# Presentation: 400351

## Capture/Phase Rotationfrom Neutrino Factoryto μ+-μ- Collider

- David Neuffer
- Cary Yoshikawa
- Fermilab f
- October 2007

## 0utline

- Introduction
- Capture and Φ-E rotation options
**Low-frequency-Single bunch**
**Isochronous capture ?**
**Induction linac: Study 2 ****ν****-Factory**
**High Frequency**** ****buncher/rotation **
**Study 2A ****ν****-Factory**
**ν****-Factory****→****μ****+****-****μ****-**** Collider**
- μ+-μ- Collider
**Shorter bunch trains  ....**
**Front end variations for Collider and ****ν****-Factory**
- Discussion

## Solenoid lens capture

**Target is immersed in high field solenoid**
**Particles are trapped in Larmor orbits**
- B= 20T -> ~2T
- Spiral with radius r = p/(0.3 Bsol) =Bρ/B
- Particles with p < 0.3 BsolRsol/2 are trapped
**p********,max**** < 0.225 ****GeV/c** for B=20T, Rsol = 0.075m
- Focuses both + and - particles

## π→μν decay in transport

**π****-lifetime is 2.60×10****-8******** s**
- L = 7.8 β m
**For ****π**** ******** ****μ****+****ν****,**
- <PT,rms> is  23.4 MeV/c, E=0.6 to 1.0Eπ
**Capture relatively low-energy ****π**** ******** ****μ**
- 100 – 300 MeV/c
**Beam is initially short in length**
- Bunch on target is 1 to **3 ns** rms length
**As Beam drifts down beam transport, energy-position (time) correlation develops:  **

- L=0m

- L=36m

- 0

- 0.4 GeV

- -20m

- 100m

## Phase-energy rotation 

**To maximize number of ~monoenergetic ****μ’s,  neutrino factory designs use phase-energy rotation**
**Requires:**
- “short” initial p-bunch (σ ≈ 3ns)
- Drift space
- Acceleration (induction linac or rf)
- at least ±100 MV
**Goal:**
- Accelerate “low-energy tail”
- Decelerate “high-energy head:
- Obtain long bunch
- with smaller energy spread

- L=1m

- L=112m

- rf

- 0

- 0.5GeV/c

- -50m

- 50m

- L

## Phase Energy rotation options

**Single bunch capture **
- Low-frequency rf (~30MHz)
- Best for collider (?) (but ~ only + or  -)
**Induction Linac****	**
- Nondistortion capture possible
- Very expensive technology, low gradient
- Captures only + or  -
**“****High Frequency” buncher and phase rotation**
- Captures into string of bunches (~200MHz)
**Captures both ********+**** and  ********-**
** **

## Phase/energy rotation

**Phase/energy rotation**

**Low-frequency rf;            capture into single long bunch**
- 25MHz – 3MV/m
- +25% 50MHz
- 10m from target to 50m
**But:**
- Low-frequency rf is very expensive

- 12 m

## Capture into high-frequency bunches

**Cooling requires high-gradient rf !**
- (>~10MV/m)
**⇒ ****> ****~200MHz**** rf frequency**
**Capture into string of rf bunches**
-  i. e., ~ 12 325 MHz bunches
- K. Paul MuCool Note 518
- > ~0.1  μ/p (~10 GeV p)
- C. Yoshikawa continuing study using G4Beamline
**For collider, cool and recombine to minimum number of bunches**
- Only captures one sign ...

## Newer simulations

| Target: 30 cm long, 1 cm diameter Fe bombarded with 8 GeV protons. | 4π Coverage Yield: ~1/POT for pi+ & pi-
Yield Leaving Target Solenoid (per POT):
   Pi+: 0.660       Pi-: 0.587   |
| --- | --- |
| Tapered Solenoid: 
   20T(z=0) to 2.2T(z=10m) | Yield at End of Taper (per POT):
    Pi+:   0.239     Pi-:   0.211
    Mu+: 0.168     Mu-: 0.175 |
| Low Freq RF Phase-Energy Rotation:
   Used 1-3rd harmonic (25MHz −75 MHz)
   Max Gradient = 3 MV/m. | Yield at 55 m inside 170<p<270 MeV/c:
    Mu+: 0.1543   Mu-:0.0406 |
| High Freq RF Bunching (325 MHz, 4 MV/m):
   1) Full strength over entire range.
   2) Gradual strength (linear) rise to max 
        gradient over first ~9 m, after which full 
        strength (4 MV/m) remains.
    | Yields for 170<p<270 MeV/c:
   Full strength at 10m: 
      Mu+: 0.0924   Mu-: 0.0215
   Gradual strength at 15m: 
      Mu+: 0.0937   Mu-: 0.0175 |

## Φ-E rotate than bunch (325 MHz)

- 325 MHz bunches not yet fully formed ...
**Need cooling (gas-filled rf)**
**for better bunch formation**
- For collider, recombine bunches to smaller number somewhere downstream...

## Variation: Isochronous Capture channel

- From Johnson/Derbenev Phys. Rev paper
- First term in parenthesis can be associated with 1/γT2.

- Produce short bunch by using Helical transport channel,
- π→μ decay within helical transport
- Isochronous for central momentum (200 MeV/c)
- Ankenbrandt, ... Yoshikawa et al. –SBIR proposal
- Obtains short bunch with large momentum spread

- HCC Design Parameters:
- Pπ: 200 MeV/c		Helical Period: 1 m
- Orbit Radius: 0.16 m
- κ=1
- Short, large δp/p could be cooled immediately (longitudinally)
- Concept needs study to determine potential
**Also could be used for ****μ→****e?**

## Study 2 Induction Linac system 

- Drift** to develop Energy- phase correlation**
**Accelerate tail; decelerate head of beam, non-distortion (280m induction linacs (!))**
- Bunch** at 200MHz, cool **
**~0.2 ********/p ****(24 GeV p)**
**Not suitable for Collider**
**Only ****μ****+**** **** ****or ****μ****-**
- Very long bunch train

## High-frequency buncher and φ-E Rotator

**Form bunches first**
**Φ****-E rotate bunches**

## High-frequency Buncher +  Rotation

- Drift (110m)
**Allows ******** beam to decay;**
**	****beam develops  ******** correlation**
- Buncher (~333230MHz)
**P****ref**** = 150 to 280 MeV/c**
**V****rf**** increases gradually from 0 to ~6 MV/m**
-  Rotation (~233200MHz)
**Adiabatic rotation**
**V****rf**** =~10 MV/m **
- Cooler(~100m long) (~200 MHz)
**fixed frequency transverse cooling system**

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

****

- Captures both **μ****+ ****and ****μ****- ****!****!**

## 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
- For 90  150m drift

**Bunches are equally** **spaced in 1/****β****(p)**

##  Rotation

- At end of buncher, change rf to decelerate high-energy bunches, accelerate low energy bunches
**Central bunch at zero phase, set ********rf** less than bunch spacing
**	****(increase rf frequency)**
- Place low/high energy bunches at accelerating/decelerating phases
**Can use **fixed frequency **(fast rotation)****   ****	****	****or**
**Change frequency along channel to maintain bunching**
- High-energy bunch decelerated
- Low-energy accelerated

## Adiabatic  Rotation 

- At end of buncher, choose:
- reference particles P0, PN
- N wavelengths apart, offset 
- Example:
- P0 = 280, P10 =154 MeV/c
- Choose N= 10, =0.08
- In ICOOL
- T0 = T0 + E0'z...;TN =TN + EN' z
-  Rotate until P0 ≅ PN
- Along rotator, keep reference particles at  (N + ) rf spacing
- EN'  ≅eV' sin(2π)
**λ****rf****  ~1.4 to 1.5 m over buncher**

- ~**Adiabatic**
- Particles remain in bunches as bunch centroids align
- Match into 201.25 MHz Cooling

******N=10.08**

******N=10.0**
**15m**

## Study2A June 2004 scenario

**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)**

## -Factory Study 2A cooling channel

**Lattice is weak-focusing **
- Bmax = 2.5T, solenoidal
- β ≅ 0.8m
**Cools transversely **
-   from ~0.018 to ~0.007m
- in ~80m
**Should be improved for Collider**

- Before

- After cooling

**-0.4m**

**+0.4m**

## Features/Flaws of Study 2A 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; 12 MV/m at B = 1.75T, 200MHz
- MTA/MICE experiments to determine if practical
- Gas-filled cavities?

**-40**

**60m**

**500 MeV/c**

## Study 2A to μ+μ- Collider

**Use front end as start of cooling channel ****R. Palmer et al****. **
- Have both signs (μ+ + μ-)
- Natural upgrade of facility
**Use only first ~21 bunches (70% of ****μ****’s) **
**After initial 6-D cooling; recombine bunches **

## Adapt to Collider (R Palmer)

**Recombine cooled bunches **
- Buncher “wiggler” (k=-3 FFAGs)
- 21 ⇒ 1 bunch (after ~200m) + 2 rf systems
- ~50% losses in rebunching ...

## Difficulties 

**>21 200MHz bunches -> 1 is awkward**
- Bunch train is too long (21 bunches =31.5m)
- Loses a lot of useful μ’s
- (decay plus using “only” 21 bunches)
**Buncher/Rotator is too long (~215m) **
- Shorter system will produce shorter bunch train
- More adiabatic than needed ...

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

**Reduce drift, buncher, rotator to get shorter bunch train:**
- 217m  ⇒ **125m  **
**57m drift, 31m buncher, 36m rotator**
**Rf voltages up to 15MV/m (×2/3)**
- Obtains **~0.27 ****μ****/p** in ref. acceptance
**Slightly better ? **
** ****~0.25 ****μ****/p for Study 2A baseline**
- 80+ m bunchtrain reduced to < 50m
**Δ****n: 18 -> 10 **

**-30**

**40m**

**500MeV/c**

##  Iteration/optimization

**Match to 201.25 MHz cooling channel**
**Reoptimize phase, frequency**
- f = 201.25 MHz, φ = 30o,
**Slightly better acceptance**
- N = 10
- 0.282 μ/pref  in study 2A acceptance
**Equivalent bunch train for RPB scenario is **
**	****~12 bunches (~18m)**
- ~0.2 μ/pref in best 12 bunches
- Can improve Study 2A acceptance with H2 gas cooling channel

## Details of ICOOL model (N=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**** = ****10.07 (240 -> 201.5 MHz)**
**Match and cool (90m)**
- 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
- Gas-filled cavities

## Simulations (n=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 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
**201.25 MHz cooling**
**Slightly worse than previous ?  **
- 80+ m bunchtrain reduced to < 30m
**18 bunch spacing dropped to 7**

**      ****-20**

**30m**

**500MeV/c**

## Details of ICOOL model (N=7)

**Drift– 37.7m**
- B=2T
**Bunch- 21m**
- Pref,1=280MeV/c, Pref,2 =154 MeV/c, nrf = 7
-  Vrf 0 to 15MV/m (0.5m rf, 0.25m drift) cells
- 350 MHz  230MHz
******-E Rotate – ****27m** –
- Vrf = 15MV/m (0.5m rf, 0.25m drift) cells
******N****V**** = ****7.1 (230 -> 204 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, 15.25MV/m, φrf =30°

## Discussion

**Guess: Optimum is ~ 12 bunches**
- (for collider)
- Looks similar to ~25 MHz large-bunch Φ-E rotate, rebunched at ~300 Mhz
**Optimum is ~1/2 × Study2A**** / ISS example**
- 215m -> 125m
**Shorter buncher/rotator is cheaper**
- cost × ~2/3  ....
**Much shorter buncher/rotator will not be as good ~**
- Need ~100MV rf for buncher; 200 for rotator
- ~10MV/m real estate gradient
- > 60m needed ?

## Conclusions

**Can use high-frequency capture to obtain bunch train for collider (~10 to 14 bunches long)**
- Recombine for collisions downstream
**Questions**
- Is 200 MHz optimal?
- If using ILC modules (1300 MHz) must go to fraction
- 325 or 163 MHz or ??
**To Do:**
- Turn into detailed design for IDS ??

## Future Plans ...

## Another example: ~88 MHz 

**Drift – 90m**
**Buncher-60m**
- Rf gradient 0 to 4 MV/m  (6MV/m in cavities)
- Rf frequency: 166→100 MHz
- Total rf voltage 120MV
**Rotator-60m **
- Rf gradient 7 MV/m – 100→87 MHz (10.5 **× ****2⁄3)**
- 420MV  total
**Acceptance ~ study 2A (but no cooling yet)**
- Less adiabatic

- 0 GeV/c

- 0.5 GeV/c

## Study 2A ICOOL simulation

**Study 2A ICOOL simulation**

**s = 1m**

**s=109****m**

** ****s=166m**

**s= 216m**

**-40**

**60**

**500****MeV/c**

**0**

**Drift**

**Bunch**

**Rotate**

**500****MeV/c**

**0**