\subsection{Target}
\label{Sect:Trgt}

\subsubsection{Introduction to the target system}

The requirements for the proton driver at the Neutrino Factory
\cite{Alsharoa:2002wu} (summarised in table \ref{tab:acc:pd:parm})
call for a target capable of intercepting and surviving a 4~MW pulsed
proton beam with a repetition rate of 50~Hz.
The assumption of 8~GeV for the proton-beam energy arises from an
optimisation study (done with
MARS~\cite{Mokhov:1995wa,Mokhov:2000ih,Mokhov:2003jq,Mokhov:2004aa,mars})
in which the target parameters were evaluated as a
function of incoming proton beam kinetic energy.
The resulting meson (``meson'' in this document denotes muons, charged pions,
and charged kaons)
production-efficiency is shown in figure
\ref{fig:acc:tgt:1a}.  
The peak production-efficiency occurs for proton kinetic energies of
6--8~GeV.
The $\beta^*$ requirement (at the centre of the beam-target crossing)
is confirmed by simulations as shown in
figure \ref{fig:acc:tgt:1b}.
\begin{figure}
  \includegraphics[width=0.8\textwidth]{02-AccWG/02-C-Target/IDR-Target-F0a.eps}
  \caption{The meson production efficiency, normalised to the beam power,
    as a function of incoming
    proton beam kinetic energy~\cite{Ding:2009zz}. Production
    efficiency is the number of mesons 50~m downstream from the target
    with kinetic energy in the range of 40--180~MeV. This criterion
    has been found to have a good correlation with the muons that are
    transmitted through the front end.}
  \label{fig:acc:tgt:1a}
\end{figure}
\begin{figure}
  \includegraphics[width=0.8\textwidth]{02-AccWG/02-C-Target/IDR-Target-F0b.eps}
  \caption{The meson production efficiency as a function of the
    $\beta^*$ of the incoming proton beam~\cite{Ding:2010zzd}. The
    data are fit to the function $y=a_1-a_2e^{-kx}$, with $x$ being
    the beta function of the beam distribution at $z=-37.5\text{ cm}$
    (the centre of the beam-target crossing)
    and $y$ being the production efficiency. The results are scaled to
    $a_1$, the limit of the fit as the beta function goes to
    infinity.}
  \label{fig:acc:tgt:1b}
\end{figure}

The proton-beam bunch-length requirement is derived from a calculation
in which the front end of a Neutrino Factory complex is simulated with
the code ICOOL~\cite{Fernow:2005cq}.
The muon throughput is obtained as a function of the mesons produced
at the target for proton beams with various bunch
lengths~\cite{Gallardo:2006zz}.  
The results are shown in figure \ref{fig:acc:tgt:1c}.
\begin{figure}
  \includegraphics[width=0.8\textwidth]{02-AccWG/02-C-Target/muc0340-f1.eps}
  \caption{The final muon throughput of the front end as a function of
    the incoming proton beam bunch length~\cite{Gallardo:2006zz}.
    Solid blue dots and red
    stars are data for two equivalent methods of creating the beam
    distribution in time.}
  \label{fig:acc:tgt:1c}
\end{figure}

The proposed target system simultaneously captures charged pions of
both signs, hence the use of solenoid magnets in the target system
(rather than toroidal magnets that primarily capture particles of only
one sign, as is typical in target systems for ``conventional''
neutrino beams).   

The target, the proton beam dump, and a shield/heat exchanger are to
be located inside a channel of superconducting solenoid magnets that
capture, confine and transport secondary pions and their decay muons
to the muon front-end (see section
\ref{Sect:FrontEnd}). 
In the present baseline configuration, most of the 4~MW beam power is
dissipated within a few meters of the target, inside the
solenoid channel, which presents severe engineering challenges.

Maximal production of low-energy pions is obtained with a proton beam
of 1--1.5~mm (RMS) radius and a target of radius three times this.
The target parameters have been determined by extensive simulations
using the MARS modelling code \cite{Ding:2010zzd}.

The effect of beam-induced shock in solid targets has been studied
using a high-current pulse with a rapid rise time to deliver a high
power-density in tungsten and tantalum wires \cite{Simos:2008zz}.
The results indicate that a system in which tungsten bars are
exchanged between beam pulses can withstand the beam-induced shock.
However, schemes for a set of moving solid targets have yet to be
shown to be compatible with the confined environment provided by the
solenoid magnets that form the pion-capture system.
Hence, the baseline target concept is for a free liquid-mercury jet.
A free-flowing jet is chosen because the intense beam-induced pressure
waves in the liquid target would damage or lead to the failure of
any pipe containing the liquid in the interaction region.  
The parameters of the present target-system baseline are summarised in
table \ref{tab:acc:tgt:parm}.
\begin{table}
  \caption{Baseline target system parameters.}
  \label{tab:acc:tgt:parm}
  \centering
  \begin{tabular}{|l|r|}
    \hline
    {\bf Parameter}                                      & {\bf Value}      \\
    \hline
    Target type                                          & Free mercury jet \\
    Jet diameter                                         & 8 mm             \\
    Jet velocity                                         & 20 m/s           \\
    Jet/solenoid axis angle                              & 96 mrad          \\
    Proton beam/solenoid axis angle                      & 96 mrad          \\
    Proton beam/jet angle                                & 27 mrad          \\
    Capture solenoid (SC-1) field strength               & 20~T             \\
    Front-end $\pi/\mu$ transport channel field strength & 1.5 T            \\
    Length of transition between 20 T and 1.5 T          & 15 m             \\
    \hline
  \end{tabular}
\end{table}

The concept of a mercury jet target within a high-field solenoid
has been validated by R\&D over the
past decade, culminating in the MERIT
experiment~\cite{Bennett:2004} that ran in the fall of 2007 at the
CERN PS.
The experiment benefited from the intensity of the beam pulses (up to
$30\times10^{12}$ protons per pulse) and the flexible beam structure
available for the extracted PS proton beam.  
Key experimental results include the demonstration that
\cite{McDonald:2009zz}:
\begin{itemize}
\item 
  The magnetic field of the solenoid greatly mitigates both the
  extent of the disruption of the mercury and the velocity of the
  mercury ejected after interception of the proton beam.  
  The disruption of a 20~m/s mercury jet in a 20~T field is
  sufficiently limited that a repetition rate as high as 70~Hz
  is feasible without
  loss of secondary particle production;
\item 
  Individual beam pulses with energies up to 115~kJ can safely be 
  accommodated;
\item 
  Subsequent proton-beam pulses separated by up to 350~$\mu$s have
  the same efficiency for secondary particle production as does the
  initial pulse; and
\item 
  The disruption of the mercury jet caused by the second of two beam
  pulses separated by more than 6~$\mu$s is unaffected by the presence
  of the first beam pulse.
\end{itemize}

In the Neutrino Factory target system,
the mercury jet is collected in a pool, inside the solenoid magnet
channel, that also serves as the proton beam-dump, as sketched in
figure \ref{fig:acc:tgt:all}.  
Disruption of this pool by the mercury
jet (equivalent to a mechanical power of 3~kW) and by the non-interacting
part of the proton beam is nontrivial, and needs further study.
\begin{figure}
  \includegraphics[width=0.8\textwidth]{02-AccWG/02-C-Target/IDR-Target-F1.eps}
  \caption{Baseline target system concept, with small changes from
    Neutrino Factory Study~II~\cite{Ozaki:2001}.  SC-$n$ are the
    superconducting magnets.}
  \label{fig:acc:tgt:all}
\end{figure}

The superconducting magnets of the target system must be shielded
against the heat and radiation damage caused by secondary
particles issuing from the target (and beam dump).  A high-density shield is
favoured to minimise the inner radii of the magnets.

The baseline shield concept is a stainless-steel vessel of complex
shape (see figure \ref{fig:acc:tgt:all}) containing water-cooled
tungsten-carbide beads.  
Calculations using MARS in an MCNP mode (MCNP mode gives more accurate
treatment of low-energy neutrons)
show that for an 8~GeV, 4~MW incoming proton beam, the radiation
penetrating the shielding (as configured in Study~II~\cite{Ozaki:2001})
results in 50~kW
of power being deposited in the superconducting coils that surround
the target~\cite{Souchlas:2010}.
This would present a severe operational burden
on the cryo-system and hence is not considered
practical. 
Effort to produce a new
baseline for the shielding is under way.

The solenoid magnets of the target system vary in strength from 20~T
(SC-1 in figure \ref{fig:acc:tgt:all}) down to 1.5~T in the subsequent
constant-field transport channel.
Table \ref{tab:acc:tgt:capturecoils} gives the solenoid parameters as
established in Study~II \cite{Ozaki:2001}.
The interface between the target station and the muon front-end is
taken to be the point at which the constant-field capture channel
begins, 15~m downstream of magnet SC-1 in the present baseline.
The initial superconducting coil (SC-1), which is responsible for
generating a 14~T field at the site of the target, has the most
challenging mechanical requirements.  The stored energy of this magnet
is 600~MJ, and the radial and hoop stresses are 110~MPa and 180~MPa,
respectively~\cite{Loveridge:2010}.
\begin{table}[htb]
\begin{center}
\caption[The Study 2 Solenoid coil parameters ]
{Solenoid coil and iron plug geometric parameters.
  The centre of the beam-target
  crossing is at $-37.5$~cm.}
\label{tab:acc:tgt:capturecoils}
\vspace{2.5mm}
\begin{tabular}{|c|c|c|c|c|c|c|c|}
\hline
  & $\bf{z}$ & $\bf{\Delta z}$ & $\bf{R_i}$ & $\bf{\Delta R}$ & $\bf{I/A}$ & $\bf{n I}$ & $\bf{n I l}$\\ 
& (m) & (m) & (m) & (m) &  (A/mm$^2$) & (A) & (A-m) \\ 
\hline
Fe
& 0.980 &  0.108 &  0.000 &  0.313 &   0.00 &  0.00 &  0.00  \\
& 1.088 &  0.312 &  0.000 &  0.168 &   0.00 &  0.00 &  0.00  \\
\hline
Cu coils 
& 1.288 &  0.749 &  0.178 &  0.054 & 24.37 &  0.98 &  1.26  \\
& 1.288 &  0.877 &  0.231 &  0.122 & 19.07 &  2.04 &  3.74  \\
& 1.288 &  1.073 &  0.353 &  0.137 & 14.87 &  2.18 &  5.78  \\
\hline
SC coils
& 0.747 &  1.781 &  0.636 &  0.642 & 23.39 & 26.77 & 160.95  \\
& 2.628 &  0.729 &  0.686 &  0.325 & 25.48 &  6.04 & 32.23  \\
& 3.457 &  0.999 &  0.776 &  0.212 & 29.73 &  6.29 & 34.86  \\
& 4.556 &  1.550 &  0.776 &  0.107 & 38.26 &  6.36 & 33.15  \\
& 6.206 &  1.859 &  0.776 &  0.066 & 49.39 &  6.02 & 30.59  \\
& 8.000 &  0.103 &  0.416 &  0.051 & 68.32 &  0.36 &  1.00  \\
& 8.275 &  2.728 &  0.422 &  0.029 & 69.27 &  5.42 & 14.88  \\
&11.053 &  1.749 &  0.422 &  0.023 & 75.62 &  3.00 &  8.18  \\
&12.852 &  1.750 &  0.422 &  0.019 & 77.37 &  2.61 &  7.09  \\
&14.652 &  1.749 &  0.422 &  0.017 & 78.78 &  2.30 &  6.22  \\
&16.451 &  1.750 &  0.422 &  0.015 & 79.90 &  2.07 &  5.59  \\
&18.251 &  2.366 &  0.422 &  0.013 & -0.85 &  2.53 &  6.80  \\
\hline
\end{tabular}
\end{center}
\end{table}


A 20~T field is beyond the capability of Nb$_3$Sn, and magnet SC-1 is
proposed as a hybrid of a 14~T superconducting coil with a 6~T
hollow-core copper solenoid insert.  A 45~T solenoid with this type of
construction (but a significantly smaller bore of 32~mm diameter)
has been operational since 2000 at the National High
Magnetic Field Laboratory (Florida, USA)~\cite{NHMFL:45T}.  A 19~T resistive magnet
with a 16~cm bore at the Grenoble High Magnetic Field
Laboratory~\cite{GHMFL:M8} was used in an earlier
phase~\cite{Fabich:2002} 
of the Neutrino Factory R\&D program.  
A topic for further study is possible
fabrication of SC-1 as a high-T$_{\text{C}}$ magnet with no
copper-solenoid insert, which could provide more space for internal
shielding of SC-1 and/or permit operation at a higher field for a
potential increase in the meson-capture efficiency.

The target system (and also the subsequent $\pi$/$\mu$ solenoid transport
channel) will be subjected to considerable activation, such that once
beam has arrived on target all subsequent maintenance must be
performed by remote-handling equipment.  
The infrastructure associated
with the target hall, with its remote-handling equipment, and
hot-cells for eventual processing of activated materials, may be the
dominant cost of the target system.

\subsubsection{Sub-systems}

\paragraph{Target}
\subparagraph{Baseline Concept}

The target itself is a free liquid mercury jet ($Z = 80$, $A = 200.6$,
density $\rho = 13.5\text{ g/cm}^3$, nuclear interaction
length $\lambda_I \approx 15\text{ cm}$) of
diameter $d = 8\text{ mm}$, flowing at $v = 20 \text{ m}/\text{s}$.
The volume-flow rate is 1.0~L/s and the mechanical power in the
flowing jet is 2.7~kW.  
The flow speed of 20~m/s ensures that the gravitational curvature of
the jet over the two nuclear interaction lengths (30~cm) through which the
proton beam passes is negligible compared to its diameter and that
more than two nuclear interaction lengths of new target material are presented
to the beam every 20~ms, the time between beam pulses at a repetition
rate of 50~Hz. 

According to a MARS15
\cite{Mokhov:1995wa,Mokhov:2000ih,Mokhov:2003jq,Mokhov:2004aa,mars} 
simulation \cite{Ding:2010zzd,Ding:2010}, about 11\% of the
beam energy is deposited in the target, corresponding to 9~kJ/pulse at
50~Hz.  
This energy is deposited over two nuclear interaction lengths along the
jet (30~cm, 15~cm$^3$), so, noting that the specific heat of mercury
is $\sim 4.7$~J/cm$^3$/K, the temperature rise of the mercury during a
beam pulse is about 130~K.  
The boiling point of mercury is 357~$^\circ$C, so the mercury jet, which
enters the target volume at room temperature, is not vaporised at
50-Hz operation.

Although the mercury jet is not vaporised, it will be disrupted and
dispersed by the pressure waves induced by the pulsed energy
deposition.  
The MERIT experiment \cite{McDonald:2010zz} showed that for pulses
equivalent to 50~Hz operation at 4~MW beam power, this disruption
results in droplets with peak velocity of $\sim 50$~m/s in a 
15~T field.
Extrapolating these results to 20~T field at the Neutrino Factory
target yields a maximum droplet-velocity of $\sim 30$~m/s.

The optimal production of pions in the acceptance of the muon
front-end is achieved by appropriate tilts of the mercury jet and
proton beam with respect to the magnetic axis.  
These tilts depend slowly on the proton-beam energy (as does the
optimum radius of the jet), and the current best values are based on
MARS15
\cite{Mokhov:1995wa,Mokhov:2000ih,Mokhov:2003jq,Mokhov:2004aa,mars}) 
simulations and are given in table \ref{tab:acc:tgt:parm}.

The Reynolds number of the mercury flow in the jet is
$R=\rho vd/\eta\approx 1400$. 
Noting that the viscosity of mercury is
$\eta=1.5$~mPa$\cdot$s,  the flow can be turbulent.  
Hence, the
quality of the jet is an issue, although operation in a high 
magnetic field damps surface perturbations~\cite{Fabich:2002}. 
The nozzle will need to be
as close as feasible to the interaction region.  
High velocity mercury may generate erosion of the nozzle, e.g., by
erosion-corrosion or by cavitation; this part of the system would need to be
carefully designed but may be studied off-line using a suitable mercury flow
loop.
Detailed design work of the nozzle is under way.

\subparagraph{Possible Target Alternatives}

Alternatives to the liquid-mercury jet target that are under 
consideration are: a liquid-metal jet using a metal that is solid at room
temperature; a helium-cooled metallic low-\textit{Z} static packed bed;
a metal-powder-jet; and a system of solid tungsten bars
that are exchanged between beam pulses.

A eutectic alloy of
lead and bismuth (melting point 124~$^\circ$C)
would have similar performance
to a mercury target, with the challenge of operating
the target flow-loop at temperatures above the boiling point of water,
with that flow-loop in thermal contact with the water-cooled shield of
the superconducting magnets.  
The activation products from a lead-bismuth target are more
troublesome than those of a mercury target. 
A helium cooled low-\textit{Z} static packed bed of beryllium (or possibly
titanium) would give a low-\textit{Z} (the advantages of which are described
below) alternative to graphite
that is considerably more tolerant to radiation damage and therefore
would have a greater lifetime than the graphite,
provided that sufficient cooling can be
achieved.
The powder-jet and solid alternatives are discussion in Appendices
\ref{App:PowderJet} and \ref{App:SolidTrgt}.

\paragraph{Proton Beam Dump}

The target system requires the proton beam dump to be inside the
superconducting magnet channel, only $\approx 1\text{ m}$ from the
target.  
The baseline design is to use the pool that collects the
mercury from the target jet as the beam dump.  
The mercury is to be
drained from the upstream end of the pool, in a passage that is a
sector of the annular space between the resistive magnet and
superconducting magnet SC-1.

The dump must dissipate the $\sim 3$~kW of mechanical power in the
mercury jet, as well as $\sim 20$~kW of power in the attenuated
proton beam. The beam dump must also be able to withstand one or two
full intensity beam pulses before the beam can be tripped in the event
that the mercury jet fails, or the beam misses the jet.
The vessel that contains the mercury pool will be subject to
substantial radiation damage and heating by the secondary particles
from the target, and must be replaced periodically.

\paragraph{Beam Windows}
\label{sec:acc:tgt:bw}

The volume that contains the target and mercury pool beam dump is the
primary containment vessel for the mercury.  
This containment vessel
includes a small window upstream through which the proton beam enters
and a larger window on the downstream face of the vessel, currently
specified to be at the boundary between superconducting magnets SC-4
and SC-5, through which the desired secondary pions and muons (as well
as other particles) pass.  
The containment vessel is to be operated with helium gas (plus mercury
vapour) at atmospheric pressure.

The upstream proton-beam window has yet to be specified, either as to
design or location. 
The larger exit window is specified to be made of beryllium.  
It will be a double window, such that the volume between
the two windows can support a flow of helium gas to cool the
window, and which can be monitored for indications of window
failure.
The complexity of such a window system is indicated in figure
\ref{fig:acc:tgt:t2k} which shows the beam window in use on the
T2K target at J-PARC~\cite{Rooney:2008}.
The window system is a replaceable item, and will be sealed to the
downstream face of the primary containment vessel and to the upstream
face of the pion-decay-channel vessel via inflatable ``pillow''
seals. 
\begin{figure}
  \centering
  \includegraphics[width=0.25\linewidth]{02-AccWG/02-C-Target/IDR-Target-F4a.eps}%
  \includegraphics[width=0.75\linewidth]{02-AccWG/02-C-Target/IDR-Target-F4b.eps}
  \caption{Photograph and schematic of the T2K beam window~\cite{Rooney:2008},
    which was designed for a 0.75~MW beam.}
  \label{fig:acc:tgt:t2k}
\end{figure}

\paragraph{The Internal Shield}
\label{sec:acc:tgt:shield}

A major challenge of the target system is the dissipation of the 4~MW
of beam power inside the superconducting magnet string without
quenching the magnets or extreme shortening of their operational
lifetime due to radiation damage.  
Most of the beam power will be dissipated in an internal shield
composed of a high-\textit{Z} material, which will have to extend well beyond
the downstream end of the target system into the muon front-end.

The baseline scenario is for a shield of tungsten-carbide beads cooled
by water.  Pure tungsten beads would provide better shielding, but
tungsten corrodes in water in a high radiation environment~(see, for
example, \cite{Li:2007}).  Random packing of spherical beads of a
single radius will result in a configuration with about 63\% by volume
of tungsten-carbide, and 37\% water~\cite{Song:2008}.  The flow path
of the coolant is not presently specified; multiple inlets and outlets
will be appropriate for a shield of total length 30--50~m.
One inlet is required at the very upstream end of the shield where the
heat load is the largest.

All high-\textit{Z} target systems proposed so far rely on recirculating target
material from the target interaction region to be externally cooled.
This requires either a radial or longitudinal gap to be engineered between
the solenoid coils and shielding.

The outer radius of the shield was specified to be 63~cm in
Feasibility Study~II \cite{Ozaki:2001}, but subsequent MARS15
simulations indicate that this would imply a load of 
$\sim 25$~kW in magnet SC-1~\cite{Ding:2010zzd}.  
A low-\textit{Z} target material would considerably reduce
neutron production compared with a high-\textit{Z} material,
which could potentially reduce this energy deposition.
Interim values of up to 75~cm for the outer
radius of the shield are being considered.  Studies are under way to determine
acceptable criteria for the total power deposition and the peak local
power deposition for the various magnets to be stable against
quenching and radiation damage.  
The details of the present baseline concept should therefore be regarded as
preliminary.

\paragraph{The solenoid magnets}
\label{sec:acc:tgt:sols}

An early concept~\cite{Palmer:1994km} for a muon collider
assumed separate targets for production/collec\-tion of positive and
negative particles.  It was soon realised that the use of solenoid magnets
would permit a single channel to operate with both
signs~\cite{Palmer:1995jy}, and that the initial capture in a
high-field solenoid followed by a series of solenoids each of slightly
lower field than the last exchanges transverse for longitudinal
momentum~\cite{Green:1995vg}.  
Another advantage is that the solenoid-magnet coils would be farther
from the high radiation due to secondary particles from the
target than would toroidal coils \cite{Mokhov:1996tp}.

The design of the first magnet, with baseline field of 20~T is
challenging.  
The use of a 6~T water-cooled, hollow-core-copper
solenoid insert is required if the superconducting outsert is
made from Nb$_3$Sn.  This copper magnet receives a very high radiation
dose (while acting as a partial shield for the superconducting outsert)
and is anticipated to be a replaceable component with a lifetime of 4
years or less.  If the presence of this copper magnet leads to a
requirement for thicker shielding and consequently larger inner
diameter for the superconducting outsert, such that the latter is
untenable, we must consider the option of only a 14~T Nb$_3$Sn magnet,
or development of a large-bore high-T$_{\text{C}}$ magnet (or more simply, a
high-T$_{\text{C}}$-Nb$_3$Sn hybrid~\cite{Gupta:2010a}; tests of YBCO
indicate that it has good resistance to radiation
damage~\cite{Gupta:2010b}).

Another issue is the very large axial forces between the various
magnets of the target system.  A further complication is the
requirement that the axial field profile in the beam-jet interaction
region be smooth, such that the mercury jet is minimally perturbed as
it enters this field.  The baseline scenario calls for an iron plug at
the upstream end of the first magnet, through which the proton beam
and mercury jet enter.  The presence of this plug adds considerable
complexity to the mechanical design of the system and is an important
technical issue.

\subsubsection{Particle Production Simulations}

Many of the studies above were performed using the
MARS
simulation code.  It is essential to understand
the dependence of particle production
on target parameters (geometry, proton energy, material, etc.), and to have
the proper values for the production rates.  This is necessary both
for particles giving the desired muons and for particles that lead
to undesired energy deposition in the surrounding system.

Computations of particle production by both MARS and
FLUKA~\cite{Fluka1,Fluka2,Back2:2010}
have been performed.  Summaries of some simulations
comparing results from different codes and lattices
are shown in figure \ref{fig:acc:tgt:gersende}.  A study~\cite{Soler:2010} of the
dependence of muon yield on target material has been performed
using G4beamline~\cite{Roberts:2008zzc} for different hadronic models.
The results from this study give a flat distribution for high-\textit{Z}
materials for a beam energy between 5 and 8~GeV, whereas low-\textit{Z}
materials give a strong dependence of the muon yield on beam energy,
favouring low energy.
\begin{figure}
  \includegraphics[width=\linewidth]{02-AccWG/02-C-Target/muonyield_comp_ecalc9f.eps}
  \caption{The muon yield, normalised to the beam power.  An initial
    beam is generated by MARS as installed at BNL (red) and CERN
    (blue), and FLUKA 2008.3c (black), with an effective bunch length
    of 0~ns (red), 3~ns (blue and black).  Mesons are then tracked
    through the front end using ICOOL 3.10 (blue) and ICOOL 3.16
    (red).  For the black points, instead of simulating, an
    acceptance map approximating the effect of passing the particle
    through ICOOL~3.10 has been applied.  After this, an acceptance
    cut is performed for a longitudinal momentum range of
    100--400~MeV/$c$, normalised longitudinal acceptance of 150~mm,
    and normalised transverse acceptance of 30~mm using
    ECALC9F~\cite{Fernow:2003zz}.  ST2
    and ST2a denote different field tapering parameters, with the
    field going from 20~T to 1.25~T and 1.75~T respectively.}
  \label{fig:acc:tgt:gersende}
\end{figure}

A recent study~\cite{Strait:2010zzb} has been made, using HARP
data~\cite{Catanesi:2008uv,Bolshakova:2009if}
convolved with the acceptance of the front-end channel of the Neutrino
Factory and correcting for the phase space not covered as well as
for thick-target effects not accounted for in the cross-section data.  The
simulations were performed with a more recent version (1509) of the MARS code.
Results from this study show that the dependence
of the muon yield on proton beam energy is relatively flat, with the
yield being within 10\% of the maximum value (at 7~GeV) in an energy
range of 4--11~GeV.  These results are in basic agreement with those
from figure \ref{fig:acc:tgt:gersende}, but show a somewhat
flatter distribution than those of the pure simulation studies.
It will be important to cross-validate these simulations against newer
versions of the simulation codes as they become available.
