# Presentation: 713393

## Muon Collider Design Workshop @BNL

- Chuck Ankenbrandt               Fermilab

- Project X as a Hi-Rep-Rate Driver for a Muon Collider

- Chuck Ankenbrandt and Milorad Popovic
- Fermilab
- December 5, 2007

## Outline

- Chuck Ankenbrandt               Fermilab

- Introduction
- What’s Project X?
- There are various ways to use Project X to drive a muon collider
- High repetition rate or low repetition rate
- 8 GeV protons or 50 GeV protons
- Use/don’t use Main Injector
- To drive a low/high emittance muon collider
- My talk / Dave Neuffer’s
- A high rep. rate, 8 GeV front end based on Project X
- Summary

## Muon Collider parameters

- Chuck Ankenbrandt               Fermilab

**Muon Collider & Ionization Cooling Issues  - Y. Alexahin, FNAL                        ****December 5, 2006**

**Muon Collider parameters**

**	****	****	*****Low Emitt.****** ******	******	******High Emitt.***
**Energy (TeV)****	****	****             0.75+0.75 (********=7098.4)**
**Average Luminosity (1e34/cm^2/s)****	****2.7****	****	****1**
**Average bending field (T)****	****10****	****	****8.33**
**Mean radius (m)****	****	****361.4****	****	****363.8**
**Number of IPs****	****	****4 (350m/2 each)****	****2 (200m each)**
**P-driver rep.rate (Hz)****	****	****65****	****	****60**
**Beam-beam parameter/IP,  ********	****0.052****	****	****0.1**
****** ****(cm)****	****	****	****0.5****	****	****3**
**Bunch length (cm),  ********z****	****	****0.5****	****	****2**
**Number of bunches/beam,  n****b****	****10****	****	****1**
**Number of muons/bunch (1e11), N********	****1****	****	****12**
**Norm.transverse emittance (********m), ************N****	****2.1****	****	****13**
**Energy spread (%)****	****	****1 ****	****	****0.1**
**Norm.longitudinal emittance (m), ********||N**** ****	****0.35 ****	****	****0.14**
**Total RF voltage (GV) at 800MHz****	****406.6 ********10****3********c**** ****	****0.26********10****3********c**
**RF bucket height (%)****	****	****23.9****	****	****0.6**
**Synchrotron tune****	****	****0.723 ********10****3********c**** ****	****0.02********10****3********c**** **
******+ ********- in collision / proton****	****	****0.15 /2****	****	****0.15**
**8GeV proton beam power (MW)****	****1.1****	****	****0.6**

** ****Low emittance option**** (advanced): owing to ideas by Yaroslav Derbenev (HCC, PIC) much lower 6D emittances seem to be feasible than previously thought of.**
** ****High emittance option**** (baseline):** **conceptually** **follows** **1999 PRSTAB Muon Collider Collaboration report**

## Introduction to Project X

- Chuck Ankenbrandt               Fermilab

- The heart of Project X is an 8-GeV H- linac based on ILC technology.
- Project X will stack beam into the Recycler to allow Main Injector to accelerate 2.2 MW of beam to 120 GeV.
- Excess beam cycles will be available at 8 GeV.
- _[http://www.fnal.gov/directorate/Fermilab_AAC/AAC_July_07/](http://www.fnal.gov/directorate/Fermilab_AAC/AAC_July_07/)_
- http://www.fnal.gov/directorate/Fermilab_AAC/AAC_July_07/Agenda_Aug_07_Rev4.htm

## Overview of Project X

- Chuck Ankenbrandt               Fermilab

- From Dave McGinnis’ talk

## Possible site layout of Project X

- Chuck Ankenbrandt               Fermilab

## H- Injection – Transverse painting (Dave Johnson)

- Chuck Ankenbrandt               Fermilab

**Final distribution after painting to 25 ******** **
**at ********H**** of 70 and ********V**** of 30 (STRUCT)**

**Cartoon of phase space painting with 3 linac pulses**

**Horizontal orbit motion during painting**

**Painting waveform for Recycler Injection **

- Aug 8, 2007                        AAC meeting                           D. Johnson

## Outline, revisited

- Chuck Ankenbrandt               Fermilab

- Introduction
- What’s Project X?
- Ways to use Project X to drive a muon collider 

## Project X: Possible 8 GeV Upgrades

- Chuck Ankenbrandt               Fermilab

- The last column has about the same Recycler intensity as when the baseline Project X accumulates 3 cycles for the Main Injector.

## Using Project X to make muons for a collider

- Chuck Ankenbrandt               Fermilab

- Proton beam power of 2 MW may be enough to drive a high-luminosity, low-emittance muon collider.
- The challenge is to “repackage” the protons into a useful form for a muon collider.
- It’s not clear what will work best for a muon collider or a neutrino factory, so flexibility would be nice at the conceptual design stage.
- The rms bunch length should be 3 nsec or less. (Really?)
- A repetition rate of 60 Hz would match the muon lifetime at 750 GeV. (However, we may end up at a different energy.)
- Will we use one or two proton bunches to make each pair of muon bunches? Or to make multiple pairs?
- How many pairs of muon bunches will we make at a time?
- “Buffer rings” (two 8 GeV storage rings with large acceptances and small circumferences) could provide the needed flexibility.

## A specific hi rep. rate, 8 GeV example

- Chuck Ankenbrandt               Fermilab

- Use Accumulator(-like) and Debuncher(-like) rings.
- Acc and Deb are leftovers from Fermilab’s Antiproton Source
- They are not very deep underground; maybe move to new tunnel?
- Paint to large (~200 pi) transverse emittances in rings with small circumference to control space charge.
- Could strip directly into “Accumulator” or do multi-turn transverse stacking from Recycler to “Accumulator”.
- Small circumference means more favorable bunching factor.
- Scale from space charge tune shift (~0.04) in Recycler ring.
- Use h=12 and h=24 rf to make 12 ~rectangular bunches.
- (Note possible constraints on h1, h2: Circumference ratio)
- Transfer two bunches at a time to the “Debuncher”.
- Do a bunch rotation in the “Debuncher”.
- Deliver two bunches at a time to the target at 60 Hz.

## Picture of the concept

- Chuck Ankenbrandt               Fermilab

## ESME-One bunch

- Chuck Ankenbrandt               Fermilab

## Twelve bunches in Accumulator

- Chuck Ankenbrandt               Fermilab

## Shorter bunches in Accumulator

- Chuck Ankenbrandt               Fermilab

## Longitudinal emittance scaling

- Chuck Ankenbrandt               Fermilab

- In the Recycler, beam will be painted to a longitudinal emittance of about 0.25 eV sec per bunch
- After transfer via transverse stacking to the Accumulator, the total longitudinal emittance will be ~ 84 times 0.25
- If we form 12 bunches, each will have 84(0.25)/12 = 1.75 eV sec.
- If we reduce the bunch length to a total t of about 10 nsec, then E will be about 0.175 GeV = +/- 0.09 GeV
- So E/E = +/- 1% , well within the momentum aperture.

## Space-charge tune shift scaling

- Chuck Ankenbrandt               Fermilab

- Scale from incoherent tune shift of 0.04 in Recycler
- The energy (8 GeV) and the total number of protons are the same in the Recycler and the Debuncher.
- The transverse stacking into the Debuncher raises the transverse emittances by a factor of eight.
- The bunching factor goes down by a factor of nine.

## Flexibility

- Chuck Ankenbrandt               Fermilab

- Above example was for 60 Hz; however...
- Could form fewer bunches in rings
- Could combine bunches externally (cf. next slide)
- Rep rate as low as 10 Hz (once per linac cycle) may be feasible
- Analogy: Tevatron Collider
- Started with one pair of bunches at design luminosity of 1030
- Went to 3x3, mainly to reduce events per crossing
- Implemented electrostatic separators and went to 6x6
- Now at 36x36

## Very High Rep Rate via CW Linac

- For a muon collider rep rate of 65 Hz with ten bunch pairs, the front end might run at 650 or 1300 Hz.
- A 50-GeV neutrino factory might also run at ~ 1 kHz.
- Those rates might best be delivered via a CW linac.
- Rol Johnson, CA and MP wrote a letter to the Fermilab Steering Group suggesting that possibility.
- Arguments for a CW linac:
- It’s easier to operate a superconducting linac CW (no transients)
- Low peak rf power => lots of inexpensive klystrons
- Jlab is existence proof
- Could be a multipurpose facility

- December 5, 2007

- Chuck Ankenbrandt               Fermilab

## An external combiner to reduce rep rate at target

- Chuck Ankenbrandt               Fermilab

- Several bunches enter

- Bunches converging upon exit

## Summary: Project X for Muon Collider 

- Chuck Ankenbrandt               Fermilab

- Summary: Project X for Muon Collider

- A flexible way to deliver short intense 8-GeV proton bunches from Project X to a muon collider target station at various rep rates has been found.
- The scheme uses the full 8-GeV capability of Project X upgraded to 2 MW of beam power.
- The scheme uses Accumulator-like and Debuncher-like storage rings.
- A CW linac could provide even higher rep rates.
- Dave Neuffer will talk about using the Main Injector as part of the strategy.

## Backup Slides

- Chuck Ankenbrandt               Fermilab

## Pros and Cons

- Chuck Ankenbrandt               Fermilab

## Muon Collider parameters

- Chuck Ankenbrandt               Fermilab

**Muon Collider & Ionization Cooling Issues  - Y. Alexahin, FNAL                        ****December 5, 2006**

**Muon Collider parameters**

**	****	****	*****Low Emitt.****** ******	******	******High Emitt.***
**Energy (TeV)****	****	****             0.75+0.75 (********=7098.4)**
**Average Luminosity (1e34/cm^2/s)****	****2.7****	****	****1**
**Average bending field (T)****	****10****	****	****8.33**
**Mean radius (m)****	****	****361.4****	****	****363.8**
**Number of IPs****	****	****4 (350m/2 each)****	****2 (200m each)**
**P-driver rep.rate (Hz)****	****	****65****	****	****60**
**Beam-beam parameter/IP,  ********	****0.052****	****	****0.1**
****** ****(cm)****	****	****	****0.5****	****	****3**
**Bunch length (cm),  ********z****	****	****0.5****	****	****2**
**Number of bunches/beam,  n****b****	****10****	****	****1**
**Number of muons/bunch (1e11), N********	****1****	****	****12**
**Norm.transverse emittance (********m), ************N****	****2.1****	****	****13**
**Energy spread (%)****	****	****1 ****	****	****0.1**
**Norm.longitudinal emittance (m), ********||N**** ****	****0.35 ****	****	****0.14**
**Total RF voltage (GV) at 800MHz****	****406.6 ********10****3********c**** ****	****0.26********10****3********c**
**RF bucket height (%)****	****	****23.9****	****	****0.6**
**Synchrotron tune****	****	****0.723 ********10****3********c**** ****	****0.02********10****3********c**** **
******+ ********- in collision / proton****	****	****0.15 /2****	****	****0.15**
**8GeV proton beam power (MW)****	****1.1****	****	****0.6**

** ****Low emittance option**** (advanced): owing to ideas by Yaroslav Derbenev (HCC, PIC) much lower 6D emittances seem to be feasible than previously thought of.**
** ****High emittance option**** (baseline):** **conceptually** **follows** **1999 PRSTAB Muon Collider Collaboration report**

## The Primary Matrix

- Chuck Ankenbrandt               Fermilab

**The Primary Matrix**

| Left wing | Center | Right wing |
| --- | --- | --- |
| Hillary |   | Rudy |
| Barack |   | Mitt |
| John |   | John |
| Ankle-biters |   | Ankle-biters |

## Choices

- Chuck Ankenbrandt               Fermilab

- Hi rep rate or low rep rate?
- 8 GeV or 50 GeV?
- Ankenbrandt or Neuffer?

## The Front End Matrix

- Chuck Ankenbrandt               Fermilab

| Rep. Rate | High |   | Low |
| --- | --- | --- | --- |
|  | Low |   | High |
| Ep | 8 GeV |   | 50 GeV |

## Introduction

- Chuck Ankenbrandt               Fermilab

- Young-Kee’s Steering Group likes Project X.
- Pier asked: Can Project X be used for a muon collider?
- We can and should provide an affirmative, simple, flexible response to Pier and the Steering Group.