% Mike's new version, received Jan.9 \section{ Neutrino Factory} \label{neufact} In this Section we describe the various components of a Neutrino Factory, based on the most recent Feasibility Study (Study~II)~\cite{EPP:studyii} that was carried out jointly by BNL and the MC. We also describe the stages that could be constructed incrementally to provide a productive physics program that evolves eventually into a full-fledged Neutrino Factory. Details of the design described here are based on the specific scenario of sending a neutrino beam from Brookhaven to a detector in Carlsbad, New Mexico. More generally, however, the design exemplifies a Neutrino Factory for which our two Feasibility Studies demonstrated technical feasibility (provided the challenging component specifications are met), established a cost baseline, and established the expected range of physics performance. As noted earlier, this design typifies a Neutrino Factory that could fit comfortably on the site of an existing laboratory, such as BNL or FNAL. A list of the main ingredients of a Neutrino Factory is given below: \begin{itemize} \item \textbf{Proton Driver:} Provides 1--4 MW of protons on target from an upgraded AGS; a new booster at Fermilab would perform equivalently. \item \textbf{Target and Capture:} A high-power target immersed in a 20~T superconducting solenoidal field to capture pions produced in proton-nucleus interactions. \item \textbf{Decay and Phase Rotation:} Three induction linacs, with internal superconducting solenoidal focusing to contain the muons from pion decays, that provide nearly non-distorting phase rotation; a ``mini-cooling'' absorber section is included after the first induction linac to reduce the beam emittance and lower the beam energy to match the downstream cooling channel acceptance. \item \textbf{Bunching and Cooling:} A solenoidal focusing channel, with high-gradient rf cavities and liquid hydrogen absorbers, that bunches the 250~MeV/c muons into 201.25~MHz rf buckets and cools their transverse normalized rms emittance from 12 mm$\cdot $rad to 2.7 mm$\cdot $rad. \item \textbf{Acceleration:} A superconducting linac with solenoidal focusing to raise the muon beam energy to 2.48 GeV, followed by a four-pass superconducting RLA to provide a 20 GeV muon beam; a second RLA could optionally be added to reach 50 GeV, if the physics requires this. \item \textbf{Storage Ring:} A compact racetrack-shaped superconducting storage ring in which $\approx $35\% of the stored muons decay toward a detector located about 3000 km from the ring. \end{itemize} \subsection{Proton Driver} The proton driver considered in Study~II is an upgrade of the BNL Alternating Gradient Synchrotron (AGS) and uses most of the existing components and facilities; parameters are listed in Table~\ref{Proton:tb1}. To serve as the proton driver for a Neutrino Factory, the existing booster is replaced by a 1.2~GeV superconducting proton linac. The modified layout is shown in Fig.~\ref{Proton:bnl}. \begin{figure}[tbh] \begin{center} \includegraphics[width=5.5in]{Proton_driver_bnl.eps} \end{center} \caption{AGS proton driver layout.} \label{Proton:bnl} \end{figure} \begin{figure}[tbh] \begin{center} \includegraphics[width=5.5in]{Proton_driver_fnal.eps} \end{center} \caption{FNAL proton driver layout from Ref. \protect\cite{FNALbooster}.} \label{Proton:fnal} \end{figure} The AGS repetition rate is increased from 0.5 Hz to 2.5 Hz by adding power supplies to permit ramping the ring more quickly. No new technology is required for this---the existing supplies are replicated and the magnets are split into six sectors rather than the two used presently. The total proton charge (10$^{14}$ ppp in six bunches) is only 40\% higher than the current performance of the AGS. However, due to the required short bunches, there is a large increase in peak current and concomitant need 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 this 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 Fermilab \cite{FNALbooster}; this too might be the basis for a proton driver design. \begin{table}[tbh] \caption{Proton driver parameters for BNL and FNAL designs.} \label{Proton:tb1} \begin{center} \begin{tabular}{|l|c|c|} \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 20--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 ($B_{z}=1.25\text{ T}$) that continues through the phase rotation to the start of bunching. Note that the longitudinal direction of the fields in this channel do not change sign from cell to cell as they do in the cooling channel. The 20~T solenoid, with a resistive 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 the 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 pion 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. Present indications \cite{Ref:ORNLtgt} are that a carbon-carbon composite target can be tailored to tolerate even a 4 MW proton beam power---a very encouraging result. Other alternative approaches, including a rotating Inconel band target, and a granular Ta target are also under consideration, as discussed in Study~II \cite{EPP:studyii}. Clearly there are several target options that could be used for the initial facility. \subsection{Phase Rotation} The function of the phase rotation section in a neutrino factory is to reduce the energy spread of the collected muon beam to a manageable level, allowing reasonable throughput in the subsequent system components. The following description refers specifically to the properties of the U.S. Feasibility Study 2 for a neutrino factory. The initial pions are produced in the mercury target with a very wide range of momenta. The momentum spectrum peaks around 250~MeV/$c$, but there is a tail of high energy pions that extends well beyond 1~GeV. The pions are spread in time over about 3 ns, given by the pulse duration of the proton driver. After the 18 m long tapered collection solenoid and an 18~m long drift section, where the beam is focused by 1.25~T solenoids, most of the low energy pions have decayed into muons. At this point the muon energy spectrum also extends over an approximately 1~GeV range and the time spectrum extends over approximately 50~ns. However, there is a strong correlation between the muon energy and time that can be used for ``phase rotation''. \begin{table} \caption{Properties of the induction linacs used in Feasibility Study 2.} \label{induc} \begin{tabular}{lcccc} Induction Linac & & 1 & 2 & 3 \\\hline\hline Length & m & 100 & 80 & 100 \\ Peak gradient & MV/m & 1.5 & -1.5 & 1.0 \\ Pulse FWHM & ns & 250 & 100 & 380 \\ Pulse start offset & ns & 55 & 0 & 55 \\ \end{tabular} \end{table} In the phase rotation process an electric field is applied at appropriate times to decelerate the leading high energy muons and to accelerate the trailing low energy ones. Since the bunch train required by a neutrino factory can be very long, it is possible to minimize the energy spread using induction linacs. The induction linac consists of a simple non-resonant structure, where the drive voltage is applied to an axially symmetric gap that encloses a toroidal ferromagnetic material. The change in flux in the magnetic core induces an axial electric field that provides particle acceleration. The induction linac is typically a low gradient structure that can provide acceleration fields of varying shapes and time durations from tens of nanoseconds to several microseconds. Some properties of the induction linacs are given in Table~\ref{induc}. \begin{figure}[tbh] \centering \includegraphics*[width=4in]{Phase_Rot1.eps} \caption[Induction cell and mini-cooling solenoid]{Cross section of the induction cell and transport solenoids.} \label{CandPR:fg1} \end{figure} Three induction linacs are used in a system that reduces distortion in the phase-rotated bunch, and permits all induction units to operate with unipolar pulses. The induction units are similar to those being built for the DARHT project \cite{daarht}. The 1.25 T beam transport solenoids are placed inside the induction cores in order to avoid saturating the core material, as shown in Fig.~\ref{CandPR:fg1}. Between the first and second induction linacs two liquid hydrogen absorbers (each 1.7~m long and 30~cm radius) are used to (1) provide some initial cooling of the transverse emittance of the muon beam and (2) lower the average momentum of the beam to match better the downstream cooling channel acceptance. This process is referred to as ``mini-cooling''. The direction of the solenoid magnetic field is reversed between the two absorbers. The presence of material in the beam path destroys the conservation of canonical angular momentum that occurs when a particle enters and leaves a solenoid in vacuum. The build-up of this angular momentum would eventually lead to emittance growth. However, this growth can be minimized by periodically reversing the direction of the field. \begin{figure}[t] \centering \includegraphics[width=\textwidth]{phaserot.eps} \caption{Evolution of the beam distribution in the phase rotation section. The graphs show the distribution before the phase rotation, after the first induction linac (top row, left to right), after mini-cooling, and after the second and third induction linacs (bottom row).} \label{fig:phaserot} \end{figure} The beam at the end of the phase rotation section has an average momentum of about 250 MeV/c and an rms fractional energy spread of $\approx$4.4\%. Figure~\ref{fig:phaserot} shows the evolution of the beam distribution in the phase rotation section. \subsection{Buncher} \begin{figure}[t] \centering \setlength\unitlength{0.2in} \input buncher.fig \caption{Evolution of beam in buncher. Plots are at the beginning of the buncher (top left), and at the ends of the three bunching stages (top right, bottom left, and bottom right, in that order).} \label{fig:buncher} \end{figure} 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 liquid hydrogen absorber in the downstream cooling channel. Their aperture radius for the 402.5~MHz cavities is 20~cm at the IRIS, while that of the 201.25~MHz cavities is 25~cm. The gradients on axis in the cavities are 6.4~MV/m for the 402.5~MHz cavities, and range from 6 to 8~MV/m for the 201.25~MHz cavities. The resulting bunches fill the 201.25~MHz stationary RF bucket. Figure~\ref{fig:buncher} shows the evolution of the longitudinal distribution in the buncher. \subsection{Cooling} The transverse emittance of the muon beam after phase rotation and bunching must be reduced in order to fit into the downstream accelerators and storage ring. Ionization cooling is currently the only feasible option for cooling the beam within the muon lifetime. In ionization cooling the transverse and longitudinal momenta are lowered in the absorbers, but only the longitudinal momentum is restored by the rf. The following description refers specifically to the properties of the U.S.\ Feasibility Study 2 for a neutrino factory. Transverse emittance cooling is achieved using cooling cells that (1) lower the beam energy by 7-12~MeV in liquid hydrogen absorbers, (2) use 201~MHz rf cavities to restore the lost energy, and (3) use 3--5~T solenoids to strongly focus the beam at the absorbers. At the end of the cooling channel the rms normalized transverse emittance is reduced to about 2.5~mm~rad. \begin{figure}[hbt!] \centering \includegraphics[width=4in]{rf_fg19.eps} \caption{Two cells of the 1.65 m cooling lattice.} \label{RF:fg18.Q} \end{figure} Each cell of the lattice contains three solenoids. The direction of the solenoidal field reverses in alternate cells in order to prevent the build-up of canonical angular momentum, as mentioned above in the discussion of mini-cooling. In analogy with the FODO lattice this focusing arrangement is referred to as a (S)FOFO lattice. Multiple Coulomb scattering together with the focusing strength determine the asymptotic limit on the transverse emittance that the cooling channel can reach. The focusing strength in the channel is tapered so that the angular spread of the beam at the absorber locations remains large compared to the characteristic spread from scattering. This is achieved by keeping the focusing strength inversely proportional to the emittance, \textit{i.e.}, increasing it as the emittance is reduced. The solenoidal field profile was chosen to maximize the momentum acceptance ($\pm$22\%) through the channel. To maintain the tapering of the focusing it was eventually necessary to reduce the cell length from 2.75~m in the initial portion of the channel to 1.65 m in the final portion. A layout of the shorter cooling cells is shown in Fig.~\ref{RF:fg18.Q}. \begin{figure}[tbh] \centering \includegraphics*[width=100mm]{emit.eps} \caption[The transverse and longitudinal emittances]{The transverse (filled circles, in mm) and longitudinal (open circles, in cm) emittances, as a function of the distance down the cooling channel.} \label{EmittCool} \end{figure} \begin{figure}[tbh] \centering \includegraphics*[width=100mm]{intoap.eps} \caption[$\protect\mu /p$ yield ratio for the two transverse emittance cuts]{Muons per incident proton in the cooling channel that would fall within a normalized transverse acceptance of 15~mm (open circles) or 9.75~mm (filled circles).} \label{YieldCool} \end{figure} Figure~\ref{EmittCool} shows a simulation of cooling in this channel. The transverse emittance decreases steadily along the length of the channel. This type of channel only cools transversely, so the longitudinal emittance increases until the rf bucket is full and then remains fairly constant as particles are lost from the bucket. A useful figure of merit for cooling at a neutrino factory is the increase in the number of muons that fit within the acceptance of the downstream accelerators. This is shown in Fig.~\ref{YieldCool}. At each axial position the number of muons is shown that fall within two acceptances appropriate to a downstream accelerator. Both acceptances require the muon longitudinal phase space be less than 150~mm. The density of particles within a normalized transverse acceptance, for example, steadily increases by a factor of about 3 over the channel length, clearly showing the results of cooling. The saturation of the yield determined the chosen channel length of 108~m. \subsection{Acceleration} \begin{figure}[tbh] \centering \includegraphics[width=\textwidth]{rla2.eps} \caption{Accelerating system layout.} \label{fig:acc:layout} \end{figure} The layout of the acceleration system is shown in Fig.~\ref{fig:acc:layout}, and its parameters are listed in Table~\ref{tab:acc:parm}. The acceleration system consists of a preaccelerator linac followed by a four-pass recirculating linac. The recirculating linac allows a reduction in the amount of RF required for acceleration by passing the beam through linacs multiple times. The linacs are connected by arcs, and a separate are is used for each pass. At low energies, however, the large emittance of the beam would require a much shorter cell length and larger aperture than is desirable and needed at higher energies. This, combined with difficulties in injecting the large emittance and energy spread beam into the recirculating accelerator, and the loss of efficiency due to the phase slip at low energies, lead to the necessity for a linac that precedes the recirculating linac. A 20~m SFOFO matching section, using normal conducting rf systems, matches the beam optics to the requirements of a 2.87 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.} \label{fig:acc:cryomod} \end{figure} \begin{table}[tbh] \caption{Parameters for three types of linac cryomodules.} \label{tab:acc:linac} \centering \begin{tabular}{|l|c|c|c|} \hline Cavities per period&1&2&4\\ Period length (m)&5&8&13\\ Number of periods&11&16&19\\ Cavity type&A&A&B\\ Solenoid full aperture (cm)&46&46&36\\ Solenoid length (m)&1&1&1.5\\ Maximum solenoid field (T)&2.1&2.1&4.2\\ \hline \end{tabular} \end{table} \begin{table}[tbh] \caption{Parameters for superconducting cavities.} \label{tab:acc:cav} \centering \begin{tabular}{|l|c|c|} \hline &A&B\\ \hline Frequency (MHz)&201.25&201.25\\ Cells per cavity&2&2\\ Aperture diameter (cm)&46&30\\ Energy gain (MV)&22.5&25.5\\ RF pulse length (ms)&3&3\\ Input Power (kW)&980&1016\\ Peak surface field (MV/m)&23.1&24.3\\ $Q_0$&$6\times10^9$&$6\times10^9$\\ \hline \end{tabular} \end{table} 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, and are all in the same horizontal plane. They also utilize triplet focusing. There are around 120 arc cells, with 2.15~m dipoles, and triplet quadrupoles which are very similar to those in the linacs. The required full quadrupole apertures vary from 20~cm to 12~cm, and the dipole gaps vary from 14~cm to 9~cm. All magnet pole tip fields are under 2~T, except in the switchyard where they are as high as 2.3~T in some cases (and the magnet apertures rise to 21~cm). \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} The total equivalent 4.5~K for the entire acceleration system is 27.9~kW. 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 RLA just described, but considerably larger. \begin{table}[tbh] \caption{Main parameters of the muon accelerator.} \label{tab:acc:parm} \begin{center} \begin{tabular}{|l|c|} \hline Injection momentum (MeV/c)/Kinetic energy (MeV) & 210/129.4 \\ Final energy (GeV) & 20 \\ Initial normalized transverse acceptance (mm~rad) & 15 \\ \quad rms normalized transverse 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. Minimizing the arc length for a given length of straight maximizes the fraction of the circumference contained in the straight section, thereby maximizing the fraction of neutrinos (around 35\% in our case) decaying toward the detector. Furthermore, the beta functions in the downward-going straight (which is pointed toward the detector) are made large to reduce the angular divergence of the beam. This ensures that the angular divergence of the beam is dominated by the calculable relativistic angular divergence of the decay neutrinos. The goal of this is not only to make the angular divergence of the neutrino beam as small as possible and therefore maximize the flux, but it also reduces the experimental uncertainty associated with an uncertainty in the flux that would come from an uncertainty in the angular divergence of the muon beam. \begin{figure}[t] \centering \includegraphics[width=\textwidth]{xupdn-a-model-view-iron5} \caption{Three-dimensional view of the storage ring magnets.} \label{fig:sr:mag} \end{figure} 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 (see Fig.~\ref{fig:sr:mag}) has been chosen that allows the majority of these electrons to exit 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. The result is a skew FODO lattice, giving diagonal oscillations, as opposed to the horizontal and vertical oscillations of the usual upright FODO lattice. 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 smokestack 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. The beam is allowed to debunch in the storage ring. In one muon lifetime (0.42~ms), a bunch with the full energy spread ($\pm\text{2.2\%}$) will have its total length increase by 0.51~$\mu$s (the storage ring is 1.19~$\mu$s long, and the bunch train starts out 0.33~$\mu$s long). If one wishes to avoid the increase in the bunch train length, one could install RF cavities, but the voltage required to avoid energy spread increase for the momentum compaction in this ring is prohibitive: a better solution would be a ring re-designed to have very low momentum compaction. \begin{table}[tb] \caption{Muon storage ring parameters.} \label{SRING:tb} \begin{center} \begin{tabular}{|l|l|} \hline Energy (GeV) & 20 \\ Circumference (m) & 358.18 \\ Normalized transverse acceptance (mm~rad) & 30 \\ Energy acceptance (\%) & 2.2 \\ Momentum compaction&0.028\\ \hline \multicolumn{2}{c}{\underline{Arc}} \\ \hline 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 \\ \hline \multicolumn{2}{c}{\underline{Production Straight}} \\ \hline 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 lattice solutions have been found for this option as well. \subsection{Overall Machine Summary} \begin{figure}[t] \centering\includegraphics[width=100mm]{allcount.eps} \caption{Muons per incident proton in the Study~II neutrino factory front end.} \label{fig:all:muonp} \end{figure} \begin{table}[t] \caption{Muon survival and losses in several sections of the Study~II neutrino factory. $\mu/p$ is the number of muons per proton at the end of that section, and ``Loss'' is the loss in that section.} \label{tab:all:muloss} \begin{tabular}{|l|r|r|} \hline Section&$\mu$/p&Loss\\ \hline Phase rotation&0.60&\multicolumn{1}{c|}{---}\\ Buncher&0.47&22\%\\ Cooling&0.22&53\%\\ Accelerator aperture&0.16&26\%\\ Preaccelerator Linac&0.15&10\%\\ Recirculating Linac&0.13&10\%\\ \hline \end{tabular} \end{table} Figure~\ref{fig:all:muonp} shows the muons per incident proton in the ``front end'' (everything before the acceleration) of the Study~II neutrino factory. Table~\ref{tab:all:muloss} gives the values at the ends of several sections and the losses in those sections. These significant losses are a necessary cost of making a low-emittance beam that can be accelerated and injected into a storage ring. An overall layout of the Neutrino Factory on the BNL site is shown in Fig.~\ref{bnlsite}. 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] %% figure 21 \centering \includegraphics[width=4.0in]{mole-hill.eps} \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] %% figure 22 \begin{center} \includegraphics[angle=90,width=0.9\linewidth]{site1-Layout1.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] %% figure 23 \begin{center} \includegraphics[width=4in,angle=270]{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, the need to maintain a high neutrino rate at these long distances requires detectors 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 final design of a Neutrino Factory, these two factors would 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.eps} \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.eps} \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 possibility for a Neutrino Factory detector is a massive liquid-argon magnetized detector~\cite{landd} that would also attempt to detect proton decay, as well as solar and supernova neutrinos. \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, neutrino 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 time projection chamber (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 mass 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 neutrino 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 ${\cal O}$(1~Hz). \subsection{Staging Options} \label{StagingOps} It seems quite possible---perhaps even likely---that the Neutrino Factory would be built in stages, both for programmatic and for cost reasons. Here we outline a possible staging concept that provides good physics opportunities at each stage. The staging scenario we consider is not unique, nor is it necessarily optimized. Depending on the results of our technical studies and the results of continued searches for the Higgs boson, it is hoped that the Neutrino Factory is really the penultimate stage, to be followed later by a Muon Collider (Higgs Factory). We assume this possibility in the staging discussion that follows. Because the physics program would be different at different stages, it is impractical at this time to consider detector details. \subsubsection{Stage 1} In the first stage, we envision a Proton Driver and a Target Facility to create superbeams. The Driver could begin with a 1 MW beam level (Stage 1) or could be designed from the outset to reach 4 MW (Stage 1a). (Since the cost differential between 1 and 4 MW is not expected to be large, we do not consider any intermediate options here.) It is assumed, as was the case for both Study~I and Study~II, that the Target Facility is built from the outset to accommodate a 4 MW beam. Based on the Study~II results, a 1 MW beam would provide about $1.2\times 10^{14}$ $\mu $/s ($1.2\times 10^{21}$ $\mu $/year) and a 4 MW beam about $5\times 10^{14}$ $\mu $/s ($5\times 10^{21}$ $\mu$/year) into a solenoid channel. In addition to the neutrino program, this stage will also benefit $\pi $, $K$, and $\overline{p}$ programs, as discussed in~\cite{proton-physics,low-pbar}. \subsubsection{Stage 2} In Stage 2, we envision a muon beam that has been phase rotated (to give a reasonably low momentum spread) and transversely cooled. In the nomenclature of Study~II, this stage takes us to the end of the cooling channel. Thus, we have access to a muon beam with a central momentum of about 200 MeV/c, a transverse (normalized) emittance of 2.7~mm~rad and an rms energy spread of about 4.5\%. The intensity of the beam would be about $4\times 10^{13}$ $\mu $/s ($4\times 10^{20}$ $\mu $/year) at 1 MW, or $1.7\times 10^{14}$ $\mu $/s ($1.7\times 10^{21}$ $\mu $/year) at 4 MW. If more intensity were needed, and if less cooling could be tolerated, the length of the cooling channel could be reduced. As an example, stopping at the end of Lattice 1 instead of the end of Lattice 2 in the Study~II cooling channel would result in an increase of transverse emittance by roughly a factor of two. This is an appropriate stage to mount an experiment to search for a non-zero muon electric dipole moment. \subsubsection{Stage 3} In Stage 3, we envision using the Pre-acceleration Linac to raise the beam energy to roughly 2.5 GeV. At this juncture, it may be appropriate to consider a small storage ring, comparable to the $g-2$ ring at BNL, to be used for the next round of muon $g-2$ experiments. \subsubsection{Stage 4} At Stage 4, we envision having a complete Neutrino Factory operating with a 20~GeV storage ring. This stage includes the RLA and the storage ring. If it were necessary to provide a 50 GeV muon beam as Stage 4a, an additional RLA and a larger storage ring would be needed. \subsubsection{Stage 5} In Stage 5, we could envision an entry-level Muon Collider operating as a Higgs Factory. Because the initial muon beam must be prepared as a single bunch of each charge, an additional ring for the proton driver to coalesce proton bunches into a single pulse is anticipated. The cooling will have to be significantly augmented. First, a much lower transverse emittance is needed, and second, it will be necessary to provide longitudinal cooling (emittance exchange) to maintain a reasonable transmission of the muons. The additional cooling will permit going to smaller solenoids and higher frequency rf systems (402.5 or perhaps 805 MHz), which should provide more cost-effective cooling. Next, we will need considerably more acceleration, though with smaller energy acceptance and aperture requirements than at present. Lastly, we will need a very low $\beta ^{\ast }$ lattice for the collider ring, along with mitigation of the potentially copious background levels near the interaction point. In this case the detector is, in effect, part of the collider ring, and its design must be an integral part of the overall ring design.