\section{Calculations of Energy Deposition and Activation Using MCNPX}
The energy deposition in, activation of, and radiation leakage
from the target module have been estimated using  the Monte Carlo
code MCNPX~\cite{Tgt:mcnpx}. This is a combination of the particle transport code
MCNP-4B~\cite{Tgt:mcnp} and the high-energy transport code LAHET-2.8~\cite{Tgt:lahet}. This code
employs a combinatorial surface/cell specification of the geometry,
which permits modeling of the problem configuration with minimal
approximations.

The MCNPX code has similar capabilities to those of the MARS code, although 
MARS describes in great details the effects of magnetic field, capability that MCNPX is lacking. In addition, there are 
subtle differences in the way the geometry is represented and
nuclear data models are linked together, and the manner in which the
activation and energy deposition analyses are carried out.  Thus, the use of
both codes provides important cross checks.

\begin{figure}[!htb]
\begin{center}
\includegraphics*[width=3.in,clip]{../template/report/ps-and-eps/simos_fig20.eps}
%\includegraphics*[width=1.3in,clip]{simos_fig22.eps}
\includegraphics*[width=1.in,clip]{../template/report/ps-and-eps/hans1.eps}   % APRIL 27
\caption[Longitudinal section through target module ]
{Longitudinal section through target module, with cell numbers shown on the
right. }
\label{TgtW:fg20}
\end{center}
\end{figure}
 An appropriate model of the
target module was created that includes the primary mercury jet, three
surrounding magnets, the downstream shield structure, and a mercury
beam stop. Two representative longitudinal and transverse
sections through this model are shown
in Figs.~\ref{TgtW:fg20} and \ref{TgtW:fg21}. 

\begin{figure}[htb!]
\begin{center}
\includegraphics*[width=3.in,clip]{../template/report/ps-and-eps/simos_fig21.eps}
\includegraphics*[width=2.in,clip]{../template/report/ps-and-eps/simos_fig23.eps}
\caption[Radial section through the target module]
{Radial section through the target module at $z = 4$ m, with cell numbers 
shown on the right. }
\label{TgtW:fg21}
\end{center}
\end{figure}
\subsection{Energy Deposition}
The energy deposition resulting from protons, neutrons, and photons
is summarized in Table~\ref{TgtW:tb2} in terms of MeV/gm-proton, 
as well as power density (W/cm$^3$) and total power per cell, 
assuming a 1-MW, 24-GeV proton beam.
\begin{table}[htb!]
\begin{center}
\caption[Energy deposition by cell ]
{Energy deposition by cell in the target system. (x) stands for $\times 10^x$.}
\label{TgtW:tb2}
\begin{tabular}{|clccc|}
\hline
Cell & Description & \multicolumn{3}{c|}{Energy Deposition} \\
Number &                        & (Mev/gm-$p$) & (W/cm$^3$) &   (kW) \\
\hline
8   & Surrounding shield            & 3.11(-4) & 0.16    & 589  \\
12  & Primary mercury target        & 2.62     & 1.48(3) & 53.1 \\
2   & Coaxial shield around target  & 1.55(-3) & 0.82    & 40.4 \\
3   & Iron plug behind target       & 1.21(-3) & 0.39    & 0.99 \\
81  & First coaxial magnet          & 2.61(-4) & 0.08    & 3.54 \\
82  & Second coaxial magnet         & 1.04(-4) & 0.03    & 4.43 \\
83  & Third coaxial magnet          & 2.38(-5) & 0.01    & 1.70 \\
91  & Mercury beam stop             & 6.04(-4) & 0.34    & 1.07 \\
92  & Mercury beam stop             & 8.64(-4) & 0.49    & 2.55 \\
93  & Mercury beam stop             & 1.13(-3) & 0.64    & 4.01 \\
94  & Mercury beam stop             & 4.80(-4) & 0.27    & 1.20 \\
95  & Mercury beam stop             & 4.42(-4) & 0.25    & 1.57 \\
96  & Mercury beam stop             & 4.89(-4) & 0.28    & 1.74 \\
97  & Mercury beam stop             & 5.34(-4) & 0.30    & 1.89 \\
98  & Mercury beam stop             & 6.87(-4) & 0.39    & 2.44 \\
99  & Mercury beam stop             & 6.61(-4) & 0.37    & 2.35 \\
100 & Mercury beam stop             & 4.86(-4) & 0.27    & 1.73 \\
101 & Mercury beam stop             & 3.65(-4) & 0.21    & 0.93 \\
\hline
\end{tabular}
\end{center}
\end{table}

The bulk of the beam power is
deposited in the surrounding coaxial shield, the mercury jet
target, and the coaxial shield surrounding the primary target
(683~kW out of 1 MW). 
The total power deposited in the target module cells is 715~kW.  
The remaining 285 kW largely appears as radiation
leakage out of the target system.

The two shield volumes are actively cooled by flowing
water, and the above heat input sets the flow rate and
the size of the heat exchanger. The iron plug immediately upstream of the
primary target also requires active cooling, since it has a
relatively high heat input. The magnets, of course, will be
cooled actively. Finally, the mercury will be a flowing system, and
the heat input determines the required capacity of the heat exchanger.
\subsection{Activation Analysis} 
The activation analysis is based on the MCNPX estimates of
neutron fluxes and spallation product masses.
The neutron fluxes are used to
determine cell-dependent activation cross sections, and the spallation
mass distributions are used to determine the distribution of possible
isotopes produced during the spallation reactions. The mass
distributions are a function of cell type and position within
the target module, since cells with the same composition in different
positions are subject to different particle fluxes. 

The time-dependent buildup of activation is based on the assumption of
100~days of operation at 1~MW with 24~GeV protons. 
%This implies a proton current of 2.589583(14) p/s. 
To estimate the activation under different conditions,
the results can be scaled by the number of MW-days. 

Following operation of the machine for 100~days, the activity after 
4~hrs, 1~day, 7~days, and 30~days of cooling has also been estimated.
In addition, the total gamma-ray activity in each cell has been calculated, 
and used as input to a secondary calculation
that determined the leakage of photons, and thus dose outside of the
target module.  

Tables~\ref{TgtW:tb3}-\ref{TgtW:tb9} list
the total neutron flux, activation, and gamma-ray
intensity in various cells.
\begin{table}[htb!]
\begin{center}
\caption[Neutron flux in various cells ]
{Neutron flux in various target system cells for 1 MW of 24-GeV protons.}
\label{TgtW:tb3}
\begin{tabular}{|cc|}
\hline
Cell&  Total neutron flux \\
Number & (cm$^{-2}$s$^{-1} \times 10^{12}$) \\
\hline
8&1.27\\
12&8.64\\
2&8.02\\
3&9.32\\
81&3.27\\
82&1.29\\
83&0.26\\
91&4.07\\
92&3.51\\
93&3.12\\
94&2.88\\
95&3.28\\
96&4.63\\
97&6.43\\
98&8.98\\
99&10.06\\
100&7.56\\
101&6.49\\
\hline
\end{tabular}
\end{center}
\end{table}

The values in Table~\ref{TgtW:tb3} are the volume-averaged total neutron fluxes.
The actual energy spectrum for each volume was used to determine the
activation cross sections.
% and the above values only give an
%indication of the variation of the neutron flux in the various cells. 
%Using the above fluxes and the spallation mass distributions
%the activation for each volume can be determined. 
Table~\ref{TgtW:tb4} shows the
resulting activation following 100~days of operation, and for selected time
frames following machine shutdown.
\begin{table}[htb!]
\begin{center}
\caption[Activation in Curies for selected cells ]
{Activation in Curies for selected cells. (x) stands for $\times 10^x$.}
\label{TgtW:tb4}
\begin{tabular}{|cccccc|}
\hline
Cell  &   \multicolumn{5}{c|}{Time after shutdown} \\
Number &  0& 4 hrs &   1 day &  7 days &  30 days \\
\hline
8 &1.59(6) &2.63(5) &2.01(5) &1.37(5) &8.92(4)\\
12  & 7.67(3)  & 4.12(3)  & 2.58(3)   &      1.16(3)   &      5.45(2)\\
2    &    1.34(5)   &      2.11(4)   &      1.62(4)    &     1.11(4)& 7.35(3)\\
3    &    6.26(2)   &      4.09(2)  &       2.95(2) & 2.51(2)& 1.87(2)\\
81   &     5.08(4)  &        3.32(4)  &        1.12(4)   &       2.12(2)  &        1.67(2)\\
82    &    7.85(4)   &       5.15(4)  &        1.74(4)  &        2.06(2) &         1.59(2)\\
83   &     2.83(4)    &      1.85(4)   &       6.25(3)   &       8.53(1) &         6.86(1)\\
91   &     1.24(3)   &       7.77(2)  &       5.08(2)  &       2.03(2) &        8.93(1)\\
92 &      2.36(3)    &     1.46(3)   &      9.57(2) &        3.87(2)   &      1.61(2)\\
93 &      2.44(3)  &       1.52(3)   &      9.99(2)   &      3.99(2)&         1.62(2)\\
94   &    1.78(3) &        1.15(3)&         7.49(2)  &       2.99(2)  &       1.26(2)\\
95&       1.75(3) &        1.12(3)   &      7.41(2)  &        2.99(2)  &       1.25(2)\\
96 &      2.39(3)  &       1.52(3) &        1.03(3)  &       4.05(2) &        1.66(2)\\
97   &    2.78(3) &        1.83(3) &        1.24(3)  &       4.88(2)  &       1.99(2)\\
98  &     3.25(3)  &       2.15(3) &        1.44(3) &        5.40(2)   &        2.23(2)\\
99   &     2.98(3)   &       1.99(3)  &        1.35(3)  &        4.94(2) &         1.96(2)\\
100   &    1.82(3)   &       1.25(3)  &        8.55(2) &         3.00(2)  &        1.17(2)\\
101 &      9.93(2)  &        7.18(2)   &       5.04(2)   &       1.91(2) &         7.55(1) \\
\hline
\end{tabular}
\end{center}
\end{table}

The results in Table~\ref{TgtW:tb4}
 are integral activation values for each of the
cells. Each value is composed of contributions from hundreds of
radioactive isotopes, which decay at different rates. Immediately
following shutdown, the number of contributing isotopes is extremely
large. However, following 30 days of decay time, only the longest lived
isotopes contribute, and generally there are only a limited number of
isotopes at that stage. Two examples are presented 
in Tables~\ref{TgtW:tb5} and \ref{TgtW:tb6}, which
list the major contributors to the activity after 30~days of
decay time in a mercury pool cell
(number 92), and a shield cell (number 8). 
\begin{table}[htb!]
\begin{center}
\caption[Activation for cell 92 (mercury) 30 days after shutdown ]
{Activation for cell 92 (mercury) 30 days after shutdown.
Only elements with more than one Curie are listed.}
\label{TgtW:tb5}
\begin{tabular}{|rrrr|}
\hline
Isotope & Activation & Isotope & Activation \\
& (Ci) & & (Ci) \\
\hline
Hg-203     &       41.09    &Lu-173    &      0.35\\
Au-196   &         0.87&   Lu-172  &        1.19\\
Au-195    &        33.09&   Lu-171   &       0.48\\
Pt-188  &          3.49 &   Yb-169  &        6.81\\
Ir-190  &          0.51&   Cs-131  &        1.78\\
Ir-189  &          9.89&    Xe-127  &        1.36\\
Ir-188  &          4.20&   I-125    &       1.38\\
Os-185  &          10.71&    Te-121  &        1.60\\
Re-183  &          7.99 &   Te-118  &        0.13\\
W-181   &          5.74 &   Sr-85     &      1.34\\
Ta-179  &          0.54 &  Rb-84   &        0.65\\
Ta-178  &          3.09 & Rb-83  &          0.62\\
Hf-175  &          2.64 & & \\
\hline
\multicolumn{4}{|c|}{\textbf{Total} 141.6 (Table~\ref{TgtW:tb4} total  161.4)}\\
\hline
\end{tabular}
\end{center}
\end{table}

The major contributions to the activation of a mercury cell come
from the isotopes closest to the target nucleus (mercury). The
dominant contributor is an isotope of mercury, but there are
significant contributions from lighter isotopes. Of particular
interest are those that are, or could potentially be, volatile under operating
conditions (Xe, Cs, Rb, {\it etc.}).  Attention must also be paid
to those elements that could pose material compatibility concerns
when they come in contact with the structural materials of the cooling
loop.
\begin{table}[htb!]
\begin{center}
\caption[Activation for cell 8 (tungsten-light water) 30 days after shutdown ]
{Activation for cell 8 (tungsten-light water) 30 days after shutdown.
Only elements with more than hundred Curies are listed.}
\label{TgtW:tb6}
\begin{tabular}{|rrrr|}
\hline
Isotope & Activation & Isotope & Activation \\
& (Ci) & & (Ci) \\
\hline
Re-183   &       305.7  &   Gd-146    &      215.9\\
Re-184   &       171.6  &   Eu-149    &      276.5\\
W-181    &       40850.0&    Eu-148   &       42.6\\
W-185    &       5779.0 &   Eu-147    &      256.9\\
W-178    &       9075.0 &   Eu-146    &      240.1\\
Ta-183   &       147.7  &   Eu-145    &      15.43\\
Ta-182   &       3122.0 &   Sm-145    &      115.2\\
Ta-179   &       3958.0 &   Pm-143    &      111.9\\
Ta-178   &       9077.0 &   Ce-139    &      174.0\\
Hf-175   &       5666.0 &   Cs-131    &      187.1\\
Hf-172   &       616.1  &   Xe-131    &      202.0\\
Lu-174   &       23.48  &   I-127     &      175.3\\
Lu-173   &       1104.0 &   Te-121    &      94.47\\
Lu-172   &       660.3  &   Te-118    &      9.849\\
Lu-171   &       576.6  &   Sn-113    &      101.3\\
Yb-169   &       2090.0 &   Ag-109m   &      47.96\\
Tm-170   &       9.611  &   Ag-105    &      190.1\\
Tm-168   &       27.28  &   Pd-103    &      105.4\\
Tm-167   &       274.0  &   Rh-103m   &      113.1\\
Dy-159   &       335.8  &   Rh-101    &      25.71\\
Gd-153   &       157.9  &   Rh-99     &      72.91\\
Gd-151    &      219.3   &  Be-7       &     1038.0\\
Gd-149   &       55.88  &   H-3       &      0.001\\
\hline
\multicolumn{4}{|c|}{\textbf{Total} 88114.0 (Table~\ref{TgtW:tb4} total 89210.0)}\\
\hline
\end{tabular}
\end{center}
\end{table}

In the shield, the major contribution to the activation again comes
from isotopes closest in mass to the target nucleus (primarily
tungsten in this case). The distribution of major radioactive isotopes
is different from the first case, although the tungsten and mercury
nuclei are relatively close in mass. The reason for this difference is
primarily due to the difference in proton energy of the spallating
projectile particle and the fact that in the tungsten shield 
there is a significant amount of water present that softens the neutron
spectrum. Finally, it should be noted that a significant amount of
Be-7 (${}^7$Be) is generated in this cell (all cells containing water will have
Be-7 as part of their radioactive inventory). This could be
significant for operating the machine and maintaining the coolant
loop. Tritium is also generated, and although it is not a major
contributor to the overall inventory, its presence needs to be
noted. 
%Comments made about material compatibility for the first case
%apply to this case as well.
 
The radioactive nuclei considered here decay primarily by emitting a 
beta or gamma ray. 
These nuclides are generally not a personnel problem (unless they are ingested),
since they are 
essentially totally self shielded by a component. However, the presence of 
gamma rays poses a  personnel problem, and thus it is necessary to determine 
the gamma ray 
source strength associated with each of the above cells. 
This strength (as a function of 
gamma ray energy) can then be used in a separate calculation to determine 
the flux of gamma-rays leaving the target module, and the directional 
variation of the emitted radiation.  The integrated source strength in 
photons per second for each volume as a 
function of time following shutdown is given in the Table~\ref{TgtW:tb9}.
\begin{table}[htb!]
\begin{center}
\caption[Gamma ray source (gamma/s) in selected cells] 
{Gamma ray source ($\gamma$/s) in selected cells following machine shutdown. 
(x) stands for $\times 10^x$.}
\label{TgtW:tb9}
\begin{tabular}{|ccccc|}
\hline
Cell &\multicolumn{4}{c|}{Time after shutdown}\\
Number    &    0 &       4 hrs. &  1 day &  30 days \\
\hline
8    &    1.31(17)   &     1.49(16)   &     9.76(15)    &    3.58(15)\\
12  &     1.01(15)   &     6.32(14)    &    2.98(14)    &    4.10(13)\\
2   &     1.11(16)   &     1.22(15)   &     8.13(14)    &    2.99(14)\\
3   &     4.35(13)   &     2.46(13)   &     1.44(13)    &    5.71(12)\\
81  &     1.54(15)    &    7.09(14)   &     2.43(14)    &    9.05(12)\\
82  &     2.26(15)    &    1.09(15)   &     3.71(14)  &        8.58(12)\\
83   &    8.26(14)    &    3.44(14)   &     1.34(14)  &      3.74(12)\\
91  &     2.05(14)   &     1.44(14)   &     6.49(13) &       7.39(12)\\
92  &     2.95(14)   &     1.99(14)   &     1.07(14) &       1.52(13)\\       
93  &     4.29(14)   &     3.08(14)   &     1.39(14)  &      1.55(13)\\
94   &    3.02(14)   &     2.21(14)   &     1.03(14)  &      1.23(13)\\
95   &    2.45(14)    &    1.71(14)   &     8.85(13)  &      1.19(13)\\
96   &    3.48(14)    &    2.45(14)   &     1.23(14)  &      1.54(13)\\
97   &    4.36(14)   &     3.14(14)   &     1.57(14)  &      1.99(13)\\
98   &    5.10(14)   &     3.88(14)   &     1.89(14)  &      2.28(13)\\
99    &   4.86(14)   &     3.66(14)   &     1.69(14)  &      1.80(13)\\
100  &    2.86(14)   &     2.17(14)   &     1.02(14)  &      1.01(13)\\
101  &    1.47(14)   &     1.16(14)   &     5.49(13) &       5.86(12)\\
\hline
\end{tabular}
\end{center}
\end{table}

\subsection{Radial Leakage of Radiation from the Target Module}
The mercury target is positioned in such a manner that it points 
downward at 100~mrad, and the proton beam points down at 67~mrad. 
Thus, the emerging shower of particles starts off in a downward 
direction. The charged particles are under the influence of the surrounding
magnetic field, but the neutral particles propagate straight on.  
%be largely stopped in the beam stop volume. 
Any leakage flux from the target 
module will exhibit this overall pattern. 
\begin{table}[htb!]
\begin{center}
\caption[Integrated neutron and gamma ray flux ] 
{Integrated neutron and gamma ray flux per proton 
leaking radially outward from the target system at $z = 4$~m, the location
of the mercury pool.}
\label{TgtW:tb17}
\begin{tabular}{|ccc|}
\hline
Cell & Neutron flux & Gamma ray flux\\
Number & (cm$^{-2}$s$^{-1}\times 10^{-4}$) & (cm$^{-2}$s$^{-1}\times 10^{-5}$) \\
\hline
204     &        1.72     &           4.10\\
205      &         1.29     &         3.14\\
206      &         1.69     &         4.24\\
207      &         3.94     &         1.11\\
\hline
\end{tabular}
\end{center}
\end{table}

The results in Table~\ref{TgtW:tb17} for radial leakage at the position of
the mercury pool show the expected azimuthal variation, 
with more leakage in the direction of the proton beam.  
The gamma ray leakage is approximately an order of magnitude below that of the 
neutron leakage. The energy spectrum of the latter was also determined,
 and is given in Table~\ref{TgtW:tb10}.
\begin{table}[htb!]
\begin{center}
\caption[Neutron energy spectrum for cell 207 ]
{Neutron energy spectrum for cell 207, the cell below the mercury pool. 
(x) stands for $\times 10^x$.}
\label{TgtW:tb10}
\begin{tabular}{|cc|}
\hline
Energy bin  &                Flux\\
(MeV)  &      \\
\hline
0.0- 0.01    &                     6.40(-5)\\
0.1- 0.1     &                     6.01(-5)\\
0.1 - 1.0    &                     1.31(-4)\\
1.0- 5.0      &                    5.89(-5)\\
5.0 - 10.0   &                     1.49(-5)\\
10.0 - 100.0   &                   5.05(-5)\\
100.0 - 1000.0   &                 1.37(-5)\\
1000.0 - 24000.0  &                        2.237(-8)\\
\hline
Total        &             3.936(-4)\\
\hline
\end{tabular}
\end{center}
\end{table}

There is a significant neutron flux leakage above the MeV energy range,
which will affect the operational life of 
 components near the target magnet system. 
 
 


