\subsection{Proton driver}
\label{Sect:ProtonDriver}

The proton driver at the Neutrino Factory is required to deliver a
proton-beam of 4~MW at a repetition rate of 50 Hz to the pion
production target.
The proton-beam energy must be in the multi-GeV range in order to
maximise the pion yield.  
In addition, the Neutrino Factory specifies a particular time structure
consisting of three very short bunches separated by about 120~$\mu$s. 
To allow the muon beam to be captured efficiently, short, 1--3~ns rms,
bunches are required. 
Each bunch from the proton driver will become a separate muon bunch train.
The bunch separation is constrained by beam loading in the downstream
muon accelerator systems and by the time scale for
disruption of the mercury-jet target.  
The proton beam parameters necessary to produce the desired number of
muons in the storage rings of the Neutrino Factory are listed in table
\ref{tab:acc:pd:parm}.
In order to achieve such short bunches, a dedicated bunch compression
system must be designed to deal with the very strong space-charge
forces.
Several proton-driver schemes fulfilling these requirements have been
proposed.  
Typically they consist of an H$^-$-ion source followed by a
radio-frequency quadrupole (RFQ),
a chopper, and a linear accelerator.  
In some cases
the final energy of the proton driver is delivered by the linac. 
In these linac-based scenarios, the beam time structure must be obtained
with the help of charge-exchange injection into an accumulator ring
followed by fast phase rotation in a dedicated compressor ring. 
\begin{table}
  \caption{
    Proton driver requirements.
    A proton kinetic energy in the range 5~GeV to 15~GeV has been shown
    to provide adequate performance.
    The number of protons, beam radius, $\beta^*$, and geometric emittance
    (see section~\ref{Sect:Trgt})
    correspond to the values
    for an 8~GeV proton beam.
  }
  \label{tab:acc:pd:parm}
  \centering
  \begin{tabular}{|l|r|}
    \hline
    {\bf Parameter}         & {\bf Value}                      \\
    \hline
    Kinetic energy          & 5--15 GeV                        \\
    Average beam power      & 4 MW                             \\
                            & ($3.125\times 10^{15}$ protons/s) \\
    Repetition rate         & 50 Hz                            \\
    Bunches per train       & 3                                \\
    Total time for bunches  & 240 $\mu$s                       \\
    Bunch length (rms)      & 1--3 ns                          \\
    Beam radius             & 1.2 mm (rms)                     \\
    Rms geometric emittance & $<5~\mu$m                        \\
    $\beta^*$ at target     & $\geq 30$~cm                     \\
    \hline
  \end{tabular}
\end{table}

Such a linac-based solution was adopted for the CERN Neutrino Factory
scenario, which would be based on the proposed 5-GeV, high-power version of
the Superconducting Proton Linac (SPL)~\cite{Gerigk:2006qi},
which can deliver $10^{14}$
protons at the repetition rate of 50~Hz \cite{Garoby:2009b}. 
In the recent past, the Superconducting Proton Linac study
evolved into an international collaboration whose aim is the
optimisation of the architecture of a pulsed superconducting
high-power proton linac.  The most recent design of the SPL and the
description of the goals of the collaboration, can be found
in~\cite{Gerigk:2010}.
In the CERN scenario,
the chopped beam from the SPL would be injected into an isochronous
accumulator ring in which 120~ns long bunches are formed without the
need for an RF system. 
The absence of synchrotron motion in the accumulator ring makes it
important to study the stability of the beam in the presence of
space-charge.
As presented in~\cite{Benedetto:2009EB},
transverse stability can be obtained with a suitable
choice of chromaticity as shown in figure~\ref{fig:acc:pd:cern1} (left
panel) and longitudinal stability can be achieved by limiting the
longitudinal broad-band impedance to a few ohms as shown in
figure~\ref{fig:acc:pd:cern1} (right panel)~\cite{Benedetto:2009EB}.  
Two-dimensional phase-space painting is used in the stripping injection
into the accumulator ring, allowing the temperature of the stripping
foil to be kept below 2000~K. 
The beam parameters after accumulation are obtained as a compromise
between the competing requirements of minimising the heating of the
injection foil, maximising the aperture, and adequate compensation of
the space-charge forces and are set to allow for RF phase-rotation
in the downstream compressor ring.  
The size of the two rings is determined by the requirement that
successive bunches must arrive at the correct location in the
compressor ring.
The compressor ring has a large phase slip factor, which is needed for
the fast phase rotation.
Tracking simulations in the compressor ring have been performed using
the ORBIT code~\cite{orbit}.
The good performance of the compressor ring is demonstrated in
figure~\ref{fig:acc:pd:cern2} (left panel).
The simulations have also been used to investigate the transverse
phase space. Figure~\ref{fig:acc:pd:cern2} (right panel)
shows that the transverse space charge can be tolerated due
to the limited number of turns of the beam in the compressor ring and
the relatively large dispersion, which effectively lowers the tune
shift by enlarging the beam size.
The parameters of the accumulator and compressor rings are listed in
table \ref{tab:acc:pd:cern1}.
More details of the CERN proton driver scenario can be found in
\cite{Garoby:2009a}.
The low energy normal-conducting part of the SPL is currently under
construction and should become operational in the following few years
as part of the LHC injector chain. The existing proton linac, the
Linac2, will be replaced soon by the more modern Linac4~\cite{Arnaudon:2006jt}
that
will accelerate H- up to 160 MeV, before injecting them in the PSB.
The linac performances will match the requirements of the program of
increasing the LHC luminosity.  The status of the construction of the
Linac4 in 2010 can be found in~\cite{Vretenar:2010}; in particular,
the construction of the new
Linac building was recently concluded.
Figure~\ref{fig:acc:pd:cernsite}
shows an overview of the Linac integration with respect to the
existing accelerator complex.
\begin{table}
  \caption{
    Parameters of the accumulator and compressor rings for the CERN
    proton driver scenario.
  }
  \label{tab:acc:pd:cern1}
  \centering
  \begin{tabular}{|l|r|}
    \hline
    {\bf Parameter}               & {\bf Value}               \\
    \hline
    \multicolumn{2}{|c|}{Accumulator ring}                    \\
    \hline
    Circumference                 &185 m                      \\
    No. of turns for accumulation & 640                       \\
    Working point (H/V)           & 7.37/5.77                 \\
    Total bunch length            & 120 ns                    \\
    RMS momentum spread           & 0.863 $\times 10^{-3}$\\
    \hline
    \multicolumn{2}{|c|}{Compressor ring}                     \\
    \hline
    Circumference                 & 200 m                     \\
    No. of turns for compression  & 86                        \\
    RF voltage                    & 1.7 MV                    \\
    Gamma transition              & 2.83                      \\
    Working point                 & 4.21/2.74                 \\
    \hline
  \end{tabular}
\end{table}
\begin{figure}
  \begin{center}
    \includegraphics[angle=270,width=0.5\linewidth]{02-AccWG/02-B-ProtonDriver/nufact_qprime2.eps}%
    \includegraphics[angle=270,width=0.5\linewidth]{02-AccWG/02-B-ProtonDriver/longQ1.eps}
  \end{center}
  \caption{Horizontal beam size evolution, for various values of
    chromaticity, assuming a transverse impedance of 1~M$\Omega$/m, $Q_R$=1,
    $f_R$=1~GHz (left).  Longitudinal emittance evolution for different values
    of $Z_{\|}/n$ (right). The lines for 3 and 4~$\Omega$ lie on top of each
    other in the figure.}
  \label{fig:acc:pd:cern1}
\end{figure}
\begin{figure}
  \begin{center}
    \includegraphics[width=0.5\linewidth]{02-AccWG/02-B-ProtonDriver/Garoby2009-Fig3a.eps}%
    \includegraphics[width=0.5\linewidth]{02-AccWG/02-B-ProtonDriver/Garoby2009-Fig3b.eps}
  \end{center}
  \caption{Phase space plots before and after bunch rotation.}
  \label{fig:acc:pd:cern2}
\end{figure}
\begin{figure}
  \begin{center}
    \includegraphics[width=0.6\linewidth]{02-AccWG/02-B-ProtonDriver/Linac4_newimage.eps}
  \end{center}
  \caption{The CERN Linac4 with respect to the rest of the site.}
  \label{fig:acc:pd:cernsite}
\end{figure}

A proton driver for a Neutrino Factory situated at Fermilab would be
based upon an upgrade of the proposed Project~X linac, as described in
Appendix \ref{sec:acc:fnal}. 
Fermilab is currently designing a high-intensity proton source that
will deliver beam at 3~GeV and 8~GeV. 
As presently conceived, the Project~X linac will deliver only $\approx
10\%$ of the proton-beam power needed for the Neutrino Factory at
8~GeV. 
However, Project~X is designed such that it can be upgraded to deliver
the full beam power (4~MW at 8~GeV) required for the Neutrino Factory. 
Just as in the CERN scheme, additional accumulator and compressor
rings will be needed to provide the correct time structure.

Project~X will accelerate H$^{-}$-ions in two superconducting linacs.
A CW linac will accelerate beam to 3~GeV, where the majority of the
beam will be used for experiments. 
A small portion of the beam will be directed into a pulsed linac to be
further accelerated to 8~GeV. 
At 8~GeV, the beam will be accumulated in the Recycler ring before
being transferred to the Main Injector.   
The proton beam will then be accelerated to higher energy for the
long-baseline neutrino program.  

The CW linac will be operated with an average current of 1~mA.
Less than 5\% of the CW-linac beam will be directed to the pulsed
linac. 
Initially, the pulsed-linac beam will provide $\approx 350$~kW of beam
power at 8~GeV.
If the pulsed linac is capable of operating 50\% of the time,
then the required beam power of 4~MW could be reached.  
The option of converting the pulsed linac into a CW linac is not being
considered.
Instead, the average current of the CW linac can be raised to 4-5~mA.
While designing Project~X, provision is being made to allow the CW
linac to be upgraded to accelerate the increased beam current that
will be required to serve the Neutrino Factory.

For Project~X to serve the Neutrino Factory, an accumulation ring will
be put at the end of the second linac.
At injection into the accumulation ring there will be a stripping
system, foil or laser based, to convert the H$^{-}$-ions to protons.
The front-end of Project~X will have a programmable chopper so that
beam will be injected into three RF buckets in the accumulation ring.
After injection is complete, the RF bucket voltage will be increased
to shorten the bunches. 
The accumulated protons will then be transferred to a separate
bunch-shortening (compressor) ring.
Bunch rotation will be used to achieve the final bunch length
(2~ns). 
The three bunches will be extracted with the proper spacing
(120~$\mu$s) to the target station.
The accumulation, bunch shortening, and targeting will be done at 50~Hz,
as required for the Neutrino Factory. 

Project~X will be located within the Tevatron ring at Fermilab.
The accumulation ring will be situated near the end of the pulsed
linac.
Once the beam has been converted from H$^{-}$-ions to protons, the
beam can be transported some distance to the bunch-shortening ring.
Extraction from the bunch shortening ring to the target sets the
orientation of the ensuing muon collection and acceleration.
All components of the Neutrino Factory, including a decay ring, fit
within the Tevatron ring footprint.  

A Neutrino Factory sited at the Rutherford Appleton Laboratory (RAL)
would be served by a proton driver based on an upgrade to the ISIS
pulsed-proton source.
In this scenario, a chain of circular accelerators, typically
Rapid Cycling Synchrotrons (RCSs), provides an alternative to the
linac-based options outlined above.
Here, bunch compression is accomplished adiabatically in
the RCS or, alternatively, in an FFAG ring as proposed in the ISS
study \cite{Apollonio:2009}.   
Recently the attractive idea of a common proton driver for the
spallation neutron source and the Neutrino Factory was proposed in the
framework of the ongoing ISIS megawatt-upgrade programme.
In such a scenario, the proton drivers for both facilities would share the
same source, chopper, linac, accumulator, and acceleration up to
3.2~GeV.  
After extraction, a number of bunches would be sent directly to the
neutron-spallation target while three others would be injected into a
second RCS or FFAG where, after acceleration to somewhere between
6.4 and 10.3~GeV followed by bunch compression, the beam
would be extracted towards the Neutrino Factory pion-production
target. 
The layout of the proton drivers using the RCS machines can be seen
in figure \ref{fig:acc:pd:ral}.
The left panel shows the solution based on an RCS booster and FFAG
ring developed during the the ISS \cite{Apollonio:2009}.
The right panel shows the layout of the common proton driver for the
spallation-neutron source and the Neutrino Factory that is presently
under development.
For the ISIS megawatt upgrade to be compatible with the Neutrino
Factory, an 800~MeV H$^-$ linac has been designed, candidate
lattices for the 3.2~GeV booster RCS have been identified, and
preliminary parameters for the final RCS ring have been proposed.
More details of the Neutrino Factory proton driver option based on an
upgrade of facilities at RAL are described in Appendix~\ref{sec:acc:ral}.
\begin{figure}
  \begin{center}
    \includegraphics[width=\linewidth]{02-AccWG/02-B-ProtonDriver/IDR_PDfig5.eps}
  \end{center}
  \caption{Left panel: Layout of the ISS proton driver based on an RCS and
    an FFAG. Right panel: Layout of the common proton driver for ISIS and
    the Neutrino Factory at RAL.}
  \label{fig:acc:pd:ral}
\end{figure}
