 π/8GeV hit sides
**But many larger radius ****π⁄μ**** are not accepted: **
- 1.39 ZM1.51 ZM  (?)
- 42%more initial; but only 9% more in acceptance cuts

## Reduce number of rf frequencies

**Study 2B discretization exercise:**
- Buncher : 12 rf frequencies; Rotator 15 rf freq.
**Buncher 31.5m – 42 cavities (× 1/3 = 14)**
- 362.15, 348.52, 335.87, 324.12, 313.15, 302.91, 293.31,
- 284.31, 275.84, 267.86, 260.33, 253.21, 246.47, 240.08
**Rotator 36m -48 cavities (× 1/3 = 16)**
- 235.95, 230.62, 225.97, 221.91, 218.36, 215.26, 212.57, 210.25, 208.26, 206.58, 205.19, 204.07, 203.20, 202.58, 202.2,202.0
**As for study 2B, simulate and compare**
- ~10% worse (not yet simulated, however)

## Rf cavity comments

**Frequencies from 360 to 200 MHz **
- 5 to 15 MV/m to ?  **In B = ~2T**
**Normal-conducting Short-pulse rf**
- 15 to 60 Hz
**Simulation cavity length – 0.5m-?? **
**Be windows? “gas-filled” ? options **
**NEED R&D to determine E****cf ****/B limits**
- 200, 800 MHz,

## Gas-filled rf cavities (w/Muons, Inc.)

**Cool here**

- Add gas** + higher gradient to obtain **cooling within rotator
**Rotator is 54m;**
- Need ~5MeV/m cooling
**150atm** equivalent 295oK gas
- Alternating Solenoid lattice in buncher/rotator
**24MV/m rf****(0.5m cavities)**
**Gas-filled cavities may enable higher gradient**
- ~0.22/p** at ε****T ****< 0.03m**
- ~0.12/p at εT < 0.015m
- ε⊥ cools to ~0.008m
- About equal to Study 2A

## Quad cooling channel for front end

- w. A. Poklonsky
**Use 1.5m long cell – FODO **
- 60o to 90o/cell at P 215MeV/c
- max = 2.6m; min=0.9 to 0.6m
- B’ = 4 to 6 T/m
**Advantages:**
**No large magnetic fields along the axis**
**Quads much cheaper ?**
**No beam angular momentum effects **
- Disadvantages
**No low ********* region **
**Relatively weak focusing**
**H****2****-cooled example as good as Study2B LiH case **

## Tilted Solenoid? – Y. Alexhin

**Tilt solenoids to insert dispersion**
- ~6cm ?
**Allows wedge absorbers to cool longitudinally**
**If wide aperture, oscillations of both ****μ****+**** and ****μ****-**** particles can be within the channel**
**Try to simulate in front end**

## Conclusions

**Can use high-frequency capture to obtain bunch train for  ****ν****-Factory ****→ ****μ****+****-****μ****- ****collider **
- (~10 to 14 bunches long at 200MHz )
- Recombine after cooling for collider mode
**Questions**
- Is ~200 MHz optimal?
- ~15 MV/m at B  2T and f  200MHz is OK?
- Is ~12 bunches OK for Collider scenario
**To Do:**
**Turn into detailed design for IDS ??**