%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Introduction}

\subsection{Overview}
The role of the target system at a Neutrino Factory is to generate a maximal
number of pions with an intense proton beam and then capture and guide them into a channel where the decay
muons can be bunched, cooled, accelerated and stored in a ring from which
the neutrinos emanate upon decay of the muons.

In this Study, the proton beam energy is 24~GeV, and the baseline beam power
is 1~MW, upgradable to 4~MW.

The spectrum of pions from GeV protons interacting with a target peaks at a 
total momentum near 250~MeV/$c$, as shown in Fig.~\ref{Tgt:e910data}
\cite{e910report}, and has an average transverse momentum $\langle {p_\perp}\rangle = 150$ 
MeV/$c$.
Thus, the majority of pions are produced at relatively large angles to the
proton beam, and are not efficiently captured by devices placed downstream
of the target.  For maximal efficiency, the pion capture system must surround the target.
\begin{figure}[!bht] %nm12
\begin{center}
\includegraphics*[width=2in]{../template/report/ps-and-eps/e910_au_18.eps}
\caption[Pion production data from BNL E910 and from MARS]
{Momentum spectra for pion production by 12.3 and 17.5~GeV protons on a gold target, from BNL E910 and from MARS calculations.} 
\label{Tgt:e910data}
\end{center}
\end{figure}

The capture mechanism considered here is a solenoidal magnetic field channel starting at 20~T near the target, then falling adiabatically to 1.25~T downstream ($\approx 18$~m) from the target.
This configuration creates a kind of magnetic bottle whose mouth is the
muon phase rotation system considered in Chapter~\ref{CHAP:DandPR}.  In a solenoidal field the
pion (and muon) trajectories are helices, with adiabatic invariants
$BR^2$ and $p_\perp^2 / B$.  We propose to capture pions with $p_\perp \leq
225$ MeV/$c$, for which an aperture of 7.5~cm is required at 20 T.  After
the adiabatic reduction of the solenoid field by a factor of 16, to 1.25~T, 
the captured pions are contained within an aperture of 30~cm and have a  
maximum $p_\perp$ of 67.5~MeV/$c$.

For proton beam energies above about 8~GeV, the pion yield per proton increases with
the atomic number of the target, as shown in Fig.~\ref{fg:mok4b} from a
MARS calculation~\cite{status-report}.  For 24~GeV protons, a high-$Z$ target is
distinctly superior in yield~\cite{muc0169}.  
\begin{figure}[hbt!]
\begin{center}
\includegraphics*[width=4in]{../template/report/ps-and-eps/mok4b.eps}
\caption[Pion yield \textit{vs.} atomic number ]
{Pion yield \emph{vs}. atomic mass number of the target at three proton beam
energies.}
\label{fg:mok4b}
\end{center}
\end{figure}

As the pions to be captured emerge from the target at large angles to the beam,
and follow helical paths that may intersect the target at more than one 
point, it is advantageous for the target to be in the form of a narrow
rod, tilted at a small angle to the magnetic axis.  As shown in 
Fig.~\ref{fg:tilt_r}, suitable parameters for a mercury target in a 20~T
solenoid are a tilt angle of 100~mrad and a target radius of 5~mm.

\begin{figure}[hbt!]
\includegraphics*[width=3in]{../template/report/ps-and-eps/mok-targ1-fg3b.eps}
\includegraphics*[width=3in]{../template/report/ps-and-eps/mok-targ1-fg4a.eps}
\begin{center}
\caption[Pion yield in Hg \textit{vs.}\ $\theta_p$ and $R_{\rm Hg}$ ]
{Pion yield from Hg  targets \emph{vs}.\ tilt angle angle between the
target/beam axis and the solenoid axis (left) and
\emph{vs}.\ the radius of the target (right).}
\label{fg:tilt_r}
\end{center}
\end{figure}

In a 1~MW beam with 15 pulses per second, each pulse contains 60~kJ energy, of
which about 10\% is deposited in a two-interaction-length high-$Z$ target.
The energy deposited in the target will heat the target to a temperature of several hundred ${}^{\circ}$C and generate substantial shock pressures.
A low-$Z$ target, as proposed in Study-I~\cite{feas00}, is expected to survive 
these shocks for a significant time with a 1.5~MW beam, but is predicted to 
have a pion production yield only half that of high-$Z$ targets, 
such as Inconel, or mercury. 
It would also be expected to get too hot with a 4~MW beam, which we 
consider to be a likely upgrade. 
A liquid-mercury-jet target, too, 
will be disrupted by the heating from the beam, but such disruption 
is not expected to have significant adverse consequences, even at 4~MW.
For this reason, a mercury-jet target
has been selected as the baseline for this study. 
If there were advantages to doing so,
liquids such as a molten lead/tin eutectic, or 
other alloys, could be used. 
%A moving band of inconel, as discussed in 
%appendix *** would also be an alternative.  
A graphite target (as considered in Study-I) 
would be available as a backup, though it would reduce the neutrino 
intensity by a factor of 1.9 (see~\cite{feas00}, Section~{3.5}).
\begin{table}[htb]
\begin{center}
\caption[Proton beam and mercury jet geometric parameters ]
{Proton beam and mercury jet geometric parameters.}
\label{targettb}
\vspace{2.5mm}
\begin{tabular}{|lc|}
\hline
Beam $\sigma_r$ (mm) & 1.5 \\
Beam angle to magnet axis $\theta_{p}$ (mrad) & $-67$ \\
Jet material & mercury \\
Velocity $v_o$ (m/s) & 30 \\
Jet radius $r_o$ (mm) & 5 \\
Jet angle to magnet axis $\theta_{\rm Hg}$ (mrad) & $-100$ \\
Crossing angle $\theta_{\rm crossing}$ (mrad) & 33 \\
$t$ between bunches (ms) & 20 \\
$z_{\rm nozzle}$ (cm) & $-60$ \\
\hline
\end{tabular}
\end{center}
\end{table}

In this Study, the beam with rms radius $\sigma_r$, 
at a vertical angle $\theta_{p}$, 
intersects the mercury jet of radius $r_o$ and 
vertical angle $\theta_{\rm Hg}$ at an angle $\theta_{\rm crossing}$. 
The forward velocity of the jet is $v_o$.The nozzle is at 
$z_{\rm nozzle}$ with respect to the intersection of the beam and jet center 
lines.
The interval between pulses is $t$. 
The Study-II baseline values of these parameters are given in 
Table~\ref{targettb}.

An alternative target concept based on a rotating Inconel band is discussed in
\cite{muc0199}.

\subsection{Target System Layout}
The  target system consists of the following components:
\begin{itemize} 
\item Target enclosure vessel 
\item Proton beam window
\item Mercury jet, including its supply line within the enclosure
vessel and the jet nozzle 
\item Magnet coils 
\item Internal shielding
\item Mercury collection pool/dump and entrance baffle
\item Downstream window 
\end{itemize} 
The overall layout of the target area is sketched in Fig.~\ref{tgtc}, with a
detail of the target region shown at the bottom of
Fig.~\ref{tgt2}. The intersection of the beam and jet 
is set at 45~cm from the nozzle.
The distribution of the resulting interactions as a function of $z$, shown at
 the top of Fig.~\ref{tgt2},
starts about 15 cm from the nozzle.


\begin{figure}[htb]
\begin{center}
%\input{tgtc.fig}
\includegraphics*[width=4in]{../template/report/ps-and-eps/tgtc.eps}
\caption[Target, capture solenoids and mercury containment ]
{Target, capture solenoids and mercury containment.}
\label{tgtc}
\end{center}
\end{figure}


\begin{figure}[htb]
\begin{center}
%\hskip1in\input{tgta.fig}
\includegraphics*[width=3.5in]{../template/report/ps-and-eps/tgta.eps}
\caption[Layout of the target area ]
{Top: Distribution of beam-target interactions as a function of $z$. 
Bottom: Layout of the target area.}
\label{tgt2}
\end{center}
\end{figure}

It will be assumed here that, after a 
pulse, all the mercury outside of the nozzle is dispersed. 
This is predicted using the finite element analysis code
FronTier~\cite{Samulyak}, as illustrated in Fig.~\ref{breakup}.
At the arrival time of a subsequent bunch, the newly established jet will extend a 
distance $\Delta z = v_o~t = 0.6$~m from the nozzle.
Only 2.5\% of the interactions occur beyond this 
location, so the disposition of the disturbed jet beyond this point has 
little effect on production.

\begin{figure}[htb]
\begin{center}
\includegraphics*[width=3.in]{../template/report/ps-and-eps/pulse0-10.eps}
\includegraphics*[width=3.in]{../template/report/ps-and-eps/pulse20-35.eps}
\caption[Beam-induced breakup of a mercury jet, calculated ]
{Beam-induced breakup of a mercury jet, as simulated by the FronTier code.
The images are for $10\ \mu$s time steps.}
\label{breakup}
\end{center}
\end{figure}



\begin{figure}[htb]
\begin{center}
\includegraphics*[ width=3in]{../template/report/ps-and-eps/event5_0.eps}
\includegraphics*[ width=3in]{../template/report/ps-and-eps/event5_18.eps}
\caption[Beam-induced breakup of a mercury jet, experiment ]
{Breakup of a 1-cm-diameter mercury jet in a 24-GeV proton beam (BNL E951).}
\label{e951jet}
\end{center}
\end{figure}

The distance over which the jet must propagate without serious magnetic 
disruption is from the nozzle to a point 0.6 m downstream, defined as $z=0$ 
in the coordinate system used here. In order to minimize the field nonuniformity
over this length, the magnetic center (approximately the
point of maximum $B_z$) is 
placed at the center of this length. {\it i.e.}, the magnetic center is at 
$z_o = -30$~cm. The intersection of the 
jet and beam is then at $z_{\rm intersection} =-15$~cm, 
and the nozzle is at $z_{\rm nozzle} = -60$ cm.

\subsection{Capture and Matching Solenoids}
The target is located in a 20~T solenoid to contain transverse momenta of 
outcoming pions up to 225~MeV/$c$, a large fraction of all pions produced. 
The central region of high field is designed to be uniform, drooping only 
5\% at its end, to limit the magnetic field gradients that might disrupt 
the mercury jet.
The solenoid is a hybrid, with copper inner coils and superconducting 
outer coils. 
It is similar to that discussed in Feasibility Study-I~\cite{feas00}. 
However, here we use hollow copper conductor for the inner
coils, 
rather than a Bitter-style magnet.  This choice is aimed at achieving 
a magnet life over 40 years (compared with 6 months in Study-I), and 
avoiding possible corrosion problems with the highly irradiated wet insulation 
in a Bitter magnet.   The main disadvantage of this choice is that it consumes more power and requires a greater field contribution from the SC coils..

Downstream of the 20~T magnet, additional superconducting coils  taper the 
axial field down smoothly 
to 1.25~T over a distance of approximately 18~m, according to the form,
\begin{equation}
B(z)~\approx~ \frac{B(0)\ \mbox{T}}{1 + k~z}\, .
\label{TgtP.1}
\end{equation}

Dimensions of the coils and the upstream iron pole are given in 
Table~\ref{capturecoils}.
The coils are shown in Fig.~\ref{tgtc}, and axial field profiles, over two 
scales of $z$, are shown in Fig.~\ref{captureB}.
%The dotted line in Fig.~\ref{captureB} is for a Gaussian with $\sigma_z=0.8$ m.
\begin{table}[htb]
\begin{center}
\caption[Solenoid coil geometric parameters ]
{Solenoid coil geometric parameters.}
\label{capturecoils}
\vspace{2.5mm}
\begin{tabular}{|ccccccccc|}
\hline
  & $z$ & Gap & $\Delta z$ & $R_i$ & $\Delta R$ & $I$/A & $n I$ & $n I l$\\ 
& (m) & (m) & (m) & (m) & (m) &  (A/mm$^2$) & (A) & (A-m) \\ 
\hline
Fe
& 0.980 & 0.980 &  0.108 &  0.000 &  0.313 &   0.00 &  0.00 &  0.00  \\
& 1.088 & 0.000 &  0.312 &  0.000 &  0.168 &   0.00 &  0.00 &  0.00  \\
\hline
Cu coils 
& 1.288 & $-0.112$ &  0.749 &  0.178 &  0.054 & 24.37 &  0.98 &  1.26  \\
& 1.288 & $-0.749$ &  0.877 &  0.231 &  0.122 & 19.07 &  2.04 &  3.74  \\
& 1.288 & $-0.877$ &  1.073 &  0.353 &  0.137 & 14.87 &  2.18 &  5.78  \\
\hline
SC coils
& 0.747 & $-1.614$ &  1.781 &  0.636 &  0.642 & 23.39 & 26.77 & 160.95  \\
& 2.628 &   0.100  &  0.729 &  0.686 &  0.325 & 25.48 &  6.04 & 32.23  \\
& 3.457 &   0.100  &  0.999 &  0.776 &  0.212 & 29.73 &  6.29 & 34.86  \\
& 4.556 &   0.100  &  1.550 &  0.776 &  0.107 & 38.26 &  6.36 & 33.15  \\
& 6.206 &   0.100  &  1.859 &  0.776 &  0.066 & 49.39 &  6.02 & 30.59  \\
& 8.000 & $-0.065$ &  0.103 &  0.416 &  0.051 & 68.32 &  0.36 &  1.00  \\
& 8.275 &   0.172  &  2.728 &  0.422 &  0.029 & 69.27 &  5.42 & 14.88  \\
&11.053 &   0.050  &  1.749 &  0.422 &  0.023 & 75.62 &  3.00 &  8.18  \\
&12.852 &   0.050  &  1.750 &  0.422 &  0.019 & 77.37 &  2.61 &  7.09  \\
&14.652 &   0.050  &  1.749 &  0.422 &  0.017 & 78.78 &  2.30 &  6.22  \\
&16.451 &   0.050  &  1.750 &  0.422 &  0.015 & 79.90 &  2.07 &  5.59  \\
&18.251 &   0.050  &  2.366 &  0.422 &  0.013 & -0.85 &  2.53 &  6.80  \\
\hline
\end{tabular}
\end{center}
\end{table}

\begin{figure}[htb]
%\hskip1in\input{captureB.fig}
\begin{center}
\includegraphics*[width=5in]{../template/report/ps-and-eps/captureB.eps}
\caption[Axial magnetic field profile ]
{The axial magnetic field (solid lines) \textit{vs.}\ length along the axis, 
on two scales.  The dotted line is
a Gaussian fit, with $\sigma_z= 0.8$~m, to the field in the jet region.}
\label{captureB}
\end{center}
\end{figure}

\subsection{Magnetic Disruption of the Mercury Jet}
As the jet moves through the magnet, eddy
currents are induced in the mercury, and the resulting ${\bf J} \times
{\bf B}$ force distorts the jet in various ways~\cite{jet_perturb,muc0182}.
Assuming a Gaussian distribution of $B_z'$ {\it vs.} $z'$ with a maximum value of 
$B_o$, where the $z'$ axis is along the jet,
jet conductivity $\kappa$, density $\rho$, and surface tension 
$T_{\rm surface}$ as given in Table~\ref{tb6},
perturbation calculations~\cite{jet_perturb} 
show that, over the extent of the jet from $- 0.6$ to 0.0 m,

\bi
\item 
The maximum axial field deviations are $\pm 1.1$ T, {\it i.e.}, $\pm 5\%$.

\item 
The axial pressure difference has a minimum of $- 0.25$ atm. 
Thus, if the jet is operating in a gas (He or Ar) at a pressure greater 
than or equal to 0.25 atm, negative  pressures will be avoided, 
and there will be no tendency to cavitate prior to the arrival of the beam.

\item 
The maximum axial velocity change of the jet, 0.06 m/s, 
is very small compared with the average jet velocity, 30 m/s.

\item 
The maximum transverse velocity, 0.4 m/s, induced by  shear forces is also small
 compared with the average jet velocity: $0.4/30 \approx 1.3\%$.

\item 
The deflection of the jet, 5 $\mu$m, is very small.

\item 
The transverse distortion of the jet (change in width relative to average
width) is approximately 0.4\% ignoring surface tension, and less than 0.2\% 
when surface tension is included.
\ei

\begin{table}[htb]
\begin{center}
\caption[Relevant properties of the mercury jet ]
{Relevant properties of the mercury jet.}
\label{tb6}
\vspace{2.5mm}
\begin{tabular}{|lc|}
\hline
$B_o$ (T)& 20 \\
$\sigma_z'$ (m) & 0.8 \\
$\kappa$ ($\Omega$-m) & $10^6$ \\
$\rho$ (kg/m$^3$) & $1.35 \times 10^5$ \\
$T_{\rm surface}$ (N/m) & 0.456 \\
\hline
\end{tabular}
\end{center}
\end{table}


These disruptions are all relatively small, and should cause no problems for
the beam-jet interaction.

Beyond the target region ($z > 0$), the magnetic effects are larger, 
but still not sufficient to break up the jet. Here, the maximum shear is about 
5~m/s, and the transverse distortion 20\%.  However, since the beam-jet
interaction will disperse the jet, a more significant effect
thereafter is magnetic damping of the dispersal.

More detailed magnetohydrodynamic calculations are under way 
\cite{Samulyak} using the
FronTier 3-D finite element analysis code that includes liquid-gas boundaries
and phase transitions.  Preliminary results are shown in 
Fig.~\ref{jetinmagnet}.


\begin{figure}[htb]
\begin{center}
\includegraphics*[width=3.in]{../template/report/ps-and-eps/jet_into_magnet.eps}
\includegraphics*[width=3.in]{../template/report/ps-and-eps/jet_out_of_magnet.eps}
\caption[Disruption of a mercury jet by a magnetic field ]
{Disruption of a mercury jet on entering and exiting a solenoid magnet, 
as simulated by the FronTier code.}
\label{jetinmagnet}
\end{center}
\end{figure}

A magnetic field also provides a desirable damping of oscillations of a
mercury jet, with a time constant of roughly 100 $\mu$s.  Figure~\ref{damping}
shows this effect in a recent study by a CERN/Grenoble collaboration as
part of their Neutrino Factory R\&D program.


\begin{figure}[htb]
\begin{center}
\includegraphics*[ width=3in]{../template/report/ps-and-eps/vel46b00t109.eps}
\includegraphics*[ width=3in]{../template/report/ps-and-eps/vel40b13t132.eps}
\caption[Damping of a mercury jet by a magnetic field ]
{Magnetic damping of oscillations of a 1-cm-diameter, 4-m/s mercury jet
in a 13-T solenoid magnet.  Left: field off; right: field on. }
\label{damping}
\end{center}
\end{figure}
\subsection{Mercury Containment}
Figure \ref{tgtc} also shows the concepts for the mercury containment vessel 
and the mercury pool beam dump, and
Fig.~\ref{tgtb} shows more detail.  The containment vessel and dump are to be
replacable, for which the hollow conductor coils must also be removed.

The mercury jet, or what remains of it, falls under gravity, and 
thus further separates from the beam axis. A system of grids or baffles slows the mercury spray before it joins the beam dump mercury 
pool. The outflow pipe is 10~cm in 
diameter to accommodate the considerable rate of filling from the jet. 
The drain would be opened only when emptying the contaiment vessel for its 
removal.

\begin{figure}[htb]
\begin{center}
%\input{tgtb.fig}
\includegraphics*[width=4in]{../template/report/ps-and-eps/tgtb.eps}
\caption[Beam dump, shielding and mercury containment detail ]
{Beam dump, shielding and mercury containment detail.}
\label{tgtb}
\end{center}
\end{figure}



\subsection{Target System Support Facility}

The Target Support Facility consists of the target region and decay
channel, a crane hall over the length of the facility, a maintenance
cell at the ground floor elevation for handling magnet components, a
hot cell at the tunnel level for mercury target system components, and
various remote-handling equipment used for maintenance tasks. The
facility is bounded by the proton beam window at the upstream end and
the first induction linear accelerator at the downstream end. It
contains the equipment for the mercury-jet target, high-field
resistive and superconducting solenoids, low-field superconducting
solenoids, water-cooled shielding to limit radiation dose and neutron
heating to the coils, shielding to protect personnel and
the environment, and a 50-ton crane that is used for the initial
assembly and installation of major components and for subsequent
maintenance activities. The target support facility is 12~m wide, and
approximately 50~m long.  Figure~\ref{Tgt:fg1} is a view of the overall 
facility looking downstream.


\begin{figure}[!tbh]
\begin{center}
\includegraphics[width=4in]{../template/report/ps-and-eps/phil_fig1.eps}
\caption{The overall target support facility.}
\label{Tgt:fg1}
\end{center}
\end{figure}

The remainder of this section presents a conceptual design for the 
target caputure magnet,
the mercury-jet target
system, the proton-beam absorber, and the facility for the target/capture 
region. 
%The mercury system is a closed loop that includes a containment structure
%in the high magnetic field region, a mercury pool beam absorber,
%conventional equipment such as magnetic-coupled pumps, valves, heat
%exchanger, and a special nozzle insert. The superconducting solenoids
%in the target region are protected from nuclear heating and radiation
%damage with water-cooled tungsten carbide shielding; the decay channel
%solenoids are protected with water-cooled steel shielding. The target
%region and decay channel have high neutron fluxes resulting in
%components that are highly activated. Therefore, the facility
%configuration is based on remotely maintaining the target system and
%the magnets, as well as providing sufficient shielding for
%personnel. 
%Summaries of cost estimates for the target system, magnet
%shielding, maintenance equipment, and the facility are also presented.
