# Presentation: 091236

## Electron Model of Linear-Field FFAG for Muon Acceleration

- MUTAC Presentation, 25 April 2005,                    Shane Koscielniak, Triumf, Vancouver, BC, Canada.

- The Study 2 FFAGs for muon acceleration are NOT MURA-style scaling FFAGs.
- They are a new breed of accelerator, using linear elements, with characteristics well matched to the rapid acceleration of beams with large  6D emittance.
- They rely on novel and, as yet, untested beam-physics
- They have been the subject of intensive study and simulation over the last 4 years at the FFAG workshops.
-  It is important to build a proof of principle model, and plans for that are the subject of this talk.

- The purpose of the electron model is to demonstrate and investigate the novel features of a nonscaling FFAG at a small fraction of the cost of the multi-GeV muon machine.

## Electron Model What does it look like?

** –  ****like the KEK ATF (36 F0D0 arc cells) but without its straight sections, and scaled down from 1.5 GeV to 20 MeV**

## Electron Model - novel accelerator physics

- The FFAG operates at fixed magnetic field with a range of central momenta spanning 50% in p/p. This has two consequences.

**Gutter Acceleration**
- The particle beam moves across the radial aperture, during acceleration, leading to changes in orbit shape which produce a quasi-parabolic time-of-flight variation. With fixed radio-frequency, this necessitates *asynchronous* acceleration within a rotation manifold outside the rf bucket.

**Momentum Compaction**
- The lattice will demonstrate the compaction of v. large range of momenta into remarkably narrow apertures. Under Livingood’s definition =(dp/p)/(dL/L),   at mid-energy for this machine.

## October 2004: Based on tracking studies, Machida reported tolerances for alignment and quad strength rms errors of 0.05mm and 0.1% - these are feasible to achieve

- This successful demonstration of resonance crossing was a key milestone to proceeding with the design work.

- Machine has natural negative chromaticity, but central momenta span 50% in p/p.
- This leads to crossing of many integer and 1⁄2-integer betatron resonances - this has not been done before.
- The new FFAG pins operation on the hope that if crossing is fast enough, no damage is done.

- But verification on a real machine is important for confidence and credibility.
- The PoP model will determine what level of random driving terms may be tolerated.

**Resonance Crossing**

## Electron Model - Specifications

- 10 MeV injection, 20 MeV extraction
- 42 identical cells. High periodicity produces self-cancellation of terms driving 1/3-integer structure resonances.
- Doublet lattice – combined function D and quad F (lowest cost)
- Cell length 0.42 m. No insertions (long straight sections)
- Split betatron tunes h>v to reduce path-length variation
- Magnets – peak field at pole tip less than 0.2T
- Injection/Extraction scenario – feasible (15cm)(0.1T)
- 20 of 1.3 GHz buncher-type cavities in alternate cells
- Voltage 40-120 kV each (18 to 6 turns)
- MA cavity or induction core for slow resonance crossing study

## Lattice functions and example orbits versus momentum

- F

- D

## News from 3-7 April 2005 FFAG workshop at FNAL

- Until now,lattice models have used sector bends.
- Trbojevic points out that R-bends benefit from edge focusing, leading to an increase of vertical tune for high-momenta.

## Insignificant effect on path-length variation

- 45 cell triplet lattice, 34 cm cell, 3 GHz RF.

- Electron models will be revised because of benefit to y. High-angle edge effects noticeable for rings with few cells, but will have v. little impact on 80-100 cell muon rings.

## Radiofrequency system

- Adopt TESLA-style linear RF distribution scheme to reduce number of waveguides

- R=1M, Q=1.4104

- Where possible adopt designs already existing at the host laboratory.

- 1.3 GHz preferred over 3 GHz: reducing RF while magnet length is fixed, implies magnets become a smaller number of RF wavelengths. This implies smaller phase slip and more turns.

**Adopt 1.3 GHz ELBE buncher cavity to be used at Daresbury 4GLS**

- Frequency variation of few 10-4 to investigate 1 or 2 fixed points operation.

- 20 cm straight for installation

## Quadrupole Magnet

- Fermilab Linac quad

**Hardware** – general principle – copying or modifying existing hardware is to be preferred over developing new designs.

- The 5cm long upgrade Fermilab linac quadrupole has peak pole-tip field near 3.5 kG, and the bore is 5cm. With a BPM installed the aperture is 3.7cm.  This is ideal for the 3 cm orbit swing envisioned for the ring. Reverse bending is effected by offsetting of quad.

- General requirements:
- Gradient: 7 T/m
- Slot length: 6 cm
- Aperture: 40 mm wide, 25 mm high
- Rep rate <1Hz

## Combined function magnet

- Specifications
- Permanent dipole component of 0.15 T
- Slot length: 10 cm
- Magnetic length: 7cm
- Permanent quad component of ~4T/m (steel shaping)
- Quad trim coil provides +/- 20%
- Magnet spacing: 5 cm
- Aperture (good field): 50 mm wide, 25 mm high
- Field uniformity  1% at pole tip
- Space for internal BPM
- 1Hz operation or less
- No cooling
- No eddy current problems

- Challenges
- Aspect ratio (gap to length)
- Squeeze so much into such a short slot
- End field

## Magnet Concept (Vladimir Kashikhin, FNAL)

- Dipole plus quad field lines

- Dipole only field lines

- Power the dipole component with permanent magnets
- Compact
- No power issues
- Thermally stable PM material
- Power the quadrupole component with a (modified) Panofsky coil
- Compatible with rectangular aperture
- Relatively short ends

- Magnet Concept (Vladimir Kashikhin, FNAL)

## Electron Model – who will host?

- Daresbury Laboratory U.K. is very enthusiastic to host the electron model downstream of their 8-35 MeV Energy Recovery Linac Prototype (ERLP) of the 4the Generation Light Source (4GLS).

- M£2.5 funding was applied for under the Basic Technology Program of the Engineering and Physical Sciences Research Council on 11th February.
- The program supports basic, high quality technology research.    Principal investigators: Leeds University (School of Physics and Astronomy) & CCLRC ASTeC
- Funding adequate for a small ring with no RF cavities; use energy-variability of linac to characterize dynamics.

- Future site of electron model

**Funding Sources?**

## Funding - Continued

- Adventure projects criteria:
- (i) outside Thematic Priorities of FP6
- (ii) high novelty, ambitious, and has high-risk/high-impact character
- Projects implemented through Specific Targeted Research Projects. There is a 2-Stage proposal.
- Outline submission 13th April 2005
- Invitation for full proposal mid-July 2005
- Signing of contracts April 2006
- Duration of project 2 years
- Principal investigator: Council for the Central Laboratory of the Research Councils (CCLRC), Accelerator Science and Technology Centre (ASTeC).
- Potential Collaborators: BNL, CCLRC, CEA Saclay, CERN, FNAL, TRIUMF; universities of Grenoble, Kyoto, Lancaster, Leeds, Liverpool, Rostock (Germany), Uppsala (Sweden).