\subsection{Overview}
\label{Sect:AccOview}

The Neutrino Factory accelerator systems are required to produce a
high-intensity, high-energy neutrino beam with a very well-known
energy spectrum and without the contamination of unwanted neutrino flavours.  
The energy spectrum is well-defined since it arises
from the decay of muons confined within a storage ring with a
relatively small energy spread. 
The muon beam is accelerated to high energy thereby creating a
high-energy neutrino spectrum.
The accelerator facility produces a high-intensity neutrino beam by
creating large numbers of muons, capturing as many of them as
possible, and minimising the loss of these muons before they can be
directed toward the detector.   
Table \ref{tab:acc:muons} quantifies these characteristics: it gives
the muon beam energy and the number of muon decays in the direction of
the neutrino detector.
The uncertainty in the neutrino flux is limited by the angular
divergence of the stored muon beam \cite{Crisan:2000gc}.
Table \ref{tab:acc:muons}, therefore, also specifies the maximum
angular divergence of the muon beam.
Two storage rings are required to serve simultaneously both the
detector at the intermediate baseline and that at the long baseline.
The decay rings have straight sections inclined so that the straight
sections point at the distant detectors.  
The lengths of the straight sections form a significant fraction of
the decay ring circumference so that the fraction of the stored muons
decaying in the direction of the detectors is maximised.  
\begin{table}[hb]
  \caption{
    Parameters characterising the muon beam produced by the
    accelerator facility.  Muon decays are a total for all
    signs and detector baselines.
  }
  \label{tab:acc:muons}
  \begin{tabular}{|l|r|}
    \hline
    {\bf Parameter}                                                & {\bf Value}       \\
    \hline
    Muon total energy                                              & 25 GeV            \\
    Production straight muon decays in $10^7$ s                    & $10^{21}$          \\
    Maximum RMS angular divergence of muons in production straight & $0.1/\gamma$      \\
    Distance to intermediate baseline detector                     & 3\,000--5\,000 km \\
    Distance to long baseline detector                             & 7\,000--8\,000 km \\
    \hline
  \end{tabular}
\end{table}

\subsubsection{Principal subsystems}

Muon beams at the Neutrino Factory are produced from the decays in
flight of pions produced by the bombardment of a target by a
high-power, pulsed proton beam.
The muons produced in this way must be captured and manipulated in
6-D phase space such that the maximum number are transported into the
phase-space region that is required for acceleration and
storage in the decay ring.  
After the phase-space manipulation, the muon beam energy is increased
to 25~GeV in a number of acceleration stages.
Finally, the beam is injected into the storage ring, where it
circulates as the muons decay into neutrinos. 

The number of muons created is approximately proportional to the power
in the proton beam, defined as the product of the number of protons
per bunch, the energy of each proton, and the rate at which bunches
hit the target.  
The power of the proton beam is chosen to be sufficient to produce the
desired number of muons (see table~\ref{tab:acc:muons}).
Other parameters are chosen such that the number of muons produced per
unit power is nearly optimal (see table~\ref{tab:acc:pd:parm}) given
the method we are using to capture the muons.  
This report will not define a specific proton driver for the Neutrino
Factory.
Rather, we describe three designs that could be implemented by
appropriately developing infrastructure at three of the world's
proton-accelerator laboratories (CERN, FNAL, and RAL).
These laboratories have been chosen as example sites to allow
practical considerations to be evaluated.
The range of proton-driver technologies being studied is
matched to the constraints of the example sites and covers the
technologies most likely to be employed.
We believe that this strategy will allow us to demonstrate that it is
feasible to deliver the required beam parameters from a number of
possible sites and using a variety of technologies.

The target that the proton beam hits is a liquid mercury jet.  
The liquid
jet avoids issues of structural damage from the beam that a solid
target faces.  
The proton beam hits the target inside a 20~T solenoid,
which tapers down to 1.5\,T in a distance of 15\,m.  
The high field and the taper give a large angular acceptance for the
pions at the target. 
The solenoid channel allows both muon signs to be captured.

The pion beam from the target decays into muons in a long decay channel,
and the resulting muon beam has a large energy spread as well as an
energy-time correlation, the latter arising because the pions are not
highly relativistic.
A sequence of RF cavities, the frequency of which decreases with
distance, then turns this distribution into a train of bunches. 
A subsequent sequence of cavities, with frequency decreasing down
the channel, then changes the energies of the individual bunches so that
all the bunches have the same energy.
These ``bunching'' and ``phase-rotation'' sections are followed by an
ionisation-cooling channel, which reduces the transverse emittance of
the bunches, thereby increasing the number of muons that can be
transmitted into the acceptance of the acceleration systems that
follow.  

Acceleration of the muon beam occurs in a number of stages.  
The first stage is a linac, which accelerates the beam to 0.9~GeV total
energy. 
This is followed by two recirculating linear accelerators (RLAs),
taking the beam to 3.6~GeV and 12.6~GeV, respectively.  
RLAs are preferable to a series of single-pass linacs since the beam
makes multiple passes through the RF cavities (4.5 passes in our
design), consequently reducing the cost of the acceleration system.
The RLA technique cannot be applied at lower energies, however,
since the beam has a low velocity which, combined with its large
relative-energy spread and large geometric emittance, would make a
linac phased for a higher energy inefficient at the lower, initial
energy.
The final stage of acceleration is performed in a fixed-field
alternating-gradient (FFAG) accelerator, which permits even more
passes (11) through the RF cavities.
The switchyard in an RLA will not permit such a large number of passes,
while the FFAG cannot achieve this large number number of turns at
lower energies.  
Each acceleration stage is thus chosen to use the most efficient
acceleration technique for its energy range.

The full-energy beam is next injected into two racetrack-shaped decay
rings.  
Each decay ring points toward one of the far detectors (the
``intermediate'' baseline or the ``long'' baseline).  
Each decay ring is capable of storing both muon signs simultaneously,
if desired.

\subsubsection{Progress within the IDS-NF accelerator study to date}

The IDS-NF adopted, with slight modifications, the specification for
the Neutrino Factory accelerator complex developed by the Accelerator
Working Group of the International Scoping Study of a future Neutrino
Factory and super-beam facility (the ISS) \cite{Apollonio:2009}.
The initial baseline (referred to as 2007/1.0) is defined in
\cite{IDS-NF-002}.
The specification of the accelerator facility presented below
(referred to as 2010/1.0) is the
result of a substantial amount of work and constitutes a revision of
the initial baseline \cite{IDS-NF-020}.
The principal developments that have resulted from the work of the
Accelerator Working Group of the IDS-NF or that have informed the
choice of baseline are summarised below.

The MERIT experiment, a test of a liquid-mercury-jet target,
has been completed, and the
data have been analysed~\cite{McDonald:2009zz}.
The mercury jet was in a high-field solenoid and was hit by a proton
beam from the CERN PS.
The experiment demonstrated that such a target is able to withstand
the high power-density that will be present at the Neutrino Factory.
MERIT also showed that if two bunches hit the target in rapid succession,
the disruption of the mercury jet caused by the first bunch does not
reduce the number of pions produced by the second bunch unless the
bunches are separated by more than 350~$\mu$s (because the disruption
increases with time).  
This result is important for the specification of the time structure
of the bunches coming from the proton driver when beam loading in the
RF cavities in the muon acceleration system is considered. 

The geometry of the proton beam and mercury jet has been optimised as
a function of energy \cite{Ding:2009zz,Ding:2010zzd}.  
The performance of the target was improved as a result, and the energy
dependence of the pion-production rate was computed more precisely.
The effect of a non-zero beam divergence was computed.
As a result of this calculation, a requirement for the proton-beam
emittance was determined (see table \ref{tab:acc:pd:parm}).
Comparisons were made between
MARS~\cite{Mokhov:1995wa,Mokhov:2000ih,Mokhov:2003jq,Mokhov:2004aa,mars}
(version 1507 is used throughout this document)
and FLUKA~\cite{Fluka1,Fluka2}
simulations for this
target system~\cite{Back1:2010}.

Very detailed studies were made of the energy deposition in the target
region~\cite{Ding:2010zzd,Back2:2010}.  
The studies indicate that the energy deposition in the superconducting
solenoids in the target region is too large,
so the solenoids in the target region
will be redesigned to allow more room for shielding.

In the muon front-end, the bunching and phase-rotation sections have
been shortened, creating a system that produces the same number of
muons in a shorter bunch train~\cite{Ankenbrandt:2009zza,Neuffer:2003zz}.  
Studies of the performance of RF cavities in magnetic fields have
continued~\cite{Huang:2009zzn} and the MICE experiment continues to
make progress towards a demonstration of the ionisation cooling
technique~\cite{Alekou:2010zz}.  
Indications that the maximum cavity-gradient may be reduced in
magnetic fields have led to the consideration of front-end lattices
that give adequate performance should the RF cavities not
reach the gradients specified for the magnetic field configuration
of the baseline lattice for the IDS-NF muon front end.
The performance of the baseline lattices, along with that
of the modified lattices, has been
computed~\cite{Gallardo:2010td,Stratakis:2010zz,Rogers:2009zzc,Alekou:2010zza,Neuffer:2009zz,Neuffer:2003zz}.
Particle losses and energy deposition in the front end have been computed,
and methods to reduce their impact are beginning to be
studied.

Tracking studies with more realistic fields
have been done on the first acceleration linac,
resulting in slight modifications to the lattice design.
The RLA designs have been improved by modifying the quadrupole
gradient profile in the linacs to increase
performance \cite{Bogacz:2009zzc}.  
A chicane has been designed for the locations where the arcs cross
each other \cite{Ankenbrandt:2009zza}.
In the arc-crossing and injection chicanes, chromatic
corrections have been incorporated and preliminary tracking results have
indicated that chromatic correction in these regions alone is
sufficient to achieve acceptable performance.

A new FFAG design has been developed that has a high average RF
gradient to reduce the effect of non-linear coupling of transverse
into longitudinal motion \cite{Berg:2009zz}.  
Injection and extraction schemes have been developed for the
FFAG ring \cite{Pasternak:2010zza} and we have begun to study the
designs of the injection and extraction kickers and septa.  
These preliminary studies indicated that longer drifts were necessary,
and as a result the FFAG design was modified.
Chromaticity correction in the FFAG has been studied more extensively
\cite{Berg:2009zz}.  

We have begun studies of diagnostics in the decay ring.  
We have a preliminary design for a polarimeter to be used for
beam-energy measurement \cite{Apollonio:2010zz}. 
In addition, a helium gas Cherenkov detector has been
considered for angular divergence measurement \cite{Piteira:2001}.
Other methods of beam-divergence measurement are now being studied as
the Cherenkov solution proved difficult.
