\subsubsection{Options for Far Detectors}

The Magnetised Iron Neutrino Detector described above is the baseline
for the distant neutrino detectors.
Alternatives to the MIND which, though currently less mature, may
offer advantages, are under consideration and will be discussed briefly
below.

\paragraph{Totally Active Scintillating Detector (TASD)}

One alternative for the MIND for the Neutrino Factory detector is to
build a totally active scintillator detector (TASD). 
Although one could consider using TASD for the baseline Neutrino
Factory with 25\,GeV muon storage rings, TASD has been primarily
studied as an option for a machine of lower energy (4\,GeV to
5\,GeV).
For this scenario, the detector must have excellent neutrino
event-detection efficiency down to event energies of
roughly 500\,MeV.  
Recently, new ideas have made plausible large, cost-effective
detectors \cite{lenf1,lenf2} for lower muon energy, and initial
studies of the corresponding physics reach suggest that an experiment
with a 4\,GeV to 5\,GeV Neutrino Factory would provide an impressive
sensitivity to the oscillation parameters. 
Furthermore, compared with high-energy facilities, a low-energy
Neutrino Factory would require a less expensive acceleration scheme
and a cheaper storage ring that presents fewer underground-engineering
issues.

\subparagraph{Overview}

The Neutrino Factory TASD being considered consists of plastic
scintillator bars with a triangular cross-section arranged in planes
which make x and y measurements.  
Optimisation of the cell cross section still needs further study, but
for now we have chosen the MINER$\nu$A extrusion
design \cite{McFarland:2006pz}.  
The scintillator bars have a length of $15$\,m and the triangular
cross-section has a base of $3$\,cm and a height of $1.5$\,cm.  

Magnetising the large detector volume presents a significant technical
challenge for a Neutrino Factory TASD.  
Conventional room temperature magnets are ruled out due to their
prohibitive power consumption, and conventional superconducting
magnets are too expensive, due to the cost of the enormous cryostats
needed in a conventional superconducting magnet design. 
In order to eliminate 
the cryostat, we have investigated a concept based on the
superconducting transmission line (STL), the technology chosen for
field excitation in MIND. 
The solenoid windings now consist of this superconducting cable which
is confined in its own cryostat (figure \ref{Fig:STL}). 
Each solenoid ($10$ are required for the full detector) consists of
$150$ turns and requires $7\,500$ m of STL. 
There is no large vacuum vessel and thus none of the large vacuum
loads which make the cryostats for large conventional superconducting
magnets so expensive. 
The 10 solenoids forming what we have called a ``Magnetic Cavern" is
shown in figure \ref{fig:MagCav}.
\begin{figure}[ht]
\begin{center}
\includegraphics[width=0.79\textwidth]{03-DetWG/figures/Mag_cav_sim}
\end{center}
\caption{Schematic of the Magnetic Cavern concept.}
\label{fig:MagCav}
\end{figure}

The Neutrino Factory TASD basic response has been simulated with
GEANT4 version 8.1.  
The GEANT4 model (figure~\ref{fig:tasd}) of the detector included each
of the individual scintillator bars, but did not include edge effects
on light collection or the effects of a central wavelength-shifting
fibre. 
A uniform 0.5 Tesla magnetic field was simulated.
\begin{figure}[ht]
\begin{center}
\includegraphics[width=0.7\textwidth]{03-DetWG/figures/TASD_sch}
\end{center}
\caption{Schematic of the Totally Active Scintillator Detector.}
\label{fig:tasd}
\end{figure}

 
Samples of isolated muons in the  momentum range between $100$~MeV$/c$
and $15$~GeV$/c$ were simulated to allow for the determination of the
detector's momentum resolution and charge identification
capabilities. 
The NUANCE \cite{Casper:2002sd} event generator was used to simulate 1
million $\nu_e$ and 1 million $\nu_\mu$ interactions. 
Events were generated in $50$ mono-energetic neutrino-energy bins
between $100$~MeV and $5$~GeV. 
The results that follow only have one thousand events processed
through the full GEANT4 simulation and reconstruction. 
 
The detector response was simulated assuming a light yield consistent
with MINER$\nu$A measurements and current photo-detector
performance \cite{Paley:2008zza}. 
In addition, a 2 photo-electron energy resolution was added through
Gaussian smearing. 
Since  a complete pattern recognition algorithm was beyond the scope
of this initial study, the Monte Carlo information was used to aid in
pattern recognition. 
All digitised hits from a given simulated particle, where the
reconstructed signal was above 0.5 photo electrons, were collected. 
When using the isolated particles, hits in neighbouring $x$ and $y$
planes were used to determine the 3 dimensional position of the
particle.
The position resolution was found to be approximately $4.5$~mm RMS
with a central Gaussian of width $2.5$~mm. 
These space points were then passed to the RecPack Kalman
track-fitting package \cite{CerveraVillanueva:2004kt}.  
 
For each collection of points, the track fit was performed with an assumed positive and negative charge. The momentum resolution and charge misidentification rates were determined by studying the fitted track in each case which had the better $\chi^2$ per degree of freedom. Figure~\ref{fig:tasd-mom} shows the momentum resolution as a function of muon momentum. 
\begin{figure}[ht]
\begin{center}
\includegraphics[width=0.5\textwidth]{03-DetWG/figures/pres}
\end{center}
\caption{TASD momentum resolution as a function of the muon momentum.}
\label{fig:tasd-mom}
\end{figure}

As a tracker, TASD achieves a resolution of better than $10\%$ over
the momentum range studied. Figure \ref{fig:Track} (left) shows the
efficiency for reconstructing positive muons as a function of the
initial muon momentum. The detector becomes fully efficient above
$400$~MeV.  The charge mis-identification rate was determined by
counting the rate at which the track fit with the incorrect charge had
a better $\chi^2$ per degree of freedom than that with the correct
charge. Figure \ref{fig:Track} (right) shows the charge mis-identification rate as a function of the initial muon momentum.
\begin{figure}[ht]
  \begin{center}
    \includegraphics[width=0.49\textwidth]{03-DetWG/figures/fig5a}
    \includegraphics[width=0.49\textwidth]{03-DetWG/figures/fig5b}
  \end{center}
  \caption{
    Left: Efficiency for reconstructing positive muons. 
    Right: Muon charge mis-identification rate as a function of the
    initial muon momentum.
  } 
  \label{fig:Track}
\end{figure}

Based on these initial studies, TASD meets the required muon charge
mis-identification rate criterion needed for physics at a Neutrino
Factory and exhibits exceptional tracking and momentum resolution.  
In order to understand fully the potential performance of TASD at a
Neutrino Factory, a Monte Carlo study with full pattern recognition
reconstruction and full neutrino event reconstruction must be
performed, as has been done for MIND.  
This will allow for a detailed and quantitative understanding of
backgrounds and thus present a realistic estimate of the detector's
full potential at a Neutrino Factory. 

\subparagraph{Performance}

In this section we will show the sensitivity to the neutrino
oscillation parameters which can be obtained by a 20 kton Totally
Active Scintillating Detector (TASD) used in conjunction with a
low-energy Neutrino Factory. 
This setup was originally considered in references~\cite{lenf1,lenf2}
and later in references \cite{LENF,mythesis,mynsi}, in which full
details can be found. 
As explained in the main text, we considered the possibility of the
addition of the platinum channels ($\nu_{\mu}\rightarrow\nu_{e}$ and
$\bar{\nu}_{\mu}\rightarrow\bar{\nu}_{e}$) in addition to the usual
golden channels ($\nu_{e}\rightarrow\nu_{\mu}$ and
$\bar{\nu}_{e}\rightarrow\bar{\nu}_{\mu}$). 
The main assumptions used to simulate the TASD are as follows: we
assume an energy threshold of 0.5 GeV with a detection efficiency of
$94\%$ above 1 GeV and $74\%$ below 1 GeV for $\nu_{\mu}$ and
$\bar{\nu}_{\mu}$ with a background of $10^{-3}$. 
For $\nu_{e}$ and $\bar{\nu}_{e}$ we assume an efficiency of $47\%$
above 1 GeV and $37\%$ below 1 GeV with a background of $10^{-2}$. 
The main sources of background are assumed to arise from charge
mis-identification and neutral-current events. 
The energy resolution is assumed to be $10\%$ for all channels. 
A 100\,kton liquid argon (LAr) detector was also simulated, with the
assumptions used to simulate the optimistic performance being the same
as for the TASD, so that the optimistic performance of a 100\,kton LAr
detector coincides roughly with that of a 100\,kton TASD.  

In figure \ref{fig:exps} we show the performance of the 20\,kton TASD
to standard oscillation parameters when used with a low-energy
Neutrino Factory with a single baseline of 1\,300 km and assuming a
muon flux of $1.4\times10^{21}$ useful muon decays per year per
polarity, running for 5 years per polarity. 
The $3\sigma$ $\theta_{13}$ discovery potential, CP discovery
potential and sensitivity to the mass hierarchy as a function of
$\sin^{2}2\theta_{13}$ in terms of the CP fraction are shown, for the
low-energy Neutrino Factory with a 20\,kton TASD (red line), the
low-energy Neutrino Factory with a 100\,kton LAr detector (blue band -
the left-hand edge corresponds to the optimistic assumptions and the
right-hand edge to the conservative assumptions), and other
experiments - the ISS baseline Neutrino Factory \cite{ISS} (black
line), various $\beta$-beams (green \cite{betabeam},
orange \cite{gamma350_1,gamma350_2}, blue \cite{4ion} lines),
T2HK \cite{ISS} (yellow line) and the wide-band beam \cite{WBB}
(purple line).
In these simulations we used the same oscillation parameters as in
reference \cite{baseline}, and have assumed a normal hierarchy.

It can be seen that a low-energy Neutrino Factory with TASD has
sensitivity to CP violation which is roughly equal to that of the
pessimistic performance of the 100 kton LAr detector. 
The sensitivity to $\theta_{13}$ is also very good and again is
roughly equal to that of the pessimistic LAr detector, whilst the
sensitivity to the mass hierarchy is better than that of the
pessimistic LAr detector.
\begin{figure}[htp]
     \centering
     \subfigure[~$\theta_{13}$ discovery potential.]{
          \includegraphics[scale=0.5]{03-DetWG/figures/th13}}
     \subfigure[~CP discovery potential.]{
          \includegraphics[scale=0.5]{03-DetWG/figures/cp}}\\
     \subfigure[~Hierarchy sensitivity.]{
          \includegraphics[scale=0.5]{03-DetWG/figures/hier}}
     \caption{$3\sigma$ allowed contours for the LENF with 20 kton
     TASD (red line) and 100 kton LAr detector (blue band), the HENF
     (black line), T2HK (yellow line), the wide-band beam (purple
     line) and three $\beta$-beams (green, orange, light blue lines)
     for a) $\theta_{13}$ discovery potential, b) CP discovery
     potential and c) hierarchy sensitivity. From reference \cite{LENF}.}
\label{fig:exps}
\end{figure}


\paragraph{Liquid Argon Detectors}
\subparagraph*{Overview\\} 
The Liquid Argon Time Projection Chamber (LArTPC) offers the possibility of
truly isotropic tracking and calorimetry with fine sampling at the level of a
few-percent of a radiation length. 
Pioneered by the ICARUS project~\cite{Amerio:2004ze}, extensive
studies and R\&D projects have proven the potential of the  LArTPC to
provide a clean identification of $\nu_\mu,\nu_e$ charged-current
events  with the efficient rejection of neutral-current backgrounds,
excellent energy resolution and sensitivity over a wide energy band
including down to very low momentum thresholds. 
These properties make the LArTPC an interesting candidate for a
large-scale far detector for a Neutrino Factory and a number of groups
worldwide are actively pursuing LArTPC concept development. Fully
contained neutrino interactions have recently been reported by ICARUS
illuminated by the CNGS beam (see figure \ref{Events}(left)) and from the
ARGONEUT collaboration situated in the NUMI beam at FNAL (see
figure \ref{Events}(right)). 
\begin{figure}[htb]
  \includegraphics[width=0.49\textwidth]{03-DetWG/figures/Neutrino10-AGuglielmi-30}
  \includegraphics[width=0.49\textwidth]{03-DetWG/figures/Neutrino10-MSoderberg-08} 
  \caption{
    Neutrino interactions as seen in the (left) ICARUS (A. Guglielmi,
    Neutrino'10) and (right) ArgoNeut detectors (M. Soderberg,
    Neutrino'10) 
  }  
\label{Events} 
\end{figure} 

The largest LArTPC constructed to date is the $2 \times 300$ ton
ICARUS T600 detector which has a maximum drift length of $1.5$ m. 
R\&D programmes underway  in Europe, USA and Japan are focused on
the issues surrounding scaling up the 
LArTPC technology to the multi-kiloton scales demanded by a Neutrino
Factory in addition to  next generation projects for particle
astrophysics and proton decay.

Several design concepts have emerged for large scale LArTPC detectors
up to $\sim 100$ kt scale 
\cite{Rubbia:2009md,Bartoszek:2004si,Cline:2006st,Angeli:2009zza,Hasegawa-talkNeutrino2010,Fleming-talkNNN09}.
These designs achieve the large mass scale by being made up either of
a number of smaller identical modules or by using a single volume
based on Liquid Natural Gas (LNG) cryogenic tank technology. 
Examples of projects from Europe, Japan and the US are shown in
figure \ref{Concepts}. 
GLACIER and the JPARC-to-Okinoshima project are both based on a single $100$
kton LNG tank with an electron drift distance of up to $20$m whereas the DUSEL
design achieves large mass scales by stacking 
$20$ kton modules thereby keeping the drift distance down to $2.5$ m. 
\begin{figure}[htb] 
  \includegraphics[height=3.cm]{03-DetWG/figures/CHIPP2008-AMarchionni-04} 
  \includegraphics[height=3.cm]{03-DetWG/figures/Neutrino10-THasegawa-12} 
  \includegraphics[height=4.cm]{03-DetWG/figures/fermilab-fn-0917-e-1} 
  \caption{
    (left) GLACIER, (middle) JPARC-to-Okinoshima 100 kt concept and
    (right) 20 kt detector for DUSEL.
  } 
  \label{Concepts} 
\end{figure} 

With all of these large scale proposals, there are three main technical areas
where R\&D solutions need to be found:
\begin{itemize}
\item Engineering issues related to constructing large LAr volumes with very
  low thermal losses, preferably in an underground location and operation over
  many years in a safe and stable environment;
\item Drift lengths of  more than $10$ times the $1.5$\,m ICARUS T600
  drift length will only be achievable if drift fields of $0.5-1$\,kV/cm can be
  applied and if the level of electro-negative impurities, which degrade the
  released ionisation charge, can be controlled at the level of a few tens of
  parts per trillion (ppt); and
\item Reconstructing the $\nu_e \rightarrow \nu_\mu$ and $\bar{\nu}_e
  \rightarrow \bar{\nu}_\mu$~`golden' oscillation channel of the
  Neutrino Factory requires that the entire LAr volume be magnetised.
\end{itemize}

\subparagraph*{R\&D Activity\\}
In this section we summarise the status of R\&D activity in liquid
argon technology. 
\begin{itemize}
  \item {\bf Readout and Electronics:}
  The 2D reconstruction of charge in ICARUS modules is read out by
  planes that cannot easily scale in size, due to their large
  capacitance.  
  An alternative proposal for single volume designs with
  drift distances $>10$ m (e.g. GLACIER) is to operate in double-phase
  liquid and gaseous Ar; ionisation charge amplification occurring in
  the gas phase. 
  A $3$ litre double-phase TPC with thick GEM readout (macroscopic hole
  multipliers fabricated in standard
  PCBs) \cite{Badertscher-IEEE,Badertscher-Pisa} has been successfully
  operated at CERN.  
  More recent developments involve the production of an $X-Y$~2D
  projective anode for a Japanese $250$ litre prototype, studies with
  bulk-micromegas \cite{Rubbia-NNN10} and imaging the secondary
  scintillation light in a single phase LAr
  volume \cite{Lightfoot:2009zz}.
  ASIC developments using cold electronics (preamplifiers, digitisers
  and multiplexers) that work inside the cryostat are under development
  both in Europe \cite{Centro-CERN} and the
  USA \cite{Fleming-talkNNN09};

\item {\bf Liquid-argon vessels:}
LAr storage vessels are based on a stainless steel vacuum-insulated
Dewar. One of the 
large-scale designs \cite{Cline:2006st} scales this technology by
installing support structures within the LAr volume. Studies of the
suitability of industrial Liquid Natural Gas (LNG) technology for
large-scale LAr storage (up to $2\times 10^5$\,m$^3$) \cite{Technodyne}
have concluded that, with only passive insulation, boil-off losses of
only $0.04 \%$/day for a $100$\,kton vessel are expected. 
A stainless
steel/Invar membrane is also being considered for the DUSEL $20$\,kton design
\cite{Fleming-talkNNN09}.  Issues surrounding the feasibility of constructing and running
safely such detectors, particularly in underground sites has been studied as
part of the LAGUNA design study \cite{Rubbia:2010zz};

\item {\bf High Voltage Systems:}
The drift time of ionisation electrons over a distance of $\sim 10$\,m is around
$10$ ms for a drift velocity of $1\, {\rm mm/\mu s}$. It is desirable for the drift velocity to be as high as possible, so drift fields in the region of a few kV/cm are needed (in the MV-range for 10\,m). The ArDM experiment \cite{Kaufmann:2007zz} are generating the high voltages required inside the LAr volume via a submerged 
Cockcroft-Walton voltage multiplier. Drift fields of $\sim 1$ kV/cm have
already been demonstrated  over a  $1.2$ m drift distance \cite{Rubbia-Strasb}.

\item {\bf Liquid-argon purity:}
Attaining and maintaining sufficient purity of LAr is a 
challenge given that electronegative impurities (mainly $O_2$) must be kept at a level of a
few tens of ppt in order to ensure electron lifetimes of the order of $10$ ms.
Proof-of-principle tests for purging with argon gas before
filling with LAr have been performed at
FNAL \cite{Jaskierny:2006sr}, KEK \cite{Maruyama-talkNNN09}, and
CERN \cite{Rubbia-Strasb} (a 6\,m$^3$ volume 
achieved $3$ ppm $O_2$ contamination after purging). 
A closed gaseous Ar purification stage (via cartridges) in addition to a LAr 
purification stage has been used in ICARUS. Options for purification cartridges  are being studied
as part of the ArDM project at FNAL \cite{Andrews:2009zza}. Direct measurements of long electron drifts are underway at CERN ($5$ m horizontal drift \cite{Cline-talkNNN09}) and at the  University of Bern
(ARGONTUBE: $5$m vertical drift);

\item {\bf Magnetisation:} 
The magnetisation of a multi-kiloton LAr volume is one of the key issues 
surrounding the evaluation of a LAr TPC as a potential Neutrino Factory
detector. Small-scale prototype  LAr TPC's have been operated in
magnetic fields; e.g. a $10$~lt, $150$~mm maximum drift length volume in a
field of $0.55$~T \cite{Badertscher:2005te}, with no significant degradation of the imaging
properties. Conceptual studies of magnetising a  multi-kiloton LAr volume
have concluded that conventional warm coils would dissipate MW's of heat
~\cite{Cline:2001pt}, so more recent ideas include immersing a
super-conducting solenoid directly into the LAr volume~\cite{Ereditato:2005yx}, or
using superconducting transmission lines ~\cite{Bross-talkNeutrino2010}. 
Studies are on-going regarding magnetisation issues or the potential of a `hybrid' detector consisting of a LAr TPC in close
proximity to a magnetised MIND-type module or measuring  $\nu/\bar{\nu}$~QE CC reactions with nuclei on a statistical basis 
\cite{Huber:2008yx} in the context of a low energy Neutrino Factory;
    
\item {\bf Algorithmic reconstruction:}
With the increased interaction rates associated with neutrino beam
intensity upgrades, it is essential that automatic reconstruction algorithms for neutrino
interaction events in LAr are developed. Studies in Europe \cite{Barker} and via the LArSoft collaboration
in the USA \cite{Spitz-talkNPC} are actively developing algorithms to reconstruct
hit clusters, tracks, event vertex points and shower objects. The resulting
`toolbox' of algorithms will be used to validate the performance assumptions for
LAr detectors in common use for neutrino oscillation physics studies (see e.g. \cite{Barger:2007jq,FernandezMartinez:2010zza}).     
These tools will also be useful in estimating reliably the feasibility of non
magnetic field solutions to $\nu-\bar{\nu}$ separation in the golden channel
discussed above; and

\item {\bf Roadmaps:}
The  R\&D programmes in Europe and Japan for future large-scale LAr detectors are closely coordinated. Work is ongoing in delivering the large electron multiplier (LEM) readout technologies, demonstration of long drift lengths (5 m), culminating with the construction of a $1$ kton device, which is widely accepted to be the largest possible 
affordable detector that will allow reliable extrapolations to $100$ kton. 
The roadmap in the USA includes the exploitation of the ArgoNeuT in a
neutrino beam, the construction of the 0.1 kton MicroBooNE detector
and delivering a 20 kton detector for DUSEL.  
\end{itemize}

\paragraph{Large-volume liquid scintillator detectors}

Large-volume liquid scintillator detectors (Borexino\cite{Alimonti:2008gc}, KamLAND \cite{Suekane:2004ny}) are presently used for low-energy neutrino physics. Even larger scintillator detectors have been proposed, such as the 50 kton LENA \nocite{Wurm:2007cy,Oberauer:2006cd,Hochmuth:2006gz,MarrodanUndagoitia:2006qs,MarrodanUndagoitia:2006qn,MarrodanUndagoitia:2006rf,MarrodanUndagoitia:2006re,Undagoitia:2005uu,Autiero:2007zj,Wurm:2010ny,Lachenmaier:2010zz} \cite{Wurm:2007cy}--\cite{Lachenmaier:2010zz} detector or the 10 kton HanoHano\cite{Batygov:2008mr,Learned:2007zz} detector. Although these are totally-active scintillator detectors (TASD), these single-volume detectors are conceptually different from segmented scintillator detectors.

The performance of a conventional large volume liquid scintillator detector for high-energy neutrinos (1--5 GeV) has been studied recently \cite{Learned:2009rv,Peltoniemi:2009xx,Smith:2010zzc,Moellenberg2010} and a more detailed study is in preparation \cite{LENA-GeV}. It was found that, if the detector, particularly the read-out electronics, is well designed, one can reconstruct the simplest events using photon-arrival times in phototubes. The lepton-flavour identification was determined to be almost perfect and the energy resolution was found to be better than 5\%. Hence a large-volume liquid-scintillator detector can be used in conventional neutrino beam experiments \cite{Peltoniemi:2009hv} and high-energy beta beam \cite{Peltoniemi:2009zk} experiments, as well as in atmospheric neutrino experiments. If it can be magnetised, it could be also be considered for the detector at a Neutrino Factory \cite{Peltoniemi:2009zb}. 

\begin{figure}[tbhp]
\begin{center}
\includegraphics[width=0.6\textwidth]{03-DetWG/figures/cross_section}
\caption{A possible layout of the detector. This shows the transverse cross section. Photomultipliers (yellow circles) are located at all sides of the detector and cameras at the upper surface. In this case the vertical magnetic field is generated by longitudinal wires.}
\label{cross}
\end{center}
\end{figure}

Here we consider a magnetised single-volume liquid scintillator detector of approximately 100 kton. A phenylxylylethane (PXE) scintillator \cite{Back:2004zn, Quirk:2008zz, MarrodanUndagoitia:2009kq, Wurm:2010ad} doped with PPO (up to 10 g PPO/1 kg PXE) is able to produce fast scintillation decay times, essential for high energy applications (such as the Neutrino Factory). Additionally, we may not need a separate tank and water shielding or buffer as in LENA, but can use rock walls with a suitable liner, thus reducing the cost and optimising the detector volume.

The required shape and volume could be achieved with a horizontal cavern of 30 m diameter and a length of 150 m. The diameter is mostly limited by the transparency of the liquid, typical attenuation lengths being of the order of 15 m \cite{MarrodanUndagoitia:2009kq, Wurm:2010ad}. Previous studies performed for LENA hint that at least 30 m width is accessible without excessive cost \cite{Nuijten2010}. 

It is assumed that photomultiplier tubes are installed in all sides of the detector volume, including the bottom, the surface and both ends. Photomultiplier tubes (PMT) designed to work in magnetic fields, possibly embedded in $\mu$-metal shields and aligned relative to the field with mirrors for light collection, will be required. As an alternative, semiconductor-based (or hybrid) photo-sensors are also under study. They may be faster and immune to magnetic fields, but may suffer from noise and are currently expensive.

Previous studies \cite{LENA-GeV} suggest that a 3\% photo-cathode coverage is sufficient for high-energy events. The devices should be able to record multiple photons reliably, with a time resolution in the ns scale, to be achieved by 16 bit Flash ADCs. We may optionally install an array of one-photon capable cameras on the upper surface, when such technology is available and affordable (see e.g. \cite{Learned:2009rv}). The liquid-air interface can be used as a lens (objective), because of the high refractive index (1.6 - 1.8) of the oil used as the scintillator. To measure the very faint scintillation light we need single-photon capable pixelized photo-sensors. Potential devices exist based on a number of different technologies such as: ICCD (CCD with image intensifier), EMCCD (Electron multiplier CCD), SPADA (Single photon avalanche diode array) or MCP (micro-channel plate) varieties with binary pixel readout. 

A severe problem with all semiconductor photodetectors is their very high noise rate. A typical noise rate is 100~kHz per pixel at room temperature. With cooling, we may expect 10 kHz per pixel at $0^\circ$ C, and no less than 1~kHz at the freezing point of the liquid, but somewhat lower at liquid nitrogen temperatures. Because of the noise, the camera readout must be externally triggered with the PMT coincidence. A local rolling memory for at least 100 ns, or the full readout time window, is required. The analysis of the PMT data determines the vertex and the end of the muon track with a precision of 20~cm. 

It is reasonable to assume 50\% quantum efficiency and 70\% geometric efficiency. If we also assume 90\% transmission through the lens, this then gives a total photo-efficiency of 30\%. Assuming a photocell composed of $64\times64$ pixels (4096 channels), a lens with a 15 cm diameter and an aperture of 0.30, we obtain a mean resolution of 10 cm at 15 m distance. With a lens diameter of 15 cm and 10\% coverage of the upper surface area, we will measure about 10 photons for a 10 cm path-length along the trajectory of a muon (assuming a typical photon yield of $10^4$ photons/MeV and 20\% transparency at a distance of 15~m). 

The detector performance with PMT time signals was simulated with the prototype code ``Scinderella". The code simulates the passage of muons and scintillation light emission, individual hadrons and electromagnetic showers and tries to make a fit to a test event using the simulated recorded data of the photo-sensors. For a more quantitative picture, a more detailed simulation applying GEANT4 and physical event generators should be used. Here we considered only the bending of muon tracks. Much more detail about the tracking capability is given elsewhere \cite{LENA-GeV}. 

It was found that the muon charge was reliably measured using the time profile information of the photo-sensors. The simulations indicate that a magnetic field strength between 0.02 T for ideal electronics and 0.05 T for current standard technology might be sufficient. Older technology designed only for low-energy events, like that used in Borexino \cite{Alimonti:2008gc}, is not sufficient. The decay time of the scintillator affected the performance. For high-energy events, the lower transparency of higher-doped scintillators is adequate, if we are not aiming for performance at low energies.

Using the additional camera setup reduces the 20 cm resolution
achieved by the PMTs down to a statistical accuracy for an individual
track to better than 5 cm. With this resolution, the charge of the
muon can be identified for $B > 0.02$ T  and a 10 MeV energy
resolution can be achieved. The camera setup, in particular, improves
the capability to distinguish multiple tracks, such as charged pions
and recoil protons. The identification of 10--80 cm long tracks is
enhanced with the addition of the cameras when compared to a PMT only
setup. The camera setup also makes recoil neutron tracks visible. The
neutrons scatter from free protons, giving the proton recoil energies
up to half of the neutron energy, within a radius of $\sim
1$~m. Moreover, the neutron may cause the spallation of additional
neutrons that are absorbed giving gammas of a few MeV. The combination
of the camera and the PMT measurement may help to identify the
absorption signals.  
 
The camera readout will improve the measurement of the energy of the hadron showers produced in multi-GeV neutrino interaction. Electrons and photons causing electromagnetic showers can be identified by observing the gap between the vertex and the shower, which is 42~cm on average. This is important for rejection of neutral-current background events (and also for proton decay $p \to e^ + \pi^ 0$). 
 
Identifying a pion (from a muon) is important for neutral current
background rejection. The pion decays with a mean life-time at rest of 26\,ns. The resulting muon (4 MeV for a decay at rest) has a path-length of about 2 cm. In the case of decay in flight, the decay is recognised by an energy bump in the time profile and a sharp change in the direction of the path. To see the angle, we need a timing resolution better than 1 ns. Negative pions may be absorbed before decaying (giving photons).
	
We can summarise that a liquid scintillator detector setup with a magnetic field $B>0.02$~T, good PMTs and adequate electronics is sufficient to determine the muon charge. Combining PMT readout with a camera system gives additional tracking capability, with very good event identification and background rejection. Further studies to quantify these effects at a neutrino beam will be carried out in the future.


