\subsubsection{MIND conceptual design}
\label{sec:MIND_conceptual_design}

The Magnetised Iron Neutrino Detector (MIND) is an iron and scintillator sampling calorimeter which is essentially a larger version of the MINOS detector \cite{Lang:2001rw}.  We have chosen a cross section of 14~m~$\times$~14~m in order to maximise the ratio of the fiducial mass to the total mass.  The magnetic field will be toroidal as in MINOS and MIND will also use extruded scintillator for the readout material.  Details on the iron plates, magnetisation, scintillator, photo-detector and electronics are given below.  

\paragraph{Iron plates}
\label{par:iron_plates}

For the iron plates in MIND, we are following the design strategy that was used for MINOS.  The plates are octagons with overall dimension of 14 m $\times$ 14~m and 3.0 cm thick.  They are fabricated from strips that are 1.5 cm thick, 2~m (or 3~m)  wide and up to 14 m long.  Two layers of crossed strips  are plug welded together to form the full plate.  MINOS used 2~m wide strips and we know that fabrication of iron components of this width and with lengths of up to 14 m is possible.  Depending on the final plate fabricator, strip widths greater than 2~m are likely to be possible, so both 2~m and 3~m strip-width models were investigated.  Initially it was thought that the much larger weight of the MIND plates (40~T versus 10~T for MINOS) would preclude the concept of hanging the plates on a rail system due to excessive stress in the ears.  However, our analysis of the expected stress (see section \ref{par:MIND_FEA} below) has shown that this is not the case.  Essentially, no R\&D on the MIND iron plates is needed.  Final specification of the plate mosaic structure will be determined once a plate fabricator is chosen.

For the 2~m strip model, seven 2~m strips will be required to make up a whole layer. The layout of the top layer will be perpendicular to the bottom layer in each plane.  For the 3~m strip model, the 14~m long strips will be both 3~m wide and 2~m wide. Four 3~m strips and one 2~m strip will be required to make up a whole layer. The layout of the top layer and the bottom layer remains perpendicular to each other in each plane. The individual plates will be held together by plug welding the top layer to the bottom layer.  Each ear of the plane is supported by a structural-steel rail which is in turn supported by structural-steel columns. The section of the MIND detector plane and the support structures are shown in figure \ref{Fig:MIND-2D} and figure \ref{Fig:MIND-3D}.
\begin{figure*}
  \centering{
    \includegraphics[width=0.6\textwidth,bb=0 0 1971 1983]%
      {03-DetWg/Figures/MIND-2D.jpg}
  }
  \caption{2D diagram of MIND plate.}
  \label{Fig:MIND-2D}
\end{figure*}
\begin{figure*}
  \centering{
    \includegraphics[width=0.6\textwidth,bb=0 0 1931 1616]%
      {03-DetWg/Figures/MIND-3D.jpg}
  }
  \caption{3D diagram of MIND plate.}
  \label{Fig:MIND-3D}
\end{figure*}

A book-end will be used to provide lateral support for the planes as the MIND detector is constructed. The plane will be attached to the bookend at the minimum of each vertex point in the octagon and each midpoint between the vertexes. This bookend will consist of a framework of structural-steel members and will be vertically supported by the floor slab and horizontally supported by the wall of the enclosure.

\paragraph{The finite-element model}
\label{par:MIND_FEA}

Two finite-element models of the detector plane were created using higher order solid elements. The 2~m strip model is shown in figure \ref{Fig:2M-model} and the 3~m strip model is shown in figure \ref{Fig:3M-model}.  Loading was simulated by the gravity load of the plane. The plane was fixed at the bottom of the ears and the two top vertexes are fixed in the $z$ direction to resist plane buckling. The linear buckling of the plane was also investigated. The total deformed shape of the 2~m strip plane is shown in figure \ref{Fig:2M-deform}. The directional deformations are shown in figures \ref{Fig:2M-X-deform}, \ref{Fig:2M-Y-deform} and \ref{Fig:2M-Z-deform} respectively. The maximum deflections occur at the ear and the bottom of the plane.

\begin{figure*}
  \centering{
    \includegraphics[width=0.9\textwidth,bb=0 0 1951 1326]%
      {03-DetWg/Figures/2M-model.jpg}
  }
  \caption{Finite-element model of plate with 2~m strips.}
  \label{Fig:2M-model}
\end{figure*}

\begin{figure*}
  \centering{
    \includegraphics[width=0.9\textwidth,bb=0 0 1958 1240]%
      {03-DetWg/Figures/3M-model.jpg}
  }
  \caption{Finite-element model of plate that utilises both 3~m and 2~m strips.}
  \label{Fig:3M-model}
\end{figure*}

\begin{figure*}
  \centering{
    \includegraphics[width=0.9\textwidth,bb=0 0 1961 1115]%
      {03-DetWg/Figures/2M-deform.jpg}
  }
  \caption{Total deformed shape of plate fabricated with 2~m strips}
  \label{Fig:2M-deform}
\end{figure*}

\begin{figure*}
  \centering{
    \includegraphics[width=0.9\textwidth,bb=0 0 1981 1128]%
      {03-DetWg/Figures/2M-X-deform.jpg}
  }
  \caption{Deformation in $x$ for plate using 2~m strips}
  \label{Fig:2M-X-deform}
\end{figure*}

\begin{figure*}
  \centering{
    \includegraphics[width=0.9\textwidth,bb=0 0 1974 1077]%
      {03-DetWg/Figures/2M-Y-deform.jpg}
  }
  \caption{Deformation in $y$ for plate using 2~m strips}
  \label{Fig:2M-Y-deform}
\end{figure*}

\begin{figure*}
  \centering{
    \includegraphics[width=0.9\textwidth,bb=0 0 1978 1074]%
      {03-DetWg/Figures/2M-Z-deform.jpg}
  }
  \caption{Deformation in $z$ for plate using 2~m strips}
  \label{Fig:2M-Z-deform}
\end{figure*}



The stresses in the 2~m strip plane are shown in figure \ref{Fig:2M-stress}. The maximum von Mises stress is 6.8 ksi at the ear. In the regions away from that, all stresses are below the 12 ksi limit for AISI 1006 low carbon steel.  The welded connections were examined by extracting nodal forces and moments from the 2~m strip plane model at 45 locations. The maximum load in the plane is in the ear area and is approximately 15,000 pounds per inch.  In the linear buckling analysis of the 2~m strip plane, the results show the first buckling mode has a load safety factor of 4.7. 
\begin{figure*}
  \centering{
    \includegraphics[width=0.9\textwidth,bb=0 0 1992 1051]%
      {03-DetWg/Figures/2M-stress.jpg}
  }
  \caption{von Mises stress in plate using 2~m strips}
  \label{Fig:2M-stress}
\end{figure*}


For comparison, the total deformed shape of the 3~m strip plane is shown in figure \ref{Fig:3M-deform}. Again, the maximum deflections occur at the ear and the bottom of the plane. The stresses in the 3~m strip plane are shown in figure \ref{Fig:3M-stress}. The maximum von Mises stress is 22 ksi at the ear. In the regions away from the concentration, all stresses are below the 12 ksi limit for AISI 1006 low carbon steel.  In the linear buckling analysis of the 3~m strip plane, the results show the first buckling mode has a load safety factor of 4.5, somewhat worse than in the case of the 2~m wide strip case.
\begin{figure*}
  \centering{
    \includegraphics[width=0.9\textwidth,bb=0 0 1993 1069]%
      {03-DetWg/Figures/3M-deform.jpg}
  }
  \caption{Total deformation for plate using 3~m and 2~m strips}
  \label{Fig:3M-deform}
\end{figure*}

\begin{figure*}
  \centering{
    \includegraphics[width=0.9\textwidth,bb=0 0 1983 1090]%
      {03-DetWg/Figures/3M-stress.jpg}
  }
  \caption{von Mises stress in plate using 3~m and 2~m strips}
  \label{Fig:3M-stress}
\end{figure*}

\paragraph{Magnetisation}

As mentioned above, MIND will have a toroidal magnetic field like that of MINOS.  For excitation, however, we plan to use the concept of the superconducting transmission line (STL) developed for the Design Study for a staged Very Large Hadron Collider (VLHC) \cite{Ambrosio:2001ej}.  In order to obtain good field uniformity in a 14 m $\times$ 14m plate, MIND requires a much larger excitation current-turn than the 15kA-turn that is used in the MINOS room temperature Cu coils.  100kA-turn is possible using the STL.  The STL consists of a cylindrical superconducting braid inside a pipe cooled by super-critical helium.  The superconductor and cryo-pipe are co-axial to a cylindrical cryostat/vacuum vessel, figure \ref{Fig:STL}.  Figure \ref{Fig:STL} shows the constructions details for the STL that was prototyped and tested for the VLHC study and consisted of: 1) a perforated Invar flow liner and support; 2) a copper stabiliser braid; 3) superconductor cable braid; 4) an Invar pipe that contains the helium; 5) the cold-pipe support; 6) cryo-shield; 7) super-insulation; and 8) the vacuum jacket/pipe.
\begin{figure*}
  \centering{
    \includegraphics[width=0.6\textwidth,bb=0 0 1608 1041]%
      {03-DetWg/Figures/STL.jpg}
  }
  \caption{Schematic of superconducting transmission line showing construction details.}
  \label{Fig:STL}
\end{figure*}

\subparagraph*{Field Map}

Using the MIND plate geometry shown in figure \ref{Fig:MIND-2D}, a 2D magnetic analysis of the plate was performed.  Figure \ref{Fig:one-eight-plate} shows the model (1/8th) that was used in the analysis.  A 100~cm diameter hole for the STL was assumed and the MINOS steel \cite{Michael:2008bc} BH curve was assumed.  For this analysis, an excitation current of 100 kA was used.  This was the critical current achieved at 6.5~K in the STL test stand assembled for the VLHC proof-of-principle.  In figure \ref{Fig:AB-field} we give the azimuthal B field along the two lines (A-B and A-C) shown in figure \ref{Fig:one-eight-plate}.  Figure \ref{Fig:Field-Map-2D} gives the 2D contour lines of constant B.

\begin{figure*}
  \centering{
    \includegraphics[width=0.4\textwidth,bb=0 0 586 631]%
      {03-DetWg/Figures/one-eight-plate.jpg}
  }
  \caption{1/8th model used for magnetic analysis.}
  \label{Fig:one-eight-plate}
\end{figure*}

\begin{figure*}
  \centering{
    \includegraphics[width=0.8\textwidth,bb=0 0 1295 856]%
      {03-DetWg/Figures/AB-field.jpg}
  }
  \caption{Magnetic field along the lines A-B and A-C in Fig ~\ref{Fig:one-eight-plate}}
  \label{Fig:AB-field}
\end{figure*}

\begin{figure*}
  \centering{
    \includegraphics[width=0.8\textwidth]%
      {03-DetWg/Figures/Field-Map-2D.eps}
  }
  \caption{Contours of constant magnetic B-field.}
  \label{Fig:Field-Map-2D}
\end{figure*}

\paragraph{R\&D Requirements}

The STL described above was optimised for the 37 km radius of the VLHC.  The loop length needed for MIND is quite a bit shorter than the 233 km needed for the VLHC.  The optimised design of a STL for MIND is therefore likely to be different.  The 2.5~cm He-flow region can most likely be reduced, for example.  In addition, we would like to consider an STL with multiple internal current loops so that a 100 kA room temperature driving source is not needed.  The total amount of superconductor would be roughly the same;  5-10 turns with a current of 20-10 kA each would be more manageable from the viewpoint of the power source.

\paragraph{Detector planes}

\subparagraph*{Scintillator \\}

Particle detection using extruded scintillator and optical fibres is a mature technology.  MINOS has shown that co-extruded solid scintillator with embedded wavelength shifting (WLS) fibres and PMT readout produces adequate light for MIP tracking and that it can be manufactured with excellent quality control and uniformity in an industrial setting.  Many experiments use this same technology for the active elements of their detectors, such as the K2K Scibar \cite{RodriguezMarrero:2007zz}, the T2K INGRID, the T2K P0D, the T2K ECAL \cite{Kudenko:2008ia} and the Double-Chooz detectors \cite{Greiner:2007zzd}.

Our initial concept for the readout planes for MIND is to have both an $x$ and a $y$ view between each plate. The simulations  done to date have assumed a scintillator extrusion profile that is 3.5 $\times$ 1.0 cm$^2$.  This gives both the required point resolution and light yield.  We are also considering an option where we use triangular extrusions similar to those used in Minerva \cite{McFarland:2006pz}.

\subparagraph*{Rectangular extrusions}

The existing MIND simulations have assumed that the readout planes will use a rectangular extrusion that is 3.5 $\times$ 1.0 cm$^2$, see figure \ref{Fig:rectanex}.  A 1 mm hole down the centre of the extrusion is provided for insertion of the wavelength shifting fibre.  This is a relatively simple part to manufacture and has already been fabricated in a similar form for a number of small-scale applications.  The scintillator strips will consist of an extruded polystyrene core doped with blue-emitting fluorescent compounds, a co-extruded TiO$_2$ outer layer for reflectivity, and a hole in the middle for a WLS fibre.  Dow Styron 665 W polystyrene pellets are doped with PPO (1\% by weight) and POPOP (0.03\% by weight). The strips have a white, co-extruded, 0.25 mm thick TiO$_2$ reflective coating.  This layer is introduced in a single step as part of a co-extrusion process.  The composition of this capstocking is 15\% TiO$_2$ (rutile) in polystyrene.  In addition to its reflectivity properties, the layer facilitates the assembly of the scintillator strips into modules. The ruggedness of this coating enables the direct gluing of the strips to each other and to the module skins which results in labour and time savings for the experiment.  This process has now been used in a number of experiments.

\begin{figure*}[htb]
  \centering{
    \includegraphics[width=0.4\textwidth,bb=0 0 1067 322]%
      {03-DetWg/Figures/Rectangular_extrusion.jpg}
  }
  \caption{Schematic of rectangular scintillator extrusion.}
  \label{Fig:rectanex}
\end{figure*} 

\subparagraph*{Minerva extrusions \\}

We are also considering using the Minerva extrusion (see
figure \ref{Fig:Minerva-triangle}) for MIND.  The triangle has a 3.3-cm
base and a 1.7-cm height, and a 2.6 mm hole for a WLS fibre (figure \ref{Fig:Minerva-triangle-line}). 

\begin{figure*}
  \centering{
    \includegraphics[width=0.5\textwidth,bb=0 0 672 503]%
      {03-DetWg/Figures/Minerva-triangle.jpg}
  }
  \caption{Minerva extrusions showing partial readout plane and wavelength shifting fibres.}
  \label{Fig:Minerva-triangle}
\end{figure*}
\begin{figure*}
  \centering{
    \includegraphics[width=0.8\textwidth,bb=0 0 949 616]%
      {03-DetWg/Figures/Minerva-triangle-line.jpg}
  }
  \caption{Minerva extrusion engineering drawing.}
  \label{Fig:Minerva-triangle-line}
\end{figure*}

\subparagraph*{Photo-detector \\}

Given the rapid development in recent years of solid-state photodetectors based on Geiger mode operation of silicon avalanche photodiodes, we have chosen this technology for MIND.  Although various names are used for this technology, we will use silicon photomultiplier or SiPM.

\subparagraph*{SiPM Overview \\}

SiPM is the often-used name for a type of photo detector formed by
combining many small avalanche photodiodes operated in the Geiger mode
to form a single detector \cite{Sadygov:1996,Bacchetta:1996dc}.
Detailed information and basic principles of operation of these
``multi-pixel"  photodiodes can be found  in a recent review paper and
the references therein \cite{Renker:2009zz}. The first generation of
these detectors use a polysilicon resistor connected to each avalanche
photodiode forming  a pixel. Pixels usually vary in size from 10
$\times 10 \, \mu$m$^2$ to 100 $\times 100 \, \mu$m$^2$ (see figure \ref{Fig:SiPM}). All the diodes are connected to a common electrical point on one side, typically through the substrate, and all the resistors are connected to a common grid with metal traces on the other side to form a two node device.  A typical SiPM will have from 100 to 10,000 of these pixels in a single device, with the total area from 1 to 10 mm$^2$.  Because all the diode and the individual quenching resistors are connected in parallel, the SiPM device as a whole appears as a single diode. In operation, the device appears to act somewhat like a conventional APD, but in detail it is radically different. Because the diodes are operated in the Geiger mode, and because every pixel of the SiPM device is nearly identical, the sum of the fired pixels gives the illusion of an analog signal that is proportional to the incident light, but it is an essentially digital device. 
 
\begin{figure*}
  \centering{
    \includegraphics[width=0.5\textwidth,bb=0 0 1000 992]%
      {03-DetWg/Figures/SiPM.jpg}
  }
  \caption{Photograph of SiPM}
  \label{Fig:SiPM}
\end{figure*}

SiPMs have a number of advantages over conventional photomultiplier tubes, including very high photon-detection efficiency, complete immunity to magnetic fields, excellent timing characteristics, compact size, and physical robustness. They are particularly well suited to applications with fibres, as the natural size of the SiPM is comparable to that of fibres \cite{Balagura:2005gh,Yokoyama:2010qa}. But the most important single feature of the SiPM is that it can be manufactured in standard microelectronics facilities using nearly standard CMOS processing. This means that huge numbers of devices can be produced without any manual labour, making the SiPMs very economical. Furthermore, it is possible to integrate the electronics into the SiPM itself, which reduces cost and improves performance. Initial steps have been taken in this direction, though most current SiPMs are not manufactured in this way. But it is widely recognized that this is the approach that makes sense in the long run for most applications. It improves performance and reduces cost, and can be tailored to a specific application. As the use of SiPMs spreads, so will the use of custom SiPMs with integrated electronics, just as ASICs have superseded standard logic in electronics. 

The photon detection efficiency (PDE) of a SiPM is the product of 3  factors:
\begin{equation}
{\rm PDE} = QE\cdot\varepsilon_{Geiger}\cdot\varepsilon_{pixel} \, ;
\label{eq:pde}
\end{equation}
where $QE$ is the wavelength-dependent quantum efficiency, $\varepsilon_{Geiger}$ is the probability  to initiate the Geiger discharge 
by a photoelectron, and $\varepsilon_{pixel}$ is the fraction of the total photodiode  area occupied by sensitive pixels. The  bias voltage affects one parameter in the expression~(\ref{eq:pde}), $\varepsilon_{Geiger}$.   The geometrical factor $\varepsilon_{pixel}$  is  completely 
determined by the photodiode topology, and is in the range 50-70\%.    The PDE of a device manufactured by Hamamatsu \cite{HAMAMATSU} (Hamamatsu uses the name multi-pixel photon counter, MPPC) as function of wavelength of detected light is shown in figure~\ref{fig:pde_mppc}.

\begin{figure}[htb]
\centering\includegraphics[width=10cm,angle=0]{03-DetWg/Figures/Y11_MPPC.eps}
\caption{Photon detection efficiency  of a Hamamatsu MPPC as a function of wavelength of the detected light at  $\Delta V$ of 1.2 and 1.5~V at 25$^{\circ}$C.  The Y11(150 ppm) Kuraray fibre emission spectrum (in a. u.) for fibre length of 150 cm (from Kuraray specification) is also shown.}
\label{fig:pde_mppc}
\end{figure}

\subparagraph*{Implementation for a very large system \\}

Although SiPMs with integrated electronics are in their infancy, we can say quite a bit about what such a device might look like in the case of instrumenting a very large system of extruded scintillator with wavelength shifting fibre readout, with a channel count of many million channels. In a system of that size, there is no question that an application specific approach, which can reduce the unit costs by factors of five to ten, will easily justify the additional non-refundable expense inherent in a custom development. In this application, the SiPM would have an area of about  one square mm, with about 100 pixels and electronics around the periphery of the device. Each cell would have a few transistors along one of the sides to provide active quenching---this differs from first-generation SiPMs, which use a passive resistor as the quenching element. In the case of active quenching, each pixel has essentially a digital latch associated with it. When a pixel fires, the latch is set, until an external reset signal arms the latch once again. This mechanism should not be confused with devices such as vertex pixel detectors. In this case, because the pixel capacitance is very small, the signal voltage is typically between 1~V and 2~V. Unlike vertex detectors, there is no amplification needed, and therefore, there is almost no standing current required in the transistors and the power dissipation is very small.  It is only slightly larger than in the case of passive SiPMs and, in any case, much smaller than in vertex detectors. Active quenching has many advantages over passive quenching. For the application we are considering here, one of the main advantages is being able to control precisely when the pixels of the SiPM are rearmed. This greatly improves the dynamic range available for a given number of pixels because each pixel can fire only once during the signal collection period and therefore it is simple to correct for the probability that some pixels were hit more than once. In the passive quenching case, the pixels will start recharging while there are still signal photons arriving, allowing some pixels to fire when the pixel is not fully charged, violating the rule that every pixel gives the same signal. This makes saturation correction complicated and unreliable, as it depends on many details of the signal and the SiPM. For the application we are considering here, an active quenching SiPM with 100 pixels gives about the same resolution as a passively quenched SiPM with 250 pixels. The smaller number of pixels reduces the ratio of the active area to the area lost to routing, resistors, and optical isolation trenches between the pixels and makes up for the added dead area associated with the active-quench circuitry.
 
\subparagraph*{Readout Electronics \\}

On the periphery of the chip there is circuitry that latches the number of fired pixels in a FIFO, adds a time stamp and issues periodic latch resets to the quenching circuits. The communication with the chip is serial, with an input, an output and a clock, all of which are differential signals. SiPM bias and ground complete the connections for a total of eight.  The power for the digital circuitry on the chip is extracted from the clock lines. A number of chips would be connected with flex cables, in a ring topology, to a data concentrator module which would service a large number of SiPMs.  A reasonable bandwidth available on differential lines over a flex cable for distances up to a few meters is between 10~Mbps and 100~Mbps. Depending on the rate of signals in the detector, and including things such as protocol overhead and data redundancy, a reasonable estimate of the number of SiPM chips that can be serviced by a single data concentrator is a few thousand. We expect that in this application, the number of SiPMs in a module associated with a single data concentrator would be limited by mechanical and operational considerations to something like 250 to 500. From the data concentrator, the data travel over optical links to higher-level data collectors.

