\section{The Solenoids}
\label{DandPR:sol}
The decay and phase rotation region includes the  IL1, the mini-cooler, IL2 and IL3, and extends from $z=18$~m (from the target) to $z = 356$~m.  Within this region, there are
four types of solenoids.
\begin{enumerate}
\item From $z = 18$~m to $z = 36$~m, there is
a decay section that has a warm
bore diameter of 600~mm.  Around this warm bore is a water-cooled copper
shield that is 100~mm thick.
The solenoid cryostat warm bore is thus 800~mm.  The 18~m of decay solenoid
is divided into six cryostats each 2.9~m long.  This same type of magnet is used for
the 9~m long mini-cooling
sections on either side of the field-flip solenoid.  As a result, there are twelve magnets of
this type. 
\item  The IL1 solenoids, which extend from $z =36$~m to 
$z = 146$~m, have a beam aperture of 600~mm diameter.  Around the bore is a 10~mm thick water-cooled
copper radiation shield.  The
warm bore of this magnet cryostat is thus 620~mm in diameter.  There are 110~magnets of this type.
\item IL2 and IL3 and the drift between them extend, 
from $z = 166$~m to $z = 356$~m. These solenoids do not require a radiation shield and have a cryostat warm bore
diameter of 600~mm.  There are 190~magnets of this type.  
\item The field-flip solenoid
between the two mini-cooling sections
is 2~m long with a warm bore diameter of 400~mm.   There is only one
such magnet. 
\end{enumerate}

Table~\ref{fofoparams} shows the design parameters for the induction linac solenoids
and the solenoids in the
decay channel and mini-cooling channel.  The 2-meter long field flip
solenoid is not included in this table. Technical details of the magnets are discussed in Chapter~\ref{SCSOLE}.

%begin{table} 
\begin{sidewaystable}[H] \def\B#1{$\displaystyle{n\choose#1}$}
%\renewcommand{\arraystretch}{0.9}
%\centerline{Magnet Physical Parameters}
\begin{center}
\caption[Decay, phase rotation, and minicool solenoids]{Decay, phase rotation, and minicool solenoid parameters.}
\label{fofoparams}
\begin{tabular}{|lccc|}  
\hline
 &   IL1  &  IL2,IL3  &   Decay Channel \\
 &   Magnets  &  Magnets  &   Magnets \\
 & & & \\
\hline
\multicolumn{4}{|c|}{Magnet Mechanical Parameters}\\
\hline
No. of cells of this Type  &  110  &  190  &   12 \\
Cell length (mm) &   1000.0 & 1000.0 & 3000.0  \\
Magnet cryostat length (mm) &      900.0 &  900.0 &  2900.0  \\
Magnet coil package length (mm) &  860.0 &  860.0 &  860.0   \\
Number of coil packages per cell &      1   &    1  &    3  \\
Number of coils in the coil package &   2   &   2   &    2  \\
Length of each SC coil (mm) &     360.0 &  360.0 &  360.0  \\
Inner cryostat radius (mm) &       310.0 &  300.0 &  400.0  \\
SC coil inner radius (mm) &       334.0 &  324.0 &  429.0  \\
SC coil thickness (mm) &  9.6  &   9.6  &   9.6 \\
Support structure thickness (mm) &         6.4  &   6.4 &    6.4 \\
Magnet cryostat thickness at ends (mm) &   55.0 &   55.0  &  80.0 \\
Magnet cryostat thickness at center (mm) &         80.0  &  80.0 &   80.0 \\
Cold mass per magnet cell (kg) &   207.6 &  201.1 &  911.1 \\
Overall mass per magnet cell (kg) &        277.3 &  268.0 &  1151.1 \\
 & & & \\
\hline
\multicolumn{4}{|c|}{Magnet Electrical Parameters}\\
\hline
Average central induction (T) &    1.25  &  1.25 &   1.25 \\
On axis induction variation (\%) &  $\pm$2.5 &$\pm$2.5 &$\pm$2.2 \\
Peak induction in the windings (T) &    $\sim$1.6   &$\sim$1.6  &$\sim$1.6 \\
Number of turns per cell &     2532  &  2532 &   7596 \\
Magnet design current (A) &        392.8 &  392.8 &  392.8 \\
Magnet design operating temperature (K) &  4.4  &  4.4 &    4.4 \\
Conductor critical current at operating T (A)  &$\sim$1600   &$\sim$1600  &$\sim$1600  \\
Magnet stored energy per cell E (kJ) &     224  &   211  &  1103 \\
Magnet self inductance per cell (H) &      2.90 &  2.74 &  14.3 \\
Superconductor matrix J (A mm$^{-2}$) &         249  &  249  &  249 \\
EJ$^2$ limit per magnet cell (J A$^2$ m$^{-4}$) &    $1.39\times 10^{22}$   &   $1.31\times 10^{22}$  & $6.86\times 10^{22}$ \\
Quench protection method &     quench-back  &   quench-back  &   quench-back \\
\hline
\end{tabular}
\end{center}
%nd{table}
\end{sidewaystable}