\section{FFAG Studies}
\subsection*{Introduction}
TRIUMF is engaged in designs for a new and novel type of
charged-particle accelerator, the non-scaling Fixed Field Alternating
Gradient (FFAG) accelerator, that promises more
cost effective acceleration of muons for HEP and of low-energy hadrons
for cancer therapy. A demonstration model, EMMA, is under construction
at Daresbury U.K.
%\subsection*{Timeline}
The TRIUMF involvement with FFAGs began in October 2003, with US-led
designs for a future Neutrino Factory and Muon Collider. Quickly it was
perceived that FFAGs were a cost-effective alternative to recirculating
linear accelerators (RLAs), such as CEBAF, because their enormous
momentum acceptance meant that the costly multiple return arcs and much
of the costly ionization cooling could be dispensed with. Later, the
studies blossomed to include a demonstration model using low-energy
electrons, and proton and carbon accelerators for cancer therapy. The
work is ongoing through 2009 at least.
\subsection*{Results \& Progress}
U.S.\ and European scientists are developing FFAG research
programs, and we have worked with them in achieving a breakthrough in
understanding how FFAG designs may be simplified and the restrictions
imposed by scaling avoided. In particular, we introduced ``serpentine''
acceleration (essential for muons), developed a theoretical
model explaining the momentum dependence of orbit shape and period,
and are helping to guide the design
of the 10-20~MeV electron model, EMMA (Electron Model with Many
Applications), which is under construction at the Daresbury Laboratory
in the U.K. As with traditional isochronous cyclotrons, which are a type
of non-scaling FFAG, this ``first generation'' machine has the demerit
of resonance crossing due to the variation of the transverse betatron
tune. Looking forward to the medical applications, and a much slower
rate of acceleration than muons, we are actively working on designs
involving wedge-shaped combined-function magnets in which the
contributions of increased path length and edge focusing are used to
stabilize the transverse tunes. If the design proves feasible, the UK
consortium intends construction of a medical prototype, PAMELA.
\begin{itemize}\footnotesize
\item S.R.~Koscielniak, M.K.~Craddock: {\em Simple Analytic Formulae for
the Properties of Nonscaling FFAG Lattices\/},
\href{http://accelconf.web.cern.ch/AccelConf/e04/PAPERS/TUPLT006.PDF}{Proc.\ 2004 European Particle
Accelerator Conf.}, Lucerne, (EPS-AG, Geneva, 2004) pp.\ 1138-40.
\item S. Koscielniak and C.~Johnstone: {\em Mechanisms for nonlinear
acceleration in FFAGs with fixed rf\/}
\href{http://dx.doi.org/10.1016/j.nima.2003.12.028}{NIM-A 523, pp.\ 25-49 (2004)}
\item C. Johnstone and S.~Koscielniak: {\em FFAGs for rapid
acceleration\/}
\href{http://dx.doi.org/10.1016/S0168-9002(03)00997-5}{NIM-A 503, pp.\ 445-457 (2003)}
\end{itemize}
\subsection*{List of Institutes}
TRIUMF is a member both of the US-led Neutrino Factory and Muon Collider
Collaboration, and of the UK-led CONFORM consortium of laboratories and
universities building the EMMA model and studying alternatives for a
proton or carbon medical accelerator design.
\subsection*{TRIUMF Role}
TRIUMF continues to play a key role in providing intellectual and
creative leadership to the development of non-scaling FFAGs: to the
understanding and optimization of the magnetic lattices, notably the
extreme momentum compaction; to the cyclotron-like method of bucketless
rf acceleration; to introducing the use of cyclotron orbit codes for
FFAGs in place of synchrotron codes, which are awkward to use for
spiral-orbit accelerators; to practical aspects of the EMMA design such
as selection of the L-band cavity design; and to a high-gradient
small-aperture version of the PAMELA concept.