# Presentation: 585290

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

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

- Shane Koscielniak, Triumf, Vancouver, BC, Canada, 15 Feb 2005

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

**Proposed magnet design:  the upgrade Fermilab linac quadrupole (the 2” long green magnet).  Its peak poletip field is near 3.5 kG, the poletip bore is 2” and has a BPM design which fits inside the quad. With a BPM installed the aperture is 1.5”.  This is ideal for the 2-3 cm orbit swing envisioned for the ring.**

## Radiofrequency system: based around 1.3 GHz ELBE buncher cavity to be used at Daresbury 4GLS

**Adopt TESLA 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.

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

**What does it do?** 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.

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

**Resonance Crossing:** The transverse focusing strength falls with increasing momentum leading to natural negative chromaticity. This leads to crossing of many integer and 1⁄2-integer betatron resonances.

**Gutter Acceleration:** The particle beam moves across the radial aperture, during acceleration, leading to change 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. (MURA 423)

## How has the design evolved over the year(s)?

- Dec 1997: Johnstone devises lattice to give infinite momentum compaction ( ) at mid energy and remarkably narrow apertues =(dp/p)/(dL/L) – Livingood definition of compaction

- Oct 2003: J.S. Berg sets basic parameters for an electron model (0.2T peak field, 3GHz RF, 5 & 15 cm drifts, 35 cm long cells)
- Between Oct 2003 and April 2004, understanding of relation between optics and ToF gleaned from muon FFAG is applied to the model. F0D0, Doublet and Triplet cells are all considered.
- April 2004: Keil realizes that longitudinal motion can be made less dispersive by operating at bottom of ToF parabola (T2/T1= 0 instead of T2/T1=1/3)   – at cost of more cells.
- Other designers obsessed by rings with small circumference.
- E.g.s Berg: 25 cell doublet, 8.8m. Koscielniak: 23 cell triplet. Trbojevic: 45 cell triplet, 15.8m. Keil: 45 cell doublet.
- Some designs published in EPAC 2004 (MOPLT023,112 & THPLT006). Keil reports alignment study via tracking with errors.

## How has the design evolved ? - continued

- October 2004: Machida reports tolerances for alignment and quad strength errors based on particle tracking (i.e. integer & 1⁄2-integer resonances); former agrees with Keil (30m r.m.s.).
- Koscielniak suggests that 25-30 cell electron model is too small: too few cells and turns (only 4 or so) – adversely impacts the study of *new* accelerator physics. Recommends reducing RF and or increasing number of cells – but with fixed magnet length.

- January-February 2005: all designers working on lattices with 36,42 or more (60) cells and 1.3GHz cavities; circumference 15 to 18 m (or more). Turns range from 7 to 10 or so.

- Koscielniak gives recipe for minimizing nonlinear longitudinal emittance growth: match ellipse to boundary of constant hamiltonian. T2/T1= 1/5 sufficiently small

## Electron Model Concept/Specification – consensus with loud objections

- 10-20 MeV
- High periodicity to produce self-cancellation of terms driving 1/3-integer structure resonances. 42 cells if affordable
- No straight sections
- Doublet lattice – combined function D, quadrupole F
- Iron core magnets – to guarantee field quality
- Peak field at poletip less than 0.2T
- 1.3 GHz buncher-type cavities in alternate cells
- Cell length 0.42 m
- Split betatron tunes h>v
- MA cavity or induction core for resonace crossing study
- Injection/Extraction scenario -- TBA

## Electron Model – who will host?

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

- M£2 funding has been applied for under a Basic Technology Grant from the EPSRC, on 11th February.
- M€5 will be applied for under an European Commission program, 13th April.
- Final draft of latter bid will be subject of FFAG workshop held at FNAL 3-7 April 2005.

- Future site of electron model

- That’s All Folks!