%\documentclass{iopart} %\usepackage{graphicx} %\begin{document} \section{Neutrino Beam Design} The geographic location of BNL on one side of the continent allows us to send beams to a variety of distances including very long baselines of 2000 km or more. This is shown in Fig. \ref{blines}. The distances from BNL to Lansing NY, Soudan MN, Lead SD(Homestake), and WIPP in NM are 350, 1770, 2540, and 2880 km, respectively. The respective dip angles are 1.7, 7.9, 11.5, and 13.0 degrees. The difficulty of building the beam and the cost increases with the dip angle. Our preliminary design for a beam to Homestake is shown in figures \ref{planview} and \ref{eleview}. This can be adapted to any far location in the western direction. Our design addresses a number of issues. At BNL we are constrained to keep the beam line above the water table which is at a shallow depth ($\sim$ 20 m) on Long Island. Therefore the beam has to be constructed on a hill that is built with the appropriate 11.5 degree slope. Fortunately, it is relatively easy, and inexpensive to build such hills on Long Island because of the flat, sandy geology. It is important to keep the height of the hill low so that the costs are not dominated by the construction of the hill. The proton beam must be elevated to a target station on top of the hill. The cost of the hill can be lowered by bending the proton beam upwards as quickly as possible. We have, however, used the design and bend angle used for the RHIC injection lines for our design because the RHIC injection lines have well known costs. The new proposed fast extracted proton beam line in the U-line tunnel will be a spur off the line feeding RHIC. It will turn almost due west, a few hundred meters before the horn-target building. In addition to its 90 degree bend, the extracted proton beam will be bent upward through 13.76 degrees to strike the proton target. The downward 11.30 degree angle of the 200 meter %667.8 ft meson decay region will then be aimed at the 2500 meter level of the Homestake Laboratory. This will require the construction of a 39 meter hill to support the target-horn building, so as to avoid any penetration of the water table. At its midpoint (about Lake Michigan) the center of the neutrino beam will be roughly 120 km below the Earth's surface. For a shorter baseline to Lansing NY in approximately the same direction as Homestake, we would not have to build the hill, which would lower the cost by a considerable amount. We are considering a number of strategies for combining the proton transport and the target station for the two different baselines. \begin{sidewaysfigure} \begin{center} \includegraphics*[angle=-90,width=\textwidth]{figs/ap-2.eps} \caption{ The beam line for sending a neutrino beam to Homestake mine, South Dakota. This same beam line can be adapted for any far location in the Western direction.} \label{planview} \end{center} \end{sidewaysfigure} \begin{sidewaysfigure} \begin{center} % \includegraphics*[bb=240 30 400 555,width=0.34\textwidth,angle=270]{figs/ap-1.eps} % \includegraphics*[bb=240 570 400 740,width=0.34\textwidth,angle=270]{figs/ap-1.eps} \includegraphics*[width=\textwidth]{figs/hill.eps} \caption{Elevation view of the neutrino beam line to Homestake, South Dakota. For a nearer location a much smaller hill can be constructed. In this beam we assume a decay tunnel length of 200 m. For a shorter tunnel the cost of the hill will reduce as shown in Table \ref{bcost}. } \label{eleview} \end{center} \end{sidewaysfigure} \begin{figure} \begin{center} \includegraphics*[width=0.9\textwidth]{figs/bnl_near.eps} \includegraphics*[width=0.9\textwidth]{figs/bnl_wipp_lead.eps} \caption{Possibilities for baselines from BNL. The distances from BNL to Lansing, Soudan, Lead (Homestake), and WIPP are 350, 1770, 2540, and 2880 km, respectively. } \label{blines} \end{center} \end{figure} \begin{figure} \begin{center} \includegraphics*[width=0.8\textwidth]{figs/fig3a19.eps} \caption{The design of the horn focussing system used for the E734 experiment adapted from the E889 proposal.} \label{horns} \end{center} \end{figure} \begin{figure} \begin{center} \includegraphics*[width=0.5\textwidth]{horngeant.epsi} \caption{ The horn geometry in the GEANT simulation. The vertical and horizontal scales are in the ratio of 1 to 13. The beam is incident from the right.} \label{horns2} \end{center} \end{figure} \subsection{Optimization of the wide band spectrum} \begin{figure} \begin{center} \includegraphics*[width=\textwidth]{copper_numu.eps} \caption{Wide band horn focussed neutrino spectrum for 28 \GeV{} protons on a Copper target. The spectrum is approximately the same if Super-Invar is used as target material. Spectra of neutrinos are calculated at various angles with respect to the 200 m decay tunnel axis at the AGS and at a distance of 1 km from the target.} \label{bnlspec} \end{center} \end{figure} For this report we have attempted to optimize the beam for the Homestake distance (2540 km). However, our optimization process could be applied to any distance. As explained in later sections, the ideal beam for Homestake should be a broadband beam that covers $\sim$0.5 GeV to $\sim$7.0 GeV range. The $\nu_\mu \to \nu_e$ process through $\Delta m^2_{12}$ (solar oscillations) could make large effects ($\sim$ 10\%) at the lowest energies. The energy range $1-3 ~GeV$ could be important for the detection of CP violation. The energy region $3-5$ GeV contains the first matter enhanced (for neutrinos with standard mass hierarchy) $\nu_\mu \to \nu_e$ oscillation maximum. In the following we will argue that the highest energies are important for establishing the existence of $\nu_\mu \to \nu_e$ signature because this region is free from the neutral curernt $\pi^0$ background and should have very good efficiency for the signal. Lastly the energy region $6-7$ GeV is important for the $\nu_\mu \to \nu_\mu$ disapearance measurement. To obtain such a broad band spectrum we have adapted the standard scheme of multiple parabolic horns. Each one focussing a different pion momentum region. The difficulty with this approach is that the lowest energy we need to capture and focus approximately 1-2 GeV pions that come from a long target. Fig. \ref{horns} and \ref{horns2} shows the design of the target and horn geometry for a conventional wide band neutrino beam similar to that used in previous experiments at BNL such as E734. The E734 design uses a water cooled 1.5 interaction length copper target. The calculated energy distributions of a $\nu_{\mu}$ beam produced by 28 \GeV{} protons is shown in Fig.~\ref{bnlspec}~\cite{e889}. The $0^\circ$ calculation has been shown consistent with neutrino beam data~\cite{e734}. The spectrum peaks at about 1 \GeV{} with a total spread at half intensity of about 1 \GeV{}. A copper target will not survive the $\sim$ 1 MW intensity of proton beam that we propose. Therefore both new materials and new focussing geometries must be considered. We discuss the target in much more detail in a later section. The two main issues in the target design are the target material and the space available for cooling the target. If a dense material such as Super-Invar is used then the spectrum will be approximately the same as shown in Fig. \ref{bnlspec}. The better approach is to use graphite as target material and modify the horn geometry to allow a longer target (Fig. \ref{horns2}). The result of these modifications is shown in Fig. \ref{ctarg1}. The electron neutrino contamination is shown on the same scale in Fig. \ref{ctarg2}. We have used a 1.5 interaction length graphite target. As shown in the figures the flux resulting from a graphite target is considerably higher in the 3.5 to 8 GeV region. There is no significant change in the ratio of electron type neutrinos to muon type neutrinos between a graphite and a copper target. We will use the flux from Figs. \ref{ctarg1} and \ref{ctarg2} for the calculation of event rates and backgrounds in the rest of this report. There is a large ($\sim 50\%$) model dependent uncertainty on the neutrino flux at high energies ($>4~GeV$). In particular the hadron production model in MARS gives lower flux than in GEANT.\cite{mars} This uncertainty will most likely be resolved by new experiments\cite{harp, e910, mipp} in the near future. %( I need some references to HARP, E951, etc. ) \begin{figure} \begin{center} \includegraphics*[width=\textwidth]{carbon_flux.eps} \caption{Wide band horn focussed muon neutrino spectrum for 28 \GeV{} protons on a graphite target. The spectra of neutrinos are calculated at various angles with respect to the 200 m decay tunnel axis and at a distance of 1 km from the target.} \label{ctarg1} \end{center} \end{figure} \begin{figure} \begin{center} \includegraphics*[width=\textwidth]{carbon_nueflux.eps} \caption{Wide band horn focussed electron neutrino spectrum for 28 \GeV{} protons on a graphite target. Spectra of $\nu_e$ are calculated at various angles with respect to the 200 m decay tunnel axis and at a distance of 1 km from the target.} \label{ctarg2} \end{center} \end{figure} Further work on the optimization of this spectrum for the very long baseline experiment is on going. Further optimization focusses on enlarging the horns to accept more lower energy pions so that the flux near 0.5 GeV can be enhanced, as well as using the hadronic hose \cite{numihose} to capture more higher energy particles. %It is very likely that we can adapt the %graphite target design used for NuMI at FNAL. Our design calls for the target to be inside the 2.5 cm diameter aperture of the first horn, where the space is limited. The resulting heat and radiation load on the materials will present a severe challenge for the mechanical construction of this device. \subsection{Cost of the beam} A preliminary estimate of the cost without any of the customary burdens is shown in Table \ref{bcost}. The costs are based on the the RHIC injector work, as well as the E889 proposal and the neutrino factory study. The conventional construction costs are dominated by the size of the hill which is approximately proportional to the third power of the decay tunnel length. In our cost estimate we assume that we will bury the beam dump underground to reduce the height of the hill. It is assumed that the target station shielding can be retrieved from existing resources. We have also estimated the cost assuming a 200 m long decay tunnel. Shortening the decay tunnel to 150 m would only save \$ 3 M and would reduce the high energy ($E_\nu >2$ GeV) flux by $\sim 25\%$. We will study this optimization further in future updates of this proposal. The spectra shown in Fig. \ref{bnlspec} are based on a 200 m long tunnel. %A shorter tunnel could reduce the intensity at higher energies %because of the longer flight paths of parent pions. \begin{table} \begin{center} \begin{tabular}{|l|l|r|} \hline Item & basis & cost \\\hline %Proton transport & RHIC injector & \$8.3 M \\ Proton transport & RHIC injector & \$11.85 M \\ Target/horn & E889 & \$3.0 M \\ Installation/Beam Dump & New & \$2.67 M \\ Decay Tunnel & E889 & \$0.45 M \\ Conventional const. (hill) & New & \$8.0 M \\ %Conventional const. (other) & E889 & \$6.77 M \\ Conventional const. (other) & E889 & \$9.1 M \\ \hline Total & & \$35.19 \\ \hline \end{tabular} \caption{Preliminary cost of building the neutrino beam with 200 meter decay tunnel. If the tunnel length were reduced to 150 meters a savings of \$3 M could be realized at a cost of losing 25\% of the neutrino flux with $E_\nu> 2$ GeV.} \label{bcost} \end{center} \end{table} \vspace{1ex} \subsection{Target Station} To use the 1 MW proton driver proposed for BNL, serious consideration must be given to the target selection. It is desirable to choose a solid target for generating a high intensity neutrino beam. For pion production with powerful protons beams, target integrity becomes an important issue. Up to now, the production of secondary particles has been limited to proton beams with average beam power on the order of 100 to 200 kW. We now have to consider a target which can survive a 1 MW or greater average power proton beam. For a 28 GeV proton beam, 1 MW beam power implies $2.23\times 10^{14}$ proton/sec. For a rep-rate of 2.5 Hz we then must consider nearly 100 TP per spill. The target must be able to withstand a 1 MW proton beam. A number of options have been considered and investigated both in terms of the material selection as well as the feasibility of target configuration. In evaluating the target choices the following concerns are being addressed: \begin{itemize} \item Heat removal from the target. \item Survivability of the target intercepting energetic, high intensity proton bunches. \item Irradiation issues \item Engineering integration issues \item Heat generation and removal from the horn \item Horn mechanical response \end{itemize} Findings of a number of recent studies \cite{study2}, including experimental results from E951 \cite{e951}, on target issues for the muon collider/neutrino factory project are taken into consideration in this effort. Figs. \ref{hkirk2} and \ref{hkirk3} show the spectra of $\pi^+$ and $\pi^-$ that are produced from a 2-interaction length target for various materials. For a conventional neutrino beam the useful part of the pion spectrum is in the energy region beyond 2 GeV. For this reason, high-Z targets are no longer advantageous. We find instead that for the production of high-energy pions, low\-Z targets are preferred. In addition to maximizing the flux, the target/horn configuration must survive the thermal shock induced by the beam and the high current. Specifically, the target scheme must (a) ensure the removal of the deposited beam energy within the 400 ms period and (b) survive the thermally induced elastodynamic stresses that are expected to be comparible to the mechanical strength of most common materials. Similar concerns are valid for the horn, itself, which will be subjected to rapid heating and, as a result, high levels of thermal stress that will propagate in its volume. In order to satisfy the first requirement, several cooling scenarios are being investigated such as edge-cooling, forced helium cooling in the space between the target and the horn, and radiation cooling. All of these schemes present challenges stemming from integration with the horn in a limited space. To satisfy the second requirement, materials must be selected such that they can withstand and attenuate the thermal shock and be radiation resistant. To address this, low-Z carbon based materials such as graphite and carbon-carbon composites are being considered. These materials, while they have a lot of promise, present some challenges. Fig. \ref{horn} shows the target mounted in the first horn. Also the helium cooling system for the target and the water cooling manifold for the horn are indicated. \begin{figure} \begin{center} \includegraphics*[width=\textwidth]{horn_drawing.eps} \caption{Sketch of the first horn with the graphite target mounted. The target is cooled by helium. The horn is cooled by spraying water on the conducting surface.} \end{center} \end{figure} Two different forms of carbon, ATJ graphite and a carbon-carbon composite are considered as candidate target materials. These two types have been exposed to the AGS beam in the E951 experiment\cite{e951}. The carbon-carbon composite is a 3-D weaved material that exhibits extremely low thermal expansion below 1000$^o$C and responds like graphite above that. Preliminary studies on the feasibility of using carbon-based targets for this neutrino beam have been conducted. Specifically, utilizing the energy deposition estimates from MARS for 1 mm and 2 mm RMS beam spots (corresponding to 3 mm and 6 mm radii of target), the thermal shock response and the survivability potential of the target were studied. The total energy deposited on the target (and which needs to be removed between pulses) is 5.1 kJ for the 1mm spot and 7.3 kJ for the 2mm spot. Since the 1 mm RMS beam spot is the most serious case, it is examined in detail. For the 100 TP beam the peak energy density is of the order of 720 J/gram. This is expected to lead to instantaneous temperature increases of $\sim 1000^\circ$C. A detailed finite-element analyses that involve both the horn and the target needs to be performed so the heat removal of the system can be optimized and, most importantly, for the thermal shock stresses need to be computed. A material with a small thermal expansion should experience smaller thermal stresses. However, carbon-carbon composite materials exhibit an increaseing thermal expansion at higher temperatures. This behavior of the material needs to be examined further. If the high temperture performance of this material is not satisfactory a larger beam spot size could be used. >From energy density considerations a 2 mm rms beam spot would have a peak temperature rise per pulse that is less than a third of the 1 mm rms case. This would ensure that the material will be well within the safe zone. Cooling of the front-end is achieved by maintaining the temperature at the surface of the first 4 cm to 27 $^o$C. %\begin{figure} % \begin{center} % \includegraphics*[width=\textwidth]{hkirk/W_pions.eps} % \caption{ } % \label{hkirk1} % \end{center} %\end{figure} \begin{figure} \begin{center} \includegraphics*[width=\textwidth]{hkirk/pi+.ps} \caption{The number of $\pi^+$ per incident proton is shown as a function of its momentum for carbon, copper and mercury targets. The target is two interactons lengths long for each material.} \label{hkirk2} \end{center} \end{figure} \begin{figure} \begin{center} \includegraphics*[width=\textwidth]{hkirk/pi-.ps} \caption{The number of $\pi^-$ per incident proton is shown as a function of its momentum for carbon, copper and mercury targets. The target is two interactons lengths long for each material.} \label{hkirk3} \end{center} \end{figure} We examine the optimal geometry for high-energy pion production utilizing a carbon target. In Fig. \ref{hkirk4} we see the result of varying the radius of a 1.5 interaction length (60 cm) long carbon target. For this analysis the target radius was constrained to 3 times the proton beam rms radius. We note that although the total secondary pion production increases with radius, the desired high-energy portion of the production spectra is enhanced with smaller beam spot sizes. In Fig. \ref{hkirk5} we fix the beam/target radius at (2mm/6mm) and find that the production of 7-9 GeV pions increases with target length up to about 80 cm (2 interaction lengths) and then remains essentially constant up to 2 m. We now explore the impact of bringing to bear 100 TP proton/spill onto a carbon target. For this analysis we utilize MARS to calculate the energy deposition due to the hadronic showering within the target. We examine the two cases of 3 mm and 6 mm radius targets shown in figure \ref{hkirk6}. We note the peak energy deposition density occurs near the entrance of the target and has the respective values of 700 and 200 J/g. As a figure of merit, 300 J/g is considered the danger regime where metal targets suffer damage due the propagation of thermal generated pressure waves through the material. There is, however, evidence that carbon can withstand energy depositions in this regime. The best evidence to date comes from experience in the NUMI target development program. The NUMI carbon target is designed to expect 390 J/g peak energy deposition. A NUMI target test, performed in 1999, utilized a specially focussed beam to produce energy depositions in the range of 400 to 1100 J/g without any external evidence of target breakup. \begin{figure} \begin{center} \includegraphics*[width=\textwidth]{hkirk/vary_r.ps} \caption{The ratio of the numbers secondaries to the number of primaries is shown as a function of RMS beam radius. The target radius is assumed to be three times the RMS beam radius and the target length is 1.5 interaction lengths.} \label{hkirk4} \end{center} \end{figure} \begin{figure} \begin{center} \includegraphics*[width=\textwidth]{hkirk/vary_l.ps} \caption{The ratio of the number of secondaries to the number of primaries is shown as a function of the target length for a target radius of 6 mm and a RMS beam size of 2 mm.} \label{hkirk5} \end{center} \end{figure} \begin{figure} \begin{center} \includegraphics*[width=\textwidth]{hkirk/carbon_edep.ps} \caption{The energy deposition is shown as a function of target axial position for a 28 GeV 100 TP beam.} \label{hkirk6} \end{center} \end{figure} %A low-Z target is preferable for the production of high-energy pions, %and will be the design option to be studied in greater detail in future. %The current study concentrated on a carbon/carbon option. However, %other candidates will also be investigated, The secondary particle shower resulting from the interaction of primary protons with the low-Z target will add to the transient heat load of the horn. This shower will be less significant for low-Z targets than for high-Z targets. However, its effect will be examined, and added to the electric resistance heat load estimated above. The resulting activation of the target and horn structure due to secondary and primary particles will be estimated. This activation will be primarily due to spallation products and activation due to neutrons generated in the secondary shower. The survival of the primary target in the radiation field needs to be examined. This can only be carried out experimentally using a prototypic proton beam on samples of the appropriate target material. The change in physical properties including, thermal expansion coefficient, elastic modulus, and yield strength need to be examined as a function of proton fluence. \subsection{Comparison of NuMI and BNL spectra} \begin{figure} \begin{center} \includegraphics*[width=\textwidth]{bnl_flux_0.4mw.eps} \caption{Wide band horn focussed muon neutrino spectrum for 28 \GeV{} protons on a Carbon target. Spectrum of neutrinos are calculated at various angles with respect to the 200 m decay tunnel axis at the AGS and at a distance of 1 km from the target.} \label{bnlmw} \end{center} \end{figure} \begin{figure} \begin{center} \includegraphics*[width=\textwidth]{numibeam.eps} \caption{ The low energy beam at the NuMI facility at FNAL. The flux is plotted on the same scale in proton beam power as the BNL beam. It has also been scaled to be at the same location (1 km) for comparison. The target-horn geometry, the length of the decay tunnel ($\sim 735 m$) and the primary proton energy (120 GeV) are different for the NuMI beam. } \label{numib} \end{center} \end{figure} In figures \ref{bnlmw} and \ref{numib} we plot the muon neutrino flux using the AGS and the FNAL main injector (the NuMI facility) on the same scale. The NuMI beam was designed to produce peak flux at 3 GeV for the MINOS experiment. Nevertheless, we see that the both fluxes are comparable when scaled to be at the same proton beam power level. The NuMI flux, of course, has higher flux at higher energy both because of the higher proton beam energy as well as longer decay tunnel. The level of electron neutrino contamination is approximately the same in both beams. %\end{document}