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\begin{document}
\title{PARTICLE PRODUCTION AND RADIATION ENVIRONMENT 
AT A NEUTRINO FACTORY TARGET STATION\thanks{Work supported 
by the Universities Research Association, 
Inc., under contract DE-AC02-76CH03000 with the U. S. Department of Energy. }}

\author{N.~V.~Mokhov\thanks{mokhov@fnal.gov}, FNAL, Batavia, IL 60510, USA}

\maketitle

\begin{abstract}

Efficient production and collection of a large number of muons is needed
to make a neutrino factory based on a muon storage ring viable. The results 
of extensive \textsc{mars} simulations are reported for Megawatt proton beams on 
a carbon rod and mercury jet in a 20-T hybrid solenoid, followed by 
a matching section and decay channel. Beam energy and power in a 2 to 30 GeV 
range, beam spot size, beam and target tilt angle, target material and dimensions, 
and capture system parameters are optimized to get maximum muon yields at the end 
of the decay channel. Other particles transported down the beam line are also 
studied for the purpose of beam instrumentation. Prompt and residual radiation 
distributions are calculated and analysis of target integrity, 
quench stability and dynamic heat load to the superconducting coils, radiation 
damage and activation of materials near the beam is performed. Absorption of 
showers in the direction of a primary beam is considered.

\end{abstract}

\section{MARS MODELING}

To achieve adequate parameters of a neutrino factory based on a muon storage
ring~\cite{bib:50-GeV,bib:20-GeV} it is necessary to produce and collect large numbers of muons.
The system starts with a proton beam impinging on a thick target sitting
in a high-field solenoid (20~T, about 1-m long, aperture radius $R_a$=7.5~cm),
followed by a matching section and a solenoidal decay channel
(1.25~T, 50-100~m in length, $R_a$=30~cm)
which collects muons resulting from pion decay.
Optimization of beam, target and solenoid parameters was done over the years
with the \textsc{mars} code~\cite{bib:mars} for a \mumu collider 
and a neutrino factory (see bibliography in Ref.~\cite{bib:nutar1,bib:nutar2}).

List of targetry issues includes $\pi/\mu$ production, other particles transported down 
the beamline, superconducting (SC) coil quench stability, heat loads,
radiation damage and activation of materials near the beam, spent proton beam, 
and numerous shielding issues from prompt radiation to ground-water activation.
All these issues were addressed in detailed \textsc{mars} simulations.
Realistic 3-D geometry together with material and magnetic field distributions
based on the solenoid magnet design optimization have been implemented into
\textsc{mars}. Graphite (C) and mercury (Hg) tilted targets were studied. 
A two interaction length target (80~cm for C of radius $R_T$=7.5~mm
and 30~cm for Hg of $R_T$=5~mm) is found to be optimal in most cases,
keeping $R_T \geq$2.5~$\sigma_{x,y}$, where $\sigma_{x,y}$ are the beam RMS
spot sizes.

\begin{figure}[htb]
\centering
\includegraphics*[width=100mm]{FOAC010-f1.eps}
\caption{A fragment of the \textsc{mars} model of target/capture system with
tilted proton beam and mercury jet.}
\label{f1}
\end{figure}

The optimized configuration for the Study-2~\cite{bib:20-GeV},
designed for a 1~MW proton beam of 24~GeV energy (upgradable to 4~MW),
is shown in Fig.~\ref{f1}. 
The beam intensity is 1.7$\times$10$^{13}$~ppb $\times$6 $\times$2.5~Hz
 = 2.55$\times$10$^{14}$~p/s, resulting in 5.1$\times$10$^{21}$~p/yr at 
2$\times$10$^{7}$~s/yr.
The model was optimized for
-2$<$z$<$36~m, r$<$1.8~m. It includes sophisticated coil 
shielding: water-cooled tungsten-carbide balls at z$<$6~m and water-cooled copper
at z$>$6~m.
A proton beam ($\sigma_x$=$\sigma_y$=1.5~mm, 
$\sigma_z$=3~ns, 67~mrad) interacts with a 5~mm radius mercury 
jet tilted by 100~mrad, which is ejected from the nozzle at z=-60~cm,
crosses the z-axis at z=0~cm, and hits a mercury pool at z=220~cm, 
x=-25~cm. With such a beam-jet crossing, about 97\% of protons
have a probability to interact with target material, generating pions
and resulting in significant energy deposition in material (Fig.~\ref{f2})
that can at some conditions destroy solid or liquid target.
A 8-cm wide mercury pool (210$<$z$<$550~cm) is a core of a sophisticated
spent beam absorber. A 2-mm beryllium window at z=610~cm withstands
beam-induced heating (with appropriate cooling), but its lifetime is
an issue because the absorbed dose in its center reaches tens of GGy/yr.

\begin{figure}[htb]
\centering
\includegraphics*[width=100mm]{FOAC010-f2.eps}
\caption{Longitudinal profiles of the energy density deposited in the mercury jet
target in three radial regions.}
\label{f2}
\end{figure}


\section{PARTICLE PRODUCTION}

Detailed optimizations were performed for the particle yield $Y$, defined as
a sum of the numbers of $\pi$, $K$ and $\mu$ of a given sign and energy
interval at the downstream end of the considered system.
It turns out that for proton energies $E_p$ from a few GeV to about 30~GeV,
the shape of the low energy spectrum of such a sum is energy-independent
and peaks around E=130~MeV, where E is $\pi /\mu$ kinetic energy.
For the given parameters, the interval of 30~MeV$<$E$<$230~MeV around
the spectrum maximum is considered as the one to be captured 
by a phase rotation system. 
The yield $Y$ grows with $E_p$, is almost material-independent
at low energies and grows with target $A$ at high energies, being almost a factor
of two higher for Hg than for C at $E_p$=16-30~GeV (Fig.~\ref{f3}).
It is interesting that the yield per beam power, i.e., $Y/E_p$ has a broad
maximum around 6~GeV.
For a 1 to 2~GeV proton beam (CERN, SNS), the optimal target material, from
the pion production point of view, is carbon with significantly lower $\pi^-$
production compared to $\pi^+$.
To avoid absorption of spiraling pions by target material, the target and beam are tilted
by an angle $\alpha$ with respect to the solenoid axis. The yield is higher by up to 30\% 
for the tilted target with a broad maximum around $\alpha$=100~mrad.
Maximum yield occurs at target radius $R_{T}$=7.5~mm for C and $R_{T}$=5~mm for 
Hg targets with $R_{T}=3.5\sigma_{x,y}$ and $R_{T}=4\sigma_{x,y}$ 
conditions for the beam spot size, respectively. The baseline criterion $R_{T}=2.5\sigma_{x,y}$ 
reduces the yield by about 10\% for the graphite target, but is more optimal
from the energy deposition point of view.
The use of a realistic 3-D magnetic field map in simulations
results in the reduction of the $\pi$+$\mu$-yield in the decay
channel by about 7\% for C and by 10-14\% for Hg targets, compared with a
simple-minded $B_z(r,z)$ model.

\begin{figure}[htb]
\centering
\includegraphics*[width=100mm]{FOAC010-f3.eps}
\caption{$\pi$+$\mu$ yield from Hg and C targets {\em vs} proton energy.}
\label{f3}
\end{figure}

The optimized results for the yield per a proton on target,
for Study-1 (16~GeV on C) are 
$Y_{\pi^+ + \mu^+}$ = 0.18 and $Y_{\pi^- + \mu^-}$ = 0.15 at z=9~m,
and for Study-2 (24~GeV on Hg, more realistic geometry and field) are
$Y_{\pi^+ + \mu^+}$ = 0.40 and $Y_{\pi^- + \mu^-}$ = 0.39 at z=36~m.
There are substantial fluxes of accompanying particles in the system,
which should be taken into account in designing beam instrumentation.
In the aperture of the Study-2 channel, at the end of the matching region 
(z=18.6~m), the numbers of particles per proton are 1.03 ($\mu$), 1.15 ($p+\pi^{\pm}$),
0.07 ($e^{\pm}$), 0.02 ($n$) and 0.46 ($\gamma$).

\section{RADIATION FIELDS}

Hadronic and electromagnetic showers are induced in the target and 
capturing system, resulting in particle fluxes and accumulated dose
in system components which can deteriorate their performance rapidly. The SC
coils are to be adequately protected to provide their short and long term
operation. 
A carefully designed coil shielding consists of two parts (Fig.~\ref{f1}): 
1) at z$<$6~m it is made of tungsten-carbide balls (80\% filling factor) cooled 
by circulating water (WCW), placed in front of the SC coils SC1-SC2 in the 20-T region
and SC3-SC6 in the matching section, and surrounds the resistive coils 
and the spent beam absorber; 2) at z$>$6~m it is made of copper (70\% filling factor) cooled 
by circulating water, and protects the potted SC7-SC12 coils in the matching
section and further in the straight 1.25-T decay channel (SC13). The calculations show 
that it does an excellent job in protecting the SC coils against radiation.

The hottest regions in the system are the one at the downstream end
of the target at the transition from the 20-T region to a matching section and
at a primary beam dump at z$\approx$4~m (Figs.~\ref{f1} and \ref{f4}). 
The shielding
reduces the peak power density to less than 0.3~mW/g (below the quench limit)
in these two regions as well as in the entire system.
The shielding provides also acceptable integrated
levels of the absorbed dose (Fig.~\ref{f4} and Table~1) and particle fluxes 
(Fig.~\ref{f5}) in the hottest spots, equalizing these to even lower levels
in the rest of the system. As Table~1 shows, estimated lifetimes of the
critical components are quite satisfactory. The component lifetimes are four times 
shorter for a 4~MW beam. In the Study-1 design~\cite{bib:50-GeV,bib:nutar2},
the annual hadron flux in a stationary graphite target
is $\sim$5$\times$10$^{21}$cm$^{-2}$ which corresponds to several month lifetime.
The annual hadron flux (E$>$0.1~MeV) and dose in the hottest spot of the inner resistive coil
are 1.2$\times$10$^{20}$cm$^{-2}$ and 3$\times$10$^{10}$~Gy, respectively.

\begin{figure}[htb]
\centering
\includegraphics*[width=103mm]{FOAC010-f4.eps}
\caption{Absorbed radiation dose (MGy/yr) in target/capture system components.}
\label{f4}
\end{figure}

\begin{figure}[htb]
\centering
\includegraphics*[width=115mm]{FOAC010-f5.eps}
\caption{Radial distribution of neutral (top) and charged (bottom)
particle fluxes (cm$^{-2}$yr$^{-1}$) in 20-T solenoid components
 at the downstream end of the target.}
\label{f5}
\end{figure}

Heat loads to the main components of the Study-2 design, calculated for a 1~MW beam
(0.979~MW to be exact), are shown in Table~2. About 12\% of the beam
power are deposited in mercury (jet plus pool), 50\% in the coil shielding,
1\% in resistive hollow conductor, and only about 0.1\% in the high-field and
potted SC coils. About 20\% dissipate in other components and
leak from the system. As Fig.~\ref{f6} shows, the inner shielding becomes
extremely radioactive, with residual dose rate up to 1~kSv/hr. 
This will require remote control and robotics for the inner parts of the system. 
It drops by two orders of magnitude after several weeks. The residual dose outside
the cryostat is significantly lower, of the order of 100~mSv/hr.
Radiation shielding needed is about 2~m of steel followed by concrete blocks
to protect ground water followed by several meters of concrete and dirt to provide 
personnel protection.


\begin{figure}[htb]
\centering
\includegraphics*[width=115mm]{FOAC010-f6.eps}
\caption{Residual dose rate (mSv/hr) in the innermost tungsten-carbide
shielding around the target {\em vs} cooling time for several
irradiation times.}
\label{f6}
\end{figure}


\begin{thebibliography}{9}

\bibitem{bib:50-GeV} N.~Holtkamp and D.~Finley, eds.,
    \emph{A Feasibility Study of a Neutrino Source Based on
    a Muon Storage Ring}, Fermilab-Pub-00/108-E, 2000.

\bibitem{bib:20-GeV} \underline{http://www.cap.bnl.gov/mumu/studyii/FS2-report.html}.

\bibitem{bib:mars} N.~V.~Mokhov, ``The MARS Code System User's Guide'', Fermilab-FN-628, 1995;
   N.~V.~Mokhov and O.~E.~Krivosheev, ``MARS Code Status'', Fermilab-Conf-00/181, 2000.
   \underline{http://www-ap.fnal.gov/MARS/}.

\bibitem{bib:nutar1} N.V.~Mokhov, ``Particle Production for a Muon Storage Ring:
   I. Targetry and $\pi/\mu$ Yield'', Neutrino Factory-2000, Monterey, CA, May 2000;
   Fermilab-Conf-00/208, 2000.

\bibitem{bib:nutar2} N.V.~Mokhov, ``Particle Production for a Muon Storage Ring:
   II. Radiation Loads'', {\em ibid}, Fermilab-Conf-00/209, 2000.

\end{thebibliography}

\begin{table}[htb]
\begin{center}
\caption{Maximum radiation doses per 2$\times$10$^7$~s/yr and 1~MW lifetimes 
of some components of the target system.}
\begin{tabular}{|l|c|c|c|}
\hline
Component            & Dose/yr         & Limit  & Life  \\
                     & (MGy)           & (MGy)  & (yr)  \\
\hline
Inner shielding      & 5$\times$10$^4$ & 10$^6$ &  20   \\
Hg containment       & 2$\times$10$^3$ & 10$^5$ &  50   \\
Hollow conductor     & 1$\times$10$^3$ & 10$^5$ & 100   \\
Superconducting coil & 6               & 10$^2$ &  16   \\
\hline
\end{tabular}
\end{center}
\end{table}

\begin{table}[htb]
\begin{center}
\caption{Power dissipation in the main target/capture system components.}
\begin{tabular}{|l|c|}
\hline
Component            & Total heat load (kW) \\
\hline
Mercury           & 119.181 \\
1-cm inner vessel & 113.873 \\
WCW shielding     & 489.118 \\
Cu-water shielding& 12.939 \\
Hollow conductor  & 9.910 \\
SC1-SC2           & 1.256 \\
SC3-SC13          & 1.385 \\
\hline
\end{tabular}
\end{center}
\end{table}


\end{document}
