\chapter{ Neutrino Factory}

\label{neufact}

\section{Description of Neutrino Factory}

In this Chapter we describe the various components of a Neutrino Factory.
The details here are taken from the most recent Feasibility Study (Study-II)
~\cite{EPP:studyii} that was carried out jointly by BNL and the MC. The
scheme we follow was outlined in Chapter 1. \ 

\subsection{Proton Driver}

The proton driver considered in Study-II is an upgrade of the BNL
Alternating Gradient Synchrotron (AGS) and uses most of the existing
components and facilities; parameters are listed in Table~\ref{Proton:tb1}.
The existing booster is replaced by a 1.2-GeV superconducting proton linac.
The modified layout is shown in Fig.~\ref{Proton:bnl}. 
\begin{figure}[tbh!]
\begin{center}
\includegraphics[width=5.5in]{Proton_driver_bnl.eps}
\end{center}
\caption{AGS proton driver layout.}
\label{Proton:bnl}
\end{figure}
\begin{figure}[tbh!]
\begin{center}
\includegraphics[width=5.5in]{Proton_driver_fnal.eps}
\end{center}
\caption{FNAL proton driver layout.}
\label{Proton:fnal}
\end{figure}
The AGS repetition rate is increased from 0.5 Hz to 2.5 Hz by adding power
supplies to permit ramping the ring more quickly. No new technology is
required for this---the existing supplies are replicated and the magnets are
split into six sectors rather than the two used presently. The total proton
charge (10$^{14}$ ppp in six bunches) is only 40\% higher than the current
performance of the AGS. Nonetheless, the large increase in peak current
argues for an improved vacuum chamber; this is included in the upgrade. The
six bunches are extracted separately, spaced by 20 ms, so that the target,
induction linacs, and rf systems that follow need only deal with single
bunches at an instantaneous repetition rate of 50 Hz (average rate of 15
Hz). The average proton beam power is 1 MW. A possible future upgrade to 2 $%
\times $10$^{14}$ ppp and 5 Hz could give an average beam power of 4 MW. At
the higher intensity, a superconducting bunch compressor ring would be
needed to maintain the rms bunch length at 3 ns.

If the facility were built at Fermilab, the proton driver would be a newly
constructed 16-GeV rapid cycling booster synchrotron~\cite{FNALbooster}. The
planned facility layout is shown in Fig.~\ref{Proton:fnal}. The initial beam
power would be 1.2 MW, and a future upgrade to 4 MW would be possible. The
Fermilab design parameters are included in Table~\ref{Proton:tb1}. A less
ambitious and more cost-effective 8-GeV proton driver option has also been
considered for FNAL \cite{FNALbooster}.

\begin{table}[tbh]
\caption{Proton driver parameters for BNL and FNAL designs.}
\label{Proton:tb1}
\begin{center}
\begin{tabular}{lcc}
\hline
& BNL & FNAL \\ \cline{2-3}
Total beam power (MW) & 1 & 1.2 \\ 
Beam energy (GeV) & 24 & 16 \\ 
Average beam current ($\mu $A) & 42 & 72 \\ 
Cycle time (ms) & 400 & 67 \\ 
Number of protons per fill & $1\times 10^{14}$ & $3\times 10^{13}$ \\ 
Average circulating current (A) & 6 & 2 \\ 
No. of bunches per fill & 6 & 18 \\ 
No. of protons per bunch & $1.7\times 10^{13}$ & $1.7\times 10^{12}$ \\ 
Time between extracted bunches (ms) & 20 & 0.13 \\ 
Bunch length at extraction, rms (ns) & 3 & 1 \\ \hline
\end{tabular}
\end{center}
\end{table}

\subsection{Target and Capture}

A mercury jet target is chosen to give a high yield of pions per MW of
incident proton power. The 1-cm-diameter jet is continuous, and is tilted
with respect to the beam axis. The target layout is shown in Fig.~\ref{tgtc} 
\begin{figure}[tbh!]
\begin{center}
%\input{tgtc.fig}
\includegraphics*[width=4in]{tgt2.ps}
\end{center}
\caption[Target, capture solenoids and mercury containment ]{Target, capture
solenoids and mercury containment.}
\label{tgtc}
\end{figure}
We assume that the thermal shock from the interacting proton bunch fully
disperses the mercury, so the jet must have a velocity of 30 m/s to be
replaced before the next bunch. Calculations of pion yields that reflect the
detailed magnetic geometry of the target area have been performed with the
MARS code~\cite{MARSstudyii}. To avoid mechanical fatigue problems, a
mercury pool serves as the beam dump. This pool is part of the overall
target---its mercury is circulated through the mercury jet nozzle after
passing through a heat exchanger.

Pions emerging from the target are captured and focused down the decay
channel by a solenoidal field that is 20 T at the target center, and tapers
down, over 18 m, to a periodic (0.5-m) superconducting solenoid channel ($%
B_{z}$ = 1 .25 T) that continues through the phase rotation to the start of
bunching. The 20-T solenoid, with a hollow copper conductor magnet insert
and superconducting outer coil, is similar in character to the higher field
(up to 45 T), but smaller bore, magnets existing at several laboratories ~
\cite{ITERmag}. The magnet insert is made with hollow copper conductor
having ceramic insulation to withstand radiation. MARS~\cite{MARSstudyii}
simulations of radiation levels show that, with the shielding provided, both
copper and superconducting magnets could have a lifetime greater than 15
years at 1 MW.

In Study-I, the target was a solid carbon rod. At high beam energies, this
implementation has a lower yield than the mercury jet, and is expected to be
more limited in its ability to handle the proton beam power, but should
simplify the target handling issues that must be dealt with. At lower beam
energies, say 6 GeV, the yield difference between C and Hg essentially
disappears, so a carbon target would be a competitive option with a lower
energy driver. Other alternative approaches, including a rotating Inconel
band target, and a granular Ta target are also under consideration, as
discussed in Study-II. Clearly there are several target options that could
be used for the initial facility.

\subsection{Phase Rotation}

Pions, and the muons into which they decay, are generated in the target over
a very wide range of energies, but in a short time pulse (1--3 ns rms). This
large energy spread is ``phase rotated,'' using drifts and induction linacs, into a
pulse with a longer time duration and a lower energy spread. The muons first
drift and spread out in time, after which the induction linacs decelerate
the early ones and accelerate the later ones. Three induction linacs (with
lengths of 100, 80, and 80 m) are used in a system that reduces distortion
in the phase-rotated bunch, and permits all induction units to operate with
unipolar pulses. The 1.25-T beam transport solenoids are placed inside the
induction cores to avoid saturating the core material, as shown in Fig.~\ref
{CandPR:fg1}. 
\begin{figure}[tbh]
\begin{center}
\includegraphics*[width=4in]{Phase_Rot1.eps}
\end{center}
\caption[Induction cell and mini-cooling solenoid]{Cross section of the
induction cell and mini-cooling solenoids.}
\label{CandPR:fg1}
\end{figure}
The induction units are similar to those being built for DARHT~\cite{daarht}.

Between the first and second induction linacs, two LH$_{2}$ absorbers (each
1.7 m long and 30 cm radius), with a magnetic field reversal between them,
are introduced to reduce the transverse emittance and lower the beam energy
to a value matched to the cooling channel acceptance (``mini-cooling''). The
beam at the end of the phase rotation section has an average momentum of
about 250 MeV/$c$.

\subsection{Buncher}

The long beam pulse (400 ns) after the phase rotation is then bunched at
201.25 MHz prior to cooling and acceleration at that frequency. The bunching
is done in a lattice identical to that at the start of the cooling channel,
and is preceded by a matching section from the 1.25-T solenoids into this
lattice. The bunching has three stages, each consisting of rf (with
increasing acceleration) followed by drifts (with decreasing length). In the
first two rf sections, second-harmonic 402.5-MHz rf is used together with
the 201.25 MHz primary frequency to improve the capture efficiency. The
402.5-MHz cavities are designed to fit into the bore of the focusing
solenoids, in the location corresponding to that of the LH$_{2}$ absorber in
the downstream cooling channel.

\subsection{Cooling}

Transverse emittance cooling is achieved by lowering the beam energy in LH$%
_{2}$ absorbers, interspersed with rf acceleration to keep the average
energy constant. Transverse and longitudinal momenta are lowered in the
absorbers, but only the longitudinal momentum is restored by the rf. The
emittance increase from Coulomb scattering is minimized by maintaining the
focusing strength such that the angular spread of the beam at the absorber
locations is large. This is achieved by keeping the focusing strength
inversely proportional to the emittance,\textit{\ i.e.}, increasing it as
the emittance is reduced. A modified Focus-Focus (SFOFO)~\cite{EPP:refsfofo}
lattice is employed. The solenoidal fields in each cell alternate in sign,
and the field shape is chosen to maximize the momentum acceptance ($\pm $
22\%). To maintain the tapering of the focusing, it was necessary to reduce
the cell length from 2.75 m in the initial portion of the channel to 1.65 m
in the final portion. A layout of the shorter cooling cell is shown in Fig.~%
\ref{RF:fg18.Q}.

\begin{figure}[hbt!]
\begin{center}
\includegraphics[width=4in]{rf_fg19.eps}
\end{center}
\caption{Cooling channel Lattice 2, two cavities per cell.}
\label{RF:fg18.Q}
\end{figure}

Figure~\ref{EmittCool} shows a simulation of cooling; the emittance falls
along the length of the channel. The increase in the number of muons that
fit within the acceptance of the downstream acceleration channel is shown in
Fig.~\ref{YieldCool}. 
\begin{figure}[tbh]
\begin{center}
%\leavevmode
\includegraphics*[width=100mm]{Emitt2D-211.eps}
\end{center}
\caption[The longitudinal and transverse emittances]{The longitudinal and
transverse emittances, obtained with the Geant4 simulation code, as a
function of channel length. The last lattice (2,3) was extended by $\approx $%
20~m to investigate the ultimate performance of the cooling channel.}
\label{EmittCool}
\end{figure}
\begin{figure}[tbh]
\begin{center}
\includegraphics*[width=100mm]{MuOPInAcc-211.eps}
\end{center}
\caption[$\protect\mu /p$ yield ratio for the two transverse emittance cuts]{
Geant4 simulations of the muon-to-proton yield ratio for two transverse
emittance cuts, clearly showing that the channel cools, \textit{i.e.}, the
density in the center of the phase space region increases. Since the
relevant yield $\protect\mu /$p$_{15}$ no longer increases for $z\leq 110$%
~m, the channel length was set to 108~m.}
\label{YieldCool}
\end{figure}

\subsection{Acceleration}

Parameters of the acceleration system are listed in Table~\ref{tab:acc:parm}%
. A 20-m SFOFO matching section, using normal conducting rf systems, matches
the beam optics to the requirements of a 2.5 GeV superconducting rf linac
with solenoidal focusing. The linac is in three parts. The first part has a
single 2-cell rf cavity unit per period. The second part, as a longer period
becomes possible, has two 2-cell cavity units per period. The last section,
with still longer period, accommodates four 2-cell rf cavity units per
period. Figure~\ref{fig:acc:cryomod} shows the three cryomodule types that
make up the linac. 
\begin{figure}[tbh]
\centering\includegraphics[angle=270,width=4.0in]{accel-010307-f03.eps}
\caption[Layouts of cryomodules.]{Layouts of short (top), intermediate
(middle) and long (bottom) cryomodules. Blue lines are the SC walls of the
cavities. Solenoid coils are indicated in red, and BPMs in yellow.}
\label{fig:acc:cryomod}
\end{figure}

This linac is followed by a single, four-pass recirculating linear
accelerator (RLA) that raises the energy from 2.5 GeV to 20 GeV. The RLA
uses the same layout of four 2-cell superconducting rf cavity structures as
the long cryomodules in the linac, but utilizes quadrupole triplet focusing,
as indicated in Fig.~\ref{fig:acc:rlalinac}. The arcs have an average radius
of 62 m. The final arc has a dipole field of 2 T. 
\begin{figure}[!tbh]
\centering\includegraphics[angle=270,width=4.0in]{accel-010307-f28.eps}
\caption{Layout of an RLA linac period.}
\label{fig:acc:rlalinac}
\end{figure}

In Study-I, where the final beam energy was chosen to be 50 GeV, a second
RLA is needed. This second RLA is similar to the first RLA but considerably
larger.

\begin{table}[tbh]
\caption{Main parameters of the muon accelerator driver.}
\label{tab:acc:parm}
\begin{center}
\begin{tabular}{lc}
\hline
Injection momentum (MeV/$c$)/Kinetic energy (MeV) & 210/129.4 \\ 
Final energy (GeV) & 20 \\ 
Initial normalized acceptance (mm-rad) & 15 \\ 
\quad rms normalized emittance (mm-rad) & 2.4 \\ 
Initial longitudinal acceptance, $\Delta pL_{b}/m_{\mu }$ (mm) & 170 \\ 
\quad momentum spread, $\Delta p/p$ & $\pm 0.21$ \\ 
\quad bunch length, $L_{b}$ (mm) & $\pm 407$ \\ 
\quad rms energy spread & 0.084 \\ 
\quad rms bunch length (mm) & 163 \\ 
Number of bunches per pulse & 67 \\ 
Number of particles per bunch\textbf{/}per pulse & $4.4\times 10^{10}$ 
\textbf{/}$3\times 10^{12}$ \\ 
Bunch frequency\textbf{/}accelerating frequency (MHz) & 201.25\textbf{/}
201.25 \\ 
Average beam power (kW) & 150 \\ \hline
\end{tabular}
\end{center}
\end{table}

\subsection{Storage Ring}

After acceleration in the RLA, the muons are injected into the upward-going
straight section of a racetrack-shaped storage ring with a circumference of
358 m. Parameters of the ring are summarized in Table~\ref{SRING:tb}.
High-field superconducting arc magnets are used to minimize the arc length
and maximize the fraction (35\%) of muons that decay in the downward-going
straight and generate neutrinos headed toward the detector located some 3000
km away.

All muons are allowed to decay; the maximum heat load from their decay
electrons is 42 kW (126 W/m). This load is too high to be dissipated in the
superconducting coils. For Study-II, a magnet design has been chosen that
allows the majority of these electrons to pass out between separate upper
and lower cryostats, and be dissipated in a dump at room temperature. To
maintain the vertical cryostat separation in focusing elements, skew
quadrupoles are employed in place of standard quadrupoles. In order to
maximize the average bending field, Nb$_{3}$Sn pancake coils are employed.
One coil of the bending magnet is extended and used as one half of the
previous (or following) skew quadrupole to minimize unused space. Figure~\ref
{EPP:fgsection} shows a layout of the ring as it would be located at BNL.
(The existing 110-m-high BNL stack is shown for scale.) For site-specific
reasons, the ring is kept above the local water table and is placed on a
roughly 30-m-high berm. This requirement places a premium on a compact
storage ring.

\begin{table}[tb]
\caption{Muon storage ring parameters.}
\label{SRING:tb}
\begin{center}
\begin{tabular}{ll}
\hline
Energy (GeV) & 20 \\ 
Circumference (m) & 358.18 \\ 
Normalized transverse acceptance (mm-rad) & 30 \\ 
Energy acceptance (\%) & 2.2 \\ 
\multicolumn{2}{c}{Arc} \\ 
Length (m) & 53.09 \\ 
No. cells per arc & 10 \\ 
Cell length (m) & 5.3 \\ 
Phase advance ($\deg $) & 60 \\ 
Dipole length (m) & 1.89 \\ 
Dipole field (T) & 6.93 \\ 
Skew quadrupole length (m) & 0.76 \\ 
Skew quadrupole gradient (T/m) & 35 \\ 
$\beta _{\text{max}}$ (m) & 8.6 \\ 
\multicolumn{2}{c}{Production Straight} \\ 
Length (m) & 126 \\ 
$\beta _{\text{max}}$ (m) & 200 \\ \hline
\end{tabular}
\end{center}
\end{table}

For Study-I, a conventional superconducting ring was utilized to store the
50 GeV muon beam. The heat load from muon decay products in this scenario is
managed by having a liner inside the magnet bore to absorb the decay
products. This approach is likewise available for BNL, provided some care is
taken to keep the ring compact; acceptable solutions have been found for
this option as well.

An overall layout of the Neutrino Factory on the BNL site is shown in Fig.~%
\ref{bnlsite}. %\textbf{Fig.~x.x (Study-II, Figure 11.4-GET\ FROM\ JUAN)}. 
Figure~\ref{fnalsite} shows the equivalent picture for a facility on the
Fermilab site. In this latter case, the layout includes the additional RLA
and longer storage ring needed to reach 50 GeV. Clearly the footprint of a
Neutrino Factory is reasonably small, and such a machine would fit easily on
the site of either BNL or Fermilab. 
\begin{figure}[tbh]
\begin{center}
\includegraphics[width=4.0in]{mole-hill.eps}
\end{center}
\caption[Top view and cross section through ring and berm]{Top view and
cross section through 20-GeV ring and berm. The existing 110-m tower, drawn
to scale, gives a sense of the height of the ring on the BNL landscape.}
\label{EPP:fgsection}
\end{figure}
\begin{figure}[tbh]
\begin{center}
\includegraphics[width=0.9\linewidth]{bnl-location-old.eps}
\end{center}
\caption[Schematic of a neutrino factory at Brookhaven]{Schematic of a
20-GeV Neutrino Factory at BNL.}
\label{bnlsite}
\end{figure}
\begin{figure}[tbh]
\begin{center}
\includegraphics[width=0.9\linewidth]{fnal-location.eps}
\end{center}
\caption[Schematic of a neutrino factory at Fermilab]{Schematic of a 50-GeV
Neutrino Factory at Fermilab.}
\label{fnalsite}
\end{figure}

\subsection{Detector}

The Neutrino Factory, plus its long-baseline detector, will have a physics
program that is a logical continuation of current and near-future neutrino
oscillation experiments in the U.S., Japan and Europe. Moreover, detector
facilities located in experimental areas near the neutrino source will have
access to integrated neutrino intensities $10^{4}$--$10^{5}$ times larger
than previously available ($10^{20}$ neutrinos per year compared with $%
10^{15}$--$10^{16}$).

The detector site taken for Study-II is the Waste Isolation Pilot Plant
(WIPP) in Carlsbad, New Mexico. The WIPP site is approximately 2900~km from
BNL. Space is potentially available for a large underground physics facility
at depths of 740--1100~m, and discussions are under way between DOE and the
UNO project~\cite{DET:uno} on the possible development of such a facility.

\subsubsection{Far Detector}

Specifications for the long-baseline Neutrino Factory detector are rather
typical for an accelerator-based neutrino experiment. However, because of
the need to maintain a high neutrino rate at these long distances, the
detectors considered here are 3--10 times more massive than those in current
neutrino experiments. Clearly, the rate of detected neutrinos depends on two
factors---the source intensity and the detector size. In the actual design
of a Neutrino Factory, these two factors must be optimized together.

Two options are considered for the WIPP site: a 50 kton
steel--scintillator--proportional-drift-tube (PDT) detector or a
water-Cherenkov detector. The PDT detector would resemble MINOS. Figure~\ref
{fg:steelwipp} shows a 50-kton detector with dimensions $8~\text{m}\times 8~%
\text{m}\times 150$~m. A detector of this size would record up to $4\times
10^{4}$ $\nu _{\mu }$ events per year. 
\begin{figure}[tbh]
\begin{center}
\includegraphics[width=3.5in]{steelwipp6.ps}
\end{center}
\caption[A possible 50 kton Steel/Scintillator/PDT detector at WIPP]{A
possible 50-kton steel-scintillator-PDT detector at WIPP.}
\label{fg:steelwipp}
\end{figure}

A large water-Cherenkov detector would be similar to SuperKamiokande, but
with either a magnetized water volume or toroids separating smaller water
tanks. The detector could be the UNO detector~\cite{DET:uno}, currently
proposed to study both proton decay and cosmic neutrinos. UNO would be a
650-kton water-Cherenkov detector segmented into a minimum of three tanks
(see Fig.~\ref{fg:unodet}). It would have an active fiducial mass of
440~kton and would record up to $3\,\times \,10^{5}$ $\nu _{\mu }$ events
per year from the Neutrino Factory beam. 
\begin{figure}[tbh]
\begin{center}
\includegraphics[width=3.0in]{unodet1.ps}
\end{center}
\caption[Block schematic of the UNO detector]{Block schematic of the UNO
detector, including initial design parameters.}
\label{fg:unodet}
\end{figure}

Another proposal for a neutrino detector is a massive liquid-argon
magnetized detector~\cite{landd} that would attempt to detect proton decay,
solar and supernova neutrinos as well as serve as a Neutrino Factory
detector.

\subsubsection{Near Detector}

As noted, detector facilities located on-site at the Neutrino Factory would
have access to unprecedented intensities of pure neutrino beams. This would
enable standard neutrino physics studies such as ${\sin }^{2}\theta _{W}$,
structure functions, $\nu $ cross sections, nuclear shadowing and pQCD to be
performed with much higher precision than previously obtainable. In addition
to its primary physics program, the near detector can also provide a precise
flux calibration for the far detector, though this may not be critical given
the ability to monitor the storage ring beam intensity independently.

A compact liquid-argon TPC (similar to the ICARUS detector~\cite{ICARUS}),
cylindrically shaped with a radius of 0.5 m and a length of 1~m, would have
an active volume of $10^{3}$ kg and a neutrino event rate \textsl{O}(10~Hz).
The TPC could be combined with a downstream magnetic spectrometer for muon
and hadron momentum measurements. At these $\nu $ intensities, it is even
possible to have an experiment with a relatively thin Pb target (1~$L_{rad}$%
~), followed by a standard fixed-target spectrometer containing tracking
chambers, time-of-flight and calorimetry, with an event rate \textsl{O}%
~(1~Hz).





