\section{FNAL Proton Driver}
\label{sec:acc:fnal}

FNAL proposes to build Project~X~\cite{Holmes:2010} as a new high
intensity proton source.
Project~X has three physics goals: 
\begin{enumerate}
\item To provide neutrino beams for long baseline neutrino oscillation
  experiments;
\item To provide intense kaon and muon beams for precision
  experiments; and 
\item To developm a path toward a muon source for a possible
  Neutrino Factory 
\end{enumerate}
The third goal provides the beam needed for a Neutrino Factory but additional accelerator rings 
will be needed to provide the correct time structure for the beam. 
A schematic layout of the Project~X reference design is shown in figure \ref{fig:acc:fnal:schem}.
 
\begin{figure}
  \includegraphics[angle=0,width=0.95\textwidth,bb=0 0 1281 734]%
    {06-Appendix/02-01-FNAL/px_schem.jpg}
  \caption{Schematic of FNAL Project~X. 3~to 8~GeV acceleration
    will be done using a pulsed linac.
  }
  \label{fig:acc:fnal:schem}
\end{figure}

Project~X will accelerate H$^{-}$ ions in two linacs. 
The first linac will be CW and accelerate beam to $\approx$3~GeV. 
The beam will then be directed either to a switchyard area to perform
precision experiments or to the second linac. 
A pulsed linac will accelerate the beam from the CW linac to $\approx$8~GeV, the injection energy of the Recycler Ring. 
After converting the H$^{-}$ beam, protons are accumulated in the Recycler Ring before transfer to 
the Main Injector where the beam is accelerated for the long baseline neutrino program. 

The beam originates from a 1---10~mA DC H$^{-}$ source.  
The beam is bunched and accelerated by a CW normal-conducting RFQ to 2.5~MeV. 
The RFQ is followed by a Medium Energy Beam Transport (MEBT) section, which includes a chopper
following a pre-programmed timeline formatting the bunch pattern. 
Since the linac average beam current is 1~mA and the beam current at
the ion source can be as high as 10~mA, up to 90\% of the beam has to
be removed by a chopper in the MEBT section.
The bunch spacing will be 3.1\,ns with a maximum intensity of
$1.9\times10^{8}$ protons per bunch exiting the front end. 
However, the CW linac will have an average beam current of 1\,mA
(averaged over 1\,$\mu$s). 

\begin{figure}
  \includegraphics[angle=0,width=\textwidth]{06-Appendix/02-01-FNAL/px_cw_linac.eps}
  \caption{Front-end and CW linac where the energy range and
    geometrical phase velocity are shown for each section.}
  \label{fig:acc:fnal:linac}
\end{figure}

The CW linac will use several types of superconducting RF cavities. 
Three types of single-spoke cavities operating at 325~MHz will be used to 
accelerate beam from 2.5~MeV to 160~MeV. 
To increase the energy to 2~GeV, two types of 650~MHz elliptical
cavities will be used. 
1300~MHz elliptical cavities complete the CW linac with a final energy
of 3~GeV.  
Figure \ref{fig:acc:fnal:linac} shows a schematic of the front end and
CW linac.
Table \ref{tab:acc:fnal:linac} contains the CW linac cavity parameters. 
Cavities and focusing elements are grouped within cryomodules. 
In the 325~MHz section of the linac focusing is provided by solenoids.  
In the 650~MHz section a standard focussing/defocussing (FD)
quadrupole doublet lattice is used, followed by a FODO lattice in the
1300~MHz section.  
All magnets are superconducting with built-in dipole correctors for
beam steering.  
\begin{table}
  \caption{
    Accelerating cavity specifications for the CW linac. $\beta_{G}$ is
    cavity geometrical phase velocity.
    The type of accelerating structure used in the various sections of
    the linac are noted on the figure: SSR refers to single spoke
    resonators; the 650\,MHz elliptical cavities are optimised for two
    geometrical phase velocities in the low energy (LE) and high
    energy (HE) sections of the linac; and the 1.3\,GHz elliptical
    cavities are referred to as ``ILC'' cavities.
  }
  \centering
  \begin{tabular}{|c|c|c|c|c|c|c|c|} \hline
 %   ~&~&~&\multicolumn{4}{c|}{Cavities}&Energy\\
    {\bf Section}&{\bf $\beta_{G}$}&{\bf Freq}&{\bf Cavity}&{\bf Number of}&{\bf Gradient}&{\bf Q$_{0}$}&{\bf Energy}\\
    ~&~&(MHz)&{\bf type}&{\bf cavities}&(MV/m)&($10^{10}$)&(MeV)\\ \hline
    SSR0&0.114&325&Single&26&6&0.6&2.5---10\\ 
    ~&~&~&Spoke&~&~&~&~\\ \hline
    SSR1&0.215&325&Single&18&7&1.1&10---32\\
    ~&~&~&Spoke&~&~&~&~\\ \hline
    SSR2&0.42&325&Single&44&9&1.3&32---160\\ 
     ~&~&~&Spoke&~&~&~&~\\ \hline
   LE650&0.61&650&Elliptic&42&16&1.7&160---500\\ \hline
    HE650&0.9&650&Elliptic&96&19&1.7&500---2000\\ \hline
    ILC&1&1300&Elliptic&72&17&1.5&2000---3000 \\ \hline
  \end{tabular}
  \label{tab:acc:fnal:linac}
\end{table}

The CW linac accelerates H$^{-}$ ions having the base bunch frequency
of 325~MHz set by the RFQ.
The beam may be steered toward the high-energy linac (pulsed linac), 
to the experimental area, or to the linac dump. 
The injection to the pulsed linac is controlled by a pulsed
switching-magnet.
If the switch magnet is off, then the beam encounters another
selection dipole magnet to steer it to the 3~GeV experimental
area or the dump.  
In the experimental area, an RF beam separator is used to split the
beam.

The 3--8~GeV pulsed linac is also a superconducting linac. 
Six 2.2~ms pulses of beam are provided at a rate of 10~Hz.
These pulses of beam are accelerated in the pulsed linac and
transferred to the Recycler/Main Injector in support of the
long-baseline neutrino program.  
The pulsed linac will deliver 26~mA-ms of charge in less than
0.75~s to the Recycler Ring;  
Project~X will deliver 345~kW at 8~GeV. 
The pulsed linac is based on 1.3~GHz, 9-cell cavities optimized for
$\beta = 1$ and International Linear Collider (ILC) type cryomodules,
providing a FODO focusing structure.
A cavity gradient of 25~MV/m, which is readily achieved with current
superconducting RF technology, means that 224 cavities are needed to
accelerate the H$^{-}$ beam from 3~to 8~GeV.

The two linacs fit comfortably within FNAL's Tevatron Ring. 
The basic idea is that, after upgrading Project~X, an accumulation
ring will be put at the end of the second linac.  
The accumulated protons would then be transferred to a separate bunch 
compression ring. 
From that ring, beam will be sent to the Neutrino Factory target
station.  
The target station and ensuing muon collection, acceleration and decay
ring will fit within the Tevatron Ring as well.  
Figure \ref{fig:acc:fnal:pd} shows a possible layout of the additional
rings and target station. 
\begin{figure}
  \includegraphics[angle=270,width=\textwidth]{06-Appendix/02-01-FNAL/px_pd.eps}
  \caption{Project~X siting within the Tevattron ring and possible
    locations of accumulator and proton ring to form a proton driver
    for a Neutrino Factory}
  \label{fig:acc:fnal:pd}
\end{figure}

To achieve 4~MW at 8~GeV, the pulsed linac will need to deliver
10~mA-ms of charge in less than 20~ms (50~Hz).
With the initial 1~mA average CW linac current, half of the CW linac
beam would have to be accelerated by the pulse linac to achieve 4~MW.
This would mean that the high energy linac would have to pulse 50\% of
the time.  
Instead of converting the pulsed linac to CW, the average injection
current can be raised.
Provisions are being designed into Project~X to support an 
upgrade of the CW linac to deliver a current of 4--5~mA. 

The transfer line from the pulsed linac to the accumulator ring will
have the same characteristics as the Project~X transfer line to the
Recycler that is being designed to avoid loss of the H$^{-}$ ions due
to Lorentz stripping, blackbody radiation stripping, and stripping
through collisions with residual gas in the beam pipe.
Dipole fields will be limited to 0.05\,T to prevent stripping of the
weakly bound second electron. 
The vacuum of the transfer line will be required to be 
$\sim 5\times10^{-9}$\,Torr.
To mitigate blackbody-radiation stripping, a liquid-nitrogen cryogenic
shield will surround the beam pipe. 
The transport line will include a transverse collimation scheme for
capturing large amplitude particles, a momentum-collimation system for
the protection of off-energy particles, and a passive phase-rotator
cavity to compensate for energy jitter.

The preliminary design for the accumulator ring has a circumference of
$\approx 250$\,m.  
Injection will incorporate a stripping system to convert H$^{-}$-ions
to protons.
Foil or laser stripping of electrons from a beam of such power will
need to be developed. 
The stripping processes are quantum mechanical which could leave 
$\sim 1$\% of the H$^{-}$ ions unaffected. 
The non-stripped beam results in a need for a $\approx 50$\,kW beam dump
integrated into the proton accumulation ring.

The major concern with a foil stripping system is the survival of the
foil.
Current systems rely upon short H$^{-}$ beam pulses.  
Pulses much longer than 1~ms will deposit enough energy to melt/damage
the foil.
The foil stripping-injection process will have to employ
transverse/longitudinal phase-space painting to spread the energy
deposition over the foil.
There must be enough time between pulses ($\approx 10$~ms) such that
the foil can radiate.
The bulk of the energy deposited in the foil comes from multiple
passes of protons.  
To reduce the number of proton hits, the circulating beam is moved
away from the foil when there is no beam being injected into the
linac. 
Development of cooled foils or a rotating foil may also increase the
stripping foil survivability.

A demonstration of high efficiency laser stripping system is needed.
A laser based stripping system depends upon two abrupt magnetic fields
and a bright-broad laser intersecting the beam. 
The H$^{-}$ beam is subjected to an abrupt exposure to a high-field dipole magnet 
where an electron will immediately Lorentz strip.
After the dipole, the hydrogen beam is exposed to a laser that excites
the remaining electron.  
A second high-field dipole magnet Lorentz strips the excited electron. 
The laser beam is divergent and at an angle with respect to the hydrogen beam 
so that the spread of Lorentz transformed photon energies matches the spread in hydrogen-beam energies. 
The laser must be bright enough to ensure a high efficiency for
exciting the hydrogen. 
The laser could be high-powered, pulsing synchronously with the beam.  
A moderate-power laser with a resonant cavity across the beam could also be used. 
Either arrangement needs development to survive in the radiation area of an accelerator enclosure. 

The CW linac front-end will be programmed to give short bursts,
injecting beam repeatedly into the same RF buckets of the proton
accumulator ring.
When $2\times10^{13}$ protons have been loaded into each of three RF buckets, 
the RF voltage is increased to shorten the bunch lengths. 
The proton beam is then transferred to the bunching ring. 
A preliminary design for both rings has been developed; beam
instabilities remain to be studied.
Space charge, as well as other conditions, will influence the high
intensity bunches. 
The bunching ring will accept the proton bunches and immediately perform 
bunch rotation of the beam to the final bunch length.  
The beam is then extracted within 240\,$\mu$s; extractions are
separated by 120~$\mu$s.  
The extracted beam is then directed to the target. 
The last transfer line magnet element will be outside the target
station shielding and equipment; the last focusing and steering
elements will be at least 3~m from the target.
