
\section{E951 R and D Effort
}

\subsection{Introduction 
}

A muon collider/neutrino factory based on a muon storage ring
 requires a tightly focused, high intensity beam on target. Specifically,
 up to 16 TP per pulse of a 24 GeV proton beam need to be delivered
 on a target. While a mercury jet is the primary target consideration
 (high-Z material and more efficient in producing pions of both
 signs), other options using graphite as target material (low-Z
 and better in avoiding the absorption of produced pions) are
 also being explored. The broad goal of E951 is to provide a
 facility that can test all the major components of a liquid
 or solid targets in intense proton pulses and in a high field
 solenoid. The first phase of E951 has focused on the interaction
 of intense proton pulses with targets and beam windows in zero
 magnetic field.

In the first phase of the E951 experiment a series of different
 experiments were designed and conducted in an effort to understand
 and evaluate a variety of issues that ranged from target material
 response to tightly focused proton beams to estimates of mercury
 dispersion velocities. Specifically, the experimental matrix
 included: (a) the study of window materials, (b) the evaluation
 of graphite and carbon-carbon composite as alternative low-Z
 target materials, (c) the behavior of a mercury pool intercepting
 the proton beam and the correlation of the energy deposited
 to ejection velocities and (d), the interaction of the proton
 beam with a mercury jet and the subsequent destruction of the
 jet including measurements of velocities of material dispersion.
\begin{figure}[thb!]
\centering
\includegraphics*[width=5in]{simos/simos-fig1.eps}
\caption[Comparison of measured strains between a 100 KHz and a 500 KHz  ]{Comparison of measured strains between a 100 KHz and a 500 KHz processed strain signal in the vicinity of the arrival of the initial shock wave at mid-radius of the aluminum window  }
\label{simos:fig1}
\end{figure}

Figure~\ref{simos:fig1} depicts the layout of the A3 beam line near the target
 station that has been configured for the transport of primary
 24 GeV protons extracted from the AGS. All targets are mounted
 inside a stainless steel vessel preventing any dispersal of
 activated fragments that can potentially be ejected from the
 tested target.  The details of each arrangement will be presented
 in later sections. Figure~\ref{simos:fig2} represents the measured beam spot
 size in the two planes at the end of the A3 line that may be
 achieved through fine-tuning of the various quadrupoles. 
\begin{figure}[thb!]
\centering
\includegraphics*[width=5in]{simos/simos-fig2.eps}
\caption{Strain measured in aluminum window in back-to-back pulses of similar intensity  }
\label{simos:fig2}
\end{figure}
\subsubsection{Window Study}

The window material study focuses on the thermo-mechanical response
 of the selected materials and their ability to survive the tightly
 focused beam for multiple pulses. Based on the required muon
 collider beam parameters, it was concluded early on that very
 few materials will be able to survive the thermal shock induced
 by even a single pulse, let alone multiple pulses. While in
 the actual muon collider target configuration the beam window
 location may be optimized (achieve bigger beam spot based on
 the beam beta function), in the E951 experiment it is required
 for the beam window to be close to the target. In order to select
 the right window material that will survive under such conditions,
 an extensive effort was undertaken to evaluate different materials
 that show promise based on their mechanical strength. 

The window study was two-fold. It included the prediction phase
 and the experimental verification. In the prediction phase,
 the energy deposition on the different window materials and
 for the anticipated AGS beam parameters were estimated using
 the hadron interaction code MARS~\cite{simos:ref1}. This was followed by
 a transient thermal analysis resulting from the deposited energy
 and finally by a thermal stress analysis that included the generation
 and propagation of stress waves. The thermal response of the
 window structure and the subsequent stress wave generation and
 propagation were computed using the finite element code ANSYS~\cite{simos:ref2}.  
In the experimental verification, the recorded transient
 strain in the actual windows was compared to the predicted strain
 levels and wave shapes. The primary goal in such comparison
 was to verify that the prediction at this lower intensity level
 is ``trustworthy'' and can safely be used to extrapolate to the
 higher intensities required and address the material failure
 potential. Additionally, and as part of the experimental verification
 study, the impact of irradiation on the mechanical/strength
 properties of the selected materials is examined closely. The
 latter is an on-going effort.
\subsubsection{Carbon Targets}
The experimental effort on low-Z solid targets included the study
 of ATJ graphite and carbon-carbon composite by exposing them
 to the tightly focused 24 GeV AGS beam. The primary goals of
 this task was to (a) assess the survivability of the graphite
 target to the anticipated high intensity beam, and (b) to experimentally
 verify the promise of the carbon-carbon composite of having
 a very small thermal expansion coefficient that, in turn, implies
 small generated stress waves. Verification of the latter will
 be significant in that a beam power of the order of 1 MW could
 be envisioned using such target.
\subsubsection{CERN Mercury Trough Target}
\begin{figure}[thb!]
\centering
\includegraphics*[width=4in]{simos/simos-fig3.eps}
\caption[Cross Correlation of signals in different gauges  ]{Cross Correlation of signals in different gauges of the same window to assess the position of the pulse relative to the gauges based on the lag time of stress pulse arrival  }
\label{simos:fig3}
\end{figure}
Part of the experimental matrix of E951 was the CERN mercury
 target configuration. This passive target arrangement, shown
 in Fig.~\ref{simos:fig3}, consisted of a pool of mercury in a well engraved
 into a stainless steel block. The target is inside a special
 container that allowed for the anticipated dispersed mercury
 to collect back into the well while permitting the capturing
 of the event by fast cameras through a side viewing window.
 The primary goal of this passive mercury target experiment was
 to measure with the fast cameras the velocity of the mercury
 ejected from the free surface of the pool and correlate it
 with the analytical predictions. Peak ejection velocities of
 70 m/s were observed during the experiment generally following
 the theoretical predictions. Such low velocity values, compared
 to the velocities that pressure waves in the mercury propagate
 with, confirm that the potential for destruction of the target
 enclosure by the mercury projectiles is nonexistent.

\subsection{Mercury Jet Target}

The active mercury target of E951 consisted of a mercury jet
 intercepting the AGS proton beam as shown in Fig.~\ref{simos:fig4}. In
 this first phase of the experiment, no magnetic solenoid field
 was integrated with the experiment.
\begin{figure}[thb!]
\centering
\includegraphics*[width=5in]{simos/simos-fig4.eps}
\caption{ Recorded strain in 1mm Inconel window }
\label{simos:fig4}
\end{figure}

The potential use of a mercury jet target for the muon collider/neutrino
 factory has raised several novel issues that needed clarification
 through experimental means. These include dispersion of the
 jet due to rapid energy deposition, destruction of the jet by
 magnetic forces, and ejection of high velocity droplets that
 can damage the confining envelope. The latter was also addressed
 in the CERN mercury target configuration. Additionally, a potentially
 challenging design issue associated with the target configuration
 is the possibility of shock wave impact and consequently potential
 damage on the jet nozzle that sends the jet into the solenoid.
 To address this design issue an attempt was made to record the
 dynamic strains in the vicinity of the nozzle. The appearance
 of strain waves, following the beam/jet interaction, will signal
 the arrival of pressure waves at the nozzle location.

E951 verified that the indeed the jet will destruct by interacting
 with a single proton pulse that has even much lower intensity
 than the 16 TP anticipated in the actual muon collider/neutrino
 factory. The good news is that the destruction process, as predicted
 by calculations, was proven to be slower than the pressure waves
 generated in the jet and that the dispersed mercury ejects with
 velocities that are a fraction of the sound speed in mercury.

Preliminary assessment of pressure wave travel back to the nozzle
 shows that, while small given the much lower intensity achieved
 during E951, there is evidence of such travel back toward the
 nozzle. It is difficult, however, based on these findings, to
 extrapolate to the actual target and assess the susceptibility
 of the nozzle to repeated loading from these waves.
\subsection{
E951  Beam Window Study
}

\subsubsection{Issues
}
Given the set of beam parameters required for the muon collider/neutrino
 factory, i.e. 16 TP intensity and 0.5mm rms sigma radius, the
 resulting energy density within the one sigma radius of the
 beam will induce a stress field that for many materials will
 exceed the yield strength limit. 

Figure~\ref{simos:fig4} is a clear example of that. It depicts peak thermal
 stresses in a 10-mil thick stainless steel window induced by
 a beam with such parameters (24 GeV, 16 TP, 0.5 mm sigma and
 100 ns pulse length). Specifically, the peak von Mises stresses
 in the window material, occurring at beam center and mid-thickness,
 approaches 2500 MPa that is more that twice the yield and ultimate
 strength of the material.

Since such severe conditions will result after a single proton
 pulse for some materials and after several pulses for the better
 materials, depending on the spacing between the pulses in the
 train, it is very important to obtain a better understanding
 of the way these materials respond to such severe exposure,
 and of the way their properties degrade with radiation exposure.
 The latter needs to be combined with fatigue failure properties
 to establish the criteria for the amount of ``beating'' a good
 window material can take before it reaches its failure limits.
 Thus, the beam window issues that E951 was set to address may
 be summarized in the following:
\begin{enumerate}
\item 
Survivability of windows based on a single beam pulse
\item Survivability of windows to a series of pulses
\item Assessment of the effects of irradiation on the mechanical properties
 of the candidate materials
\end{enumerate}
Detailed dynamic analysis that capture the window structure response
 helped guide the selection of materials to be tested. These
 analysis also provided the basis needed for quantitative comparison
 with the experimental results. Confidence in the methodology
 used to make the predictions will allow for the extrapolation
 of the data to conditions required in the real muon collider
 target. These conditions were not anticipated to be achieved
 in the first phase of E951, simultaneously at least. The material
 matrix that was finally selected included a 10-mil thick 3000
 series aluminum window, a 9-mil thick titanium alloy, an 11-mil
 thick havar, and two inconel-718 alloy windows in two thicknesses
 (1~mm and 6~mm).
\subsection{Goals of Experimental Effort
}
The goals of the first phase of the window experiment effort
 are summarized below:
\begin{enumerate}
\item 
Verification of the predictions to form the basis for extrapolation
 of results for the more intense beam as well as the design of
 the ``real thing''
\item 
``Real'' environment exposure of the selected materials as window
 structures and understanding of their response based on measurable
 quantities that can be directly connected to the failure mechanism,
 i.e. stress and strain
\item 
Assessment of  ``thin'' vs. ``thick'' in windows. Given that the
 ability of a beam window structure to ``diffuse'' an undiluted
 beam is a function of a number of parameters (sound velocity,
 beam structure and thickness), the controllable parameter of
 thickness and its effect is addressed in the experiment
\item 
Address ``failure'' in the window material. Given that failure
 means different things to different people, the goals of E951
 were to (a) qualitatively assess the potential that the window
 materials failed by monitoring the breach of vacuum in the enclosed
 space of a double window arrangement, and (b) to examine the
 affected zone window  that intercepted the beam for possible
 degradation of its overall mechanical properties or changes
 in the micro-structure.
\end{enumerate}

\section{Theoretical Predictions on Beam Window Response -- Background}
Consider a thin window structure of radius \textbf {R} and thickness \textbf {h}
 intercepting an energetic, focused proton beam of Gaussian profile.
 Energy is deposited in the material with radial symmetry about
 the window center while some variation of energy deposited is
 expected to be present, no matter how thin the window, through
 the thickness h.
\begin{figure}[thb!]
\centering
%\includegraphics*[width=5in]{simos/simos-fig5.eps}
\caption{Predicted strain in 1mm Inconel window      }
\label{simos:fig5}
\end{figure}

In evaluating the thermoelastic equation of motion in the beam
 window it is assumed that the thermal expansivity is isotropic
 and the effects of heat conduction on the dynamics are neglected.
 Further, as first approximation, no attenuation of the acoustic
 pulse is accounted for even though some fraction of the energy
 is dissipated in the material. It is also assumed throughout
 that the energy deposited in the window material is immediately
 converted to thermal energy. As noted in~\cite{simos:ref6} this is a very
 good approximation given that the acoustic relaxation time is
 of the order of nsec whereas ``thermalization'' times, at least
 in metals are of the order of $10 ^{-11}~s.$

Based on the above considerations, the issue to address is how
 does a thin window structure respond as it intercepts a fast
 and intense proton pulse. While ``thermalization'' is assumed
 to take place instantly, thus generating a quasi-static state
 of stress in the affected zone, the acoustic relaxation time
 still plays a role in defining both the generation and the level
 of thermal shock stresses. Specifically, the amplitude of the
 stress waves emanating from the ``heated'' zone depends on the
 relation between the rate of energy deposition (pulse length)
 and the acoustic relaxation time (time required for an acoustic
 wave to traverse the region of energy deposition). If the time
 of energy deposition is smaller than the acoustic relaxation,
 the amplitude of the stress wave will be maximum. If acoustic
 relaxation is smaller then the amplitude will be reduced by
 the ratio of the two characteristic times.


While the above considerations define the response of the thin
 window in the radial sense of stress wave generation and propagation,
 the most important consideration in assessing its survivability
 is the thermoelastic response through the window thickness.
 As the affected zone is thermalized in the cylindrical volume
 between the two surfaces, stress waves initiate at each of the
 surfaces and travel toward the opposite surface. The governing
 principle is basically a 1-D response similar to the response
 of a heated 1-D rod with free edges. Figure [] graphically demonstrates
 the response of the heated zone by capturing the propagation
 and reflection of elastic waves through the thickness and out
 of the zone in a series of snap shots. Since energy is moving
 out of the region in the radial direction, the amplitude of
 the stress ``ringing'' through the thickness reduces in time.
 The impact on the window material, however, could dramatic since
 a significant number of stress cycles of considerable amplitude
 can accumulate following a proton pulse. 
\begin{figure}[thb!]
\centering
\includegraphics*[width=5in]{simos/simos-fig6.eps}
\caption[Recorded strain in a 6-mm Inconel window   ]{Recorded strain in a 6-mm Inconel window by two strain gauges 180 deg apart. Also shown is the recorded signal by the 100 KHz bandwidth.      }
\label{simos:fig6}
\end{figure}

To demonstrate the severity of the beam-window interaction under
 such tight focusing, the thermal stress induced in a 10-mil
 thick stainless steel window by the beam of the required parameters
 (24 GeV, 16 TP, 0.5 mm sigma and 100 ns pulse length) is shown
 in Fig.~\ref{simos:fig6}. Specifically, the peak von Mises stresses in the
 window material, occurring at beam center and mid-thickness,
 approaches 2500 MPa that is more that twice the yield and ultimate
 strength of the material. According to this prediction such
 window will not be able to survive a single pulse let alone
 multiple pulses. Figure~\ref{simos:fig3} shows the temperature rise in the
 stainless steel window as a result of a single pulse.

Also depicted in Figure~\ref{simos:fig3} is the ``ringing'' regime that follows
 the energy deposition. The peak von Mises stress occurs within
 the window thickness some time between the initiation of the
 pulse and the time required for the sound to traverse the thickness
 for the first time. 

Initial estimates of energy deposition in various materials for
 a 24 GeV proton beam, 16 TP intensity, a beam spot down to 0.5
 mm rms and a pulse length of approximately 100 ns painted a
 very bleak picture for most commonly used materials for beam
 windows. An additional concern in bringing beam on the AGS A3
 line was the ability of existing aluminum windows  to survive
 even though there were expected to see a larger spot (based
 on the beta function of the beam). Given the severity of the
 problem, an experimental set-up to study the response of window
 materials as part of the E951 muon targetry experiment was introduced.
 Four (4) different window materials were selected for testing
 in the beam line at AGS. Three of the materials, Inconel-718,
 Havar and Titanium alloy, showed promise of surviving the proton
 beam pulses. Their selection was based on material properties
 and extensive thermal shock predictions.  Figure~\ref{simos:fig7} shows von
 Mises stresses generated in a titanium alloy (6 Al--6 V). Under
 the required parameters of 24 GeV, 16 TP intensity and 0.5~mm
 rms spot, the stresses are below yield, thus making it a favorable
 candidate. Figure~\ref{simos:fig8} presents similar results in a Havar window
 and shows that under such beam parameters the peak stresses
 are approaching the yield stress limit.
\begin{figure}[thb!]
\centering
\includegraphics*[width=5in]{simos/simos-fig7.eps}
\caption{Predicted strains in the 6mm-thick Inconel window  }
\label{simos:fig7}
\end{figure}
\begin{figure}[thb!]
\centering
%\includegraphics*[width=5in]{simos/simos-fig8.eps}
\caption{Recorded strains in back-to-back pulses in a 11mil-thick Havar window  }
\label{simos:fig8}
\end{figure}

The fourth material selected is Aluminum (3000-Series). Based
 on the theoretical predictions, this window material could fail
 even if 6 TP are delivered on target.  Given that at initial
 stages of E951 6 TP beam is more likely to be delivered and
 because of the proximity of this window material to the failure
 condition, experimental data associated with this material and
 its potential failure, would be very useful in benchmarking
 failure prediction. 

Since the calculations show that the window thickness, in conjunction
 with the material acoustic velocity and the pulse structure
 and duration, has a dramatic effect on the peak stresses generated
 in the material, two (2) thicknesses (1-mm and 6-mm) of the
 Inconel-718 material were selected for study.
\section{E951 Experiment}
\begin{figure}[thb!]
\centering
%\includegraphics*[width=5in]{simos/simos-fig9.eps}
\caption{AGS A3 Line layout at E951 target station  }
\label{simos:fig9}
\end{figure}

Figure [] depicts the layout of the window test experiment. There
 are two parallel beam lines within the target enclosure. It
 all rests on a moving table such that both lines can be exposed
 to the proton beam. Shown in Figure [] and in one of the lines
 is a set of double windows with vacuum in the space between
 the two plates. Each window is made of one of the selected experiment
 materials. The main goal is to make a qualitative assessment
 of window failure when it intercepts the proton beam. In other
 words, any loss of vacuum, which is continuously monitored,
 in the space between the double windows will indicate mechanical
 failure.

Along the second beam line a set of single windows instrumented
 with fiber-optic strain gauges are placed. 

\subsubsection{Window Strain Measurement Set-Up}
The goal of the strain experiment is to capture the radial strain
 at a specified distance from the beam spot location. While the
 governing shock stress in determining the safety of the window
 material is the von Mises stress at the center of the spot and
 through the material thickness, there is no measurable quantity
 in that orientation. However, by predicting the radial strain
 at a safe distance from the beam (minimize the radiation damage
 on the strain gauges), the whole stress tensor can be estimated.
  Figure [] depicts the arrangement of four (4) fiber-optic strain
 gauges that were placed on the front surface of each of the
 tested windows. The strain gauges are designed around an interferometer
 by FISO Technologies Inc. The basic active element (cavity)
 consists of two mirrors facing each other. The acquired signal
 goes through custom-made filtering and at the end of the process
 a 500 KHz strain signal is deduced. 

The wavelength of the shock front (uncorrupted in nature) and
 the ability of recording system to capture it is vital to the
 analysis of strain amplitude and time structure.

\subsubsection{Window Strain Measurements: Comparison 
}
During the window tests of the E951 experiment a beam intensity
 of approximately 2.5 TP was delivered on target. The beam spot
 size (originally estimated at 1 mm rms sigma radius), and which
 closely fits an ellipse rather than the circle that was assumed
 in the theoretical predictions thus far, is currently being
 re-evaluated using radiation exposure techniques. 

While the combination of beam intensity and spot was far from
 being critical for any of the windows, strain measurements that
 can be used to verify the predictions have been generated. 
 Shown in Figure [] is the radial strain in one of the four gauges
 of the 10-mil aluminum window. The very first part of the record
 is the noise in the fiber-optic system. The arrival of the proton
 beam is indicated by the high frequency noise corruption of
 the signal. The arrival of the compressive wave at the active
 element of the gauge (approximately at 0.5-inch from center)
 is shown by the first dip. What follows is the arrival of the
 tensile wave phase at precisely the time that is expected.

Following the rapid thermalization of the affected material (within
 the beam spot) two waves are generated at the edge of the heated
 zone. One travels outward as a compressive wave and arrives
 at the strain gauge first (dip). The second wave travels toward
 the center of the beam spot as compressive, reflects at the
 center by changing sign, and travels outward as a tensile wave.

The remaining cycles represent reflections at the edge of the
 window and its center. 

Figure [] depicts the calculated strains for the same beam parameters
 but with a ``true'' round Gaussian profile. The agreement between
 experiment and theory is very good both in terms of amplitude
 and time structure.  

Figure [] depicts the recorded strain of the same gauge as seen
 from two bandwidths of the acquisition system. The stain record
 shows the arrival of the initial shock wave and some reflections
 of the pulse between the edge and the center of the window disk.
 Based on the AGS pulse structure, spot size and pulse length,
 it was assessed that the 100 KHz bandwidth was insufficient
 to record the stress pulse arrival at the strain gauge location.
 Indeed, Figure [] clearly demonstrates that no signal was recorded
 by the acquisition system operating at this bandwidth. Not shown
 here is the complete record (up to 0.1 sec) which shows that
 overall response of the window dominated by lower frequencies
 is captured by both bandwidths.   

Figure [] shows the strain measurements at the same gauge in
 two back-to-back pulses with approximately the same beam intensity.
 The duplication of the response is a sign of stability in the
 measurements.  However, it should be noted that fiber-optic
 strain signal is very sensitive to the beam arrival and the
 ensuing flux of photons (shown as high frequency bunch at the
 start of the record and sharp peaks in the transient response).
 A filtering effort is under way to ``clean'' the records from
 the inherent and induced noise.

An additional source of discrepancy is the actual position of
 the beam with regard to the four gauges. A beam shift toward
 one of them will alter the strain measurements by inducing higher
 strains in the closest gauge. To estimate the ``true'' position
 of the beam, a cross-correlation process (typical results shown
 in Figure []) of the gauge signals has been introduced that,
 in first order, indicates the relative arrival of the signal.

 In Figures [] \&  [] the measured and predicted strains in the
 1mm-thick Inconel--718 window are shown.  It should be noted
 that based on the ``preliminary'' analysis and comparison of experimental
 to theoretical results, it has been observed that the thicker
 the window gets the higher the deviation between the two.

In Figure [] the strain recorded in the 6mm-thick window are
 shown. As expected, the ``thickness'' effect becomes more prominent
 in that there is presence of surface waves that have been enabled
 to form and propagate as well as delayed reflections from the
 opposite surfaces.  Figure [] depicts the theoretical predictions
 in the same window but with a Gaussian spot at the center of
 the window. It is evident that general characteristics of the
 response are predicted quite well. Lastly, in Figure [] the
 recorded strains from back-to-back pulses are shown for the
 thin Havar window demonstrating the stability of the acquisition
 system.
\subsection{Summary--Beam Window Study}

The first phase of the window study of experiment E951 provided
 the opportunity to test, in addition to targets, window structures
 that are integral part of any target system and normally experience
 similar shock conditions. Despite the fact that the pulse intensity
 that was delivered to the windows was much lower than was hoped
 for, still important conclusions could be drawn. Specifically,
 from the overall experimental/theoretical study thus far the
 following is assessed:
\begin{enumerate}
\item 
Predictions are generally in agreement with the results of the
 actual experiment. This implies that the energy deposition estimated
 by the neutronic code calculations agrees with the energy left
 in the material by the beam. It should be noted that in this
 first phase of data post-processing and comparison, influential
 material properties such as damping have been accounted for
 in the theoretical predictions. Subsequent analysis with energy
 dissipation considerations would help the agreement both in
 terms of amplitude and pulse shape and dispersion even further.
 In addition, as noted earlier, a re-evaluation of the actual
 beam spot is under way which is expected to provide a picture
 closest to the ``real thing''. In light of this information, the
 theoretical model used to calculate the predictions will be
 modified accordingly and the predicted strains will also be
 re-evaluated.
\item 
Because of the lower than anticipated intensity and possibly
 larger beam spot, the failure conditions for the weakest window
 (aluminum) were never approached.
\item 
The thicker the window, the more difficult to predict amplitudes
 and structure of the signal due to multiple wave phases and
 reflection. A key piece of information, however, that was deduced
 is that higher levels of strain were observed in the thicker
 window.
\item 
Given the nature of shock waves in the materials, a further increase
 in the measuring system bandwidth is desirable.
\end{enumerate}
\subsection{Proposed New Studies
}
To shed more light in this critical aspect of window material
 selection and its long-term survival in the proposed muon collider
 target space, it is important that the experimental studies
 continue. Specifically, in the next experimental phase the following
 should be considered:
\begin{enumerate}
\item Close examination of the exposed windows and especially of the
 directly affected area for possible micro-structural failure
\item Properties of materials having the most promise of long-term
 survival should be evaluated from the point of view of radiation
 exposure and degradation 
\item Expose the windows already tested to proton pulses with higher
 intensity. Reaching intensities that will cause mechanical failure
 in the ``weakest'' window and calibrating the prediction model
 to that condition, will provide a very important tool to be
 used in predicting failure for other materials that will be
 considered in the muon collider/neutrino factory target system.
\end{enumerate}
\subsection{E951 Mercury Jet Target Study 
}
\subsection{Background--Issues/Goals
}
The use of a mercury jet target raises a number of issues that
 need considerable attention. These issues are associated with
 the presence of a strong magnetic field, the rapid heating of
 the mercury by the proton beam and the subsequent dispersion.
 As the mercury jet enters the field eddy currents are induced
 in the jet and the Lorentz force on these currents could lead
 to the distortion of the jet. An important point to be made
 is the generated magnetic pressure on the mercury jet that,
 in turn, is expected to damp mechanical perturbations and also
 add inward radial pressure. Figure [] is an overall schematic
 of the target space including the solenoid.

Preliminary estimates have shown that the mercury jet will disperse
 after it interacts with a single proton pulse. What is key,
 however, is estimating the time scale of jet destruction. For
 one scenario in particular that requires six (6) 2-ns micro-pulses
 to be delivered within $2\mu$s, the time of destruction is important
 given that one needs to have all six micro-pulses see an intact
 jet. A consequence of the jet's dispersion is the ejection of
 droplets that, if ejected at very high velocities, can cause
 serious damage to the target space. 

As noted earlier, a concern related to the survivability of the
 jet nozzle experiencing a pressure wave traveling upstream potentially
 exists. For a continuous jet with the interaction zone starting
 at some distance downstream of the nozzle, pressure waves are
 expected to travel through the undisturbed jet and reach the
 nozzle. While pressure amplitudes are expected to attenuate
 by the time the front reaches the nozzle, the many cycles over
 the life of the target enclosure could lead to nozzle fatigue
 failure.  Within the scope of E951 experiment, an attempt was
 made to address the issue and preliminary experimental results
 are shown.

For all scenarios of beam delivery, the energy deposited in the
 mercury jet has been calculated using the MARS code. In the
 co-linear interaction scenario of proton beam and jet, peak
 energies of approximately 130 Joules/gm have been estimated.
 This peak energy is observed about 5 cm into the jet from the
 start of the interaction region. In the latest scheme, however,
 with the mercury jet tilted by 100 mrad and the proton beam
 by 67 mrad the peak energy deposition is approximately 49 Joules/g
 and it occurs about 25 cm downstream from the start of the interaction
 region.  Table~\ref{simos:tb1}, lists some of the physical properties
 of mercury that were used in the various estimations
\begin{table}[hbt!]
\centering
\caption{Physical Properties of Mercury}
\label{simos:tb1}
\begin{tabular}{|lc|}
\hline
Density,  $\rho$ & $13.5$~g/cm\textsuperscript{3}\\

Compressibility,  $\kappa$ & $0.45 10^{-10}$~m\textsuperscript{2}/N\\
Volumetric Thermal expansion, $\alpha _{v}$ & $ 18.1 10^{-5}$~K\textsuperscript{-1}\\

Specific Heat, c$_{v}$ & 140 J/Kg K\\
Velocity of Sound & 1300 m/s\\
Critical Point Temperature, T$_{cr}$ & 1593\textsuperscript{o} C\\
Critical Point Pressure, P$_{cr}$ & 185 MPa\\
\hline
\end{tabular}
\end{table}
\subsubsection{Predictions of Pressure Wave Generation 
}
Estimates of pressure wave generation and propagation were made
 using the capabilities of the ANSYS [] code, the equation of
 state for mercury provided by the SESAME [ ] library and the
 energy deposition calculations of the MARS [] code.

The outward velocity of mercury was estimated prior to the experiment
 by considering the volumetric change of an infinitesimal volume
 of mercury $dV$
 experiencing a change of temperature 
 $\Delta T$
 and pressure 
 $\Delta P$ 
that result from the fast proton beam. Relations below lead to
 the estimate the outward velocity 
$U_r$ as function of sound velocity $c$
 of material in the jet

\begin{eqnarray}
K.E.& =& \frac{1}{2} \rho  dV U_{r}^2\Delta P \delta (dV)\nonumber \\
\Delta P &\approx & \alpha_v \Delta T/k\nonumber\\
\alpha_{v } &
= &(\partial V/\partial T)_{P}\nonumber\\
\delta (dV)& = &\alpha_{v}dV \Delta T\nonumber\\
\textbf{U}_{r}^2\textbf{c}^2 &
 =& 2 \alpha_{v}^2\Delta T^2\nonumber\\
\textbf{U}_{r}^2 &
 = &\sqrt{2} [\alpha_{v}\Delta T] 
\textbf{c}
\end{eqnarray}
It is apparent from the above relations that the movement of
 bulk material as a result of thermal gradients is just a percentage
 of the velocity of sound that generated pressure waves travel.
 So, while the pressure field is experiencing the passage of
 the generated pressure waves (superimposed onto the thermodynamic
 pressure) the exchange of heat, as well as bulk material movement,
 is governed by a much slower processes. The verification of
 this significant relation was one of the goals of E951 in proving
 that the projectile velocity is much smaller than the velocity
 of sound and thus the potential for damage to the surrounding
 target space greatly reduced.
\subsubsection{Pressure Wave-Jet Nozzle Interaction}
While it is anticipated that the interaction zone of the jet
 may be broken up several microseconds after the proton beam
 arrival, the upstream section of the jet is still intact and
 will allow for the propagation of pressure waves toward the
 nozzle. At issue is the amplitude of the pressure wave front
 when it arrives at the nozzle and impacts on the walls. The
 estimated time of the arrival of the front is approximately
 $100\mu$s based on a 15-cm distance between the beginning of the
 interaction zone and the nozzle. 

Figures []-[] depict the schematic of the beam/jet interaction
 arrangement and snapshots of the pressure profile along the
 mercury jet in a cut through the long axis. While pressures
 start out as positive, a result of the rapid energy deposition
 and the inability of the Hg to accommodate thermal expansions,
 they quickly turn negative at the center of the interaction
 zone. This is the result of the wave reflections and sign reversal
 from the free surface of the jet. While part of the interaction
 region may be destroyed, the pressure front will advance toward
 the nozzle through the undisturbed jet.

As expected, the pressure wave will attenuate as it travels through
 the undisturbed part of the jet. Figure [] depict predictions
 of the pressure wave fluctuation and amplitude in the nozzle
 vicinity. While much lower than the initial pressures may make
 it to the nozzle, a large number of such impacts will accumulate
 during the operation of the machine that may potentially lead
 to fatigue failure. The latter becomes more of an issue considering
 the high irradiation doses the structural materials will receive
 because of their proximity to the target.

\subsubsection{E951 Set-Up}
A schematic of the mercury jet target chamber is shown in Figure
 [ ]. Also shown is the location of the array of fiber-optic strain
 gauges that were mounded to record strain waves arriving at
 the nozzle.

To record the mercury jet dispersal two camera systems were used
 with recording capabilities: 1) at rate of 4 kHz with shutter
 settings for each frame set to $25\mu$s and 2) 16 frames at speeds
 up to 1 MHz and exposure time of 150 ns per frame.
\subsubsection{Mercury Jet Experimental Results}
In the E951 experiment the mercury jet trajectory overlapped
 with the proton beam for 19 cm. The diameter of the jet at the
 interaction region ranged between 0.7 cm and 1.7 cm. Achieved
 proton beam intensities ranged between 0.5-4.0 TP and spot sizes
 were of the order of 1.6 mm in x-dir and 0.9 mm in y-dir rms
 sigma radius. 

Dispersal of the mercury was observed by viewing prominences
 as they left the bulk of the mercury jet. Figure [] depicts
 a series of frames recorded during the experiment showing the
 evolution of the jet dispersion. Important parameter is the
 time scale in which events occur. Specifically, the appearance
 of material emanating from the free jet surface occurs at 0.75
 ms. However, a fast camera with capabilities of 1 frame/$\mu$~s revealed
 that the initiation of jet dispersion occurred at a time of
  {\textasciitilde}  $40~\mu$s.

Such delay time from the onset of proton beam/jet interaction
 is well in line with the estimates made on the basis of volumetric
 expansion within the jet. Further, measured velocities of 5
 to 50 m/s also tend to agree with velocities estimated from
$\textbf{U}_r=\sqrt{2}[\alpha_v \Delta T]\textbf{c}$ 
in which, as observed, the bulk velocity of ejected material
 is proportional to the temperature rise, which in turn is directly
 proportional to the intensity of the impinging protons. \fontsize{11}{1}%
\subsubsection{Jet Nozzle Results}
Four fiber optic strain gauges were placed at selected locations
 in the mercury line (shown in Figure [ ]). Specifically, a gauge
 was placed on the line that supplies mercury to the jet just
 upstream of the nozzle. This gauge, placed along the pipe as
 shown, is expected to register any activity associated with
 a wave returning from the jet. The geometry and size of the
 supply pipe did not allow for the gauge to be placed with hoop
 orientation. Potential strains along the hoop direction in the
 pipe wall are expected to be much higher than the axial and
 thus more easily detectable. Strains in the supply pipe will
 be the direct result of the pressure in the contained mercury.

In addition to the nozzle gauge, one was placed at the valve
 outlet (furthest location in the supply pipe upstream of the
 nozzle) and two were installed on the nozzle mounting plate
 on either side of the nozzle. Strains for beam intensities ranging
 between 0 TP and 4 TP (0 TP being the case of jet activity alone)
 were recorded.  While the beam intensity was much lower than
 anticipated, thus keeping the potential strain aggravation due
 to shock quite low, still some clear evidence of activity was
 recorded. Shown in Figure [ ] is the strain recorded by the
 nozzle gauge for back-to-back pulses with similar intensities
 (3.75 TP). The stability in the measuring system is shown to
 be excellent. The front part of the record is the noise from
 the flowing Hg in the supply pipe. The spike indicates the arrival
 of the proton beam and it is the effect of photons on the gauges.
 Beyond that there is evidence of activity induced by the proton
 beam interacting with the jet. 

Figure [ ] quantifies the effect by comparing the strain induced
 by the jet alone with that of the interaction with the proton
 beam.

Further examination of these results is needed to make firm assessments.
 The difficulty stems from the fact that the proton beam intensity
 received during the first experimental phase was much too low
 to both qualify and quantify the effects at the nozzle location
 and draw conclusions about its survival in the actual target
 setting.
\section{E951 Graphite \&  Carbon-Carbon Target Study}
\subsection{Background--Issues/Goals}
The need for an alternative target option using a low-Z material
 with good yield prompted the studies on graphite as one of the
 candidate materials.

The experimental effort on graphite and carbon-carbon composite
 as target material for potential use in a high power source
 had as primary goals the following:
\begin{itemize}
\item Attempt to establish limits of material integrity of a particular
 form of graphite (ATJ grade) as it intercepts the high-energy
 undiluted proton beam. Of interest in the experimental study
 was to observe the behavior of the material as it approaches
 its mechanical strength limits that were anticipated in E951
\item
Assess the response of the carbon-carbon composite target and
 verify that its promise of very low thermal expansion coefficient
 holds true. Verification of the latter will imply that the generated
 stress conditions within the composite are also very small and
 thus it can maintain its integrity as a solid target material
\item
Enable the numerical verification of the response of the solid
 targets on the basis of recorded strain waves. This part of
 the effort is extremely useful in that it provides two crucial
 pieces of information, namely, the calibration of the theoretical/computational
 model so it can be of use in further studies of solid targets
 for their susceptibility to failure, and that the comparison
 of predicted with recorded strain data can provide an additional
 verification of the estimated energy deposition in the targets
\end{itemize}
\subsection{E951 Set-Up}
Figures [] and [] represent the schematic arrangement and the
 actual set-up of the ATJ graphite and carbon-carbon composite
 targets. Along the axis of one of the beam lines, two 12-inch,
 1-cm diameter ATJ rods were placed, while on the other, the
 two 5-inch, 1-cm diameter carbon-carbon composite rods were
 set.  All four target rods were instrumented with fiber-optic
 strain gauges that were to record axial strain. Specifically,
 the front ATJ rod had 8 gauges (4 in the middle separated by
 a quadrant, two near the front at 180 degrees apart and two
 near the back side also at 180 degrees apart. The rear ATJ rod
 had 7 gauges connected to it (four, two and one respectively).
 On the carbon-carbon side the front rod was instrumented with
 3 gauges and the rear with just two. Special fixtures secured
 the rods in position with minimal interference to their dynamic
 response.  
\subsection{Experimental Results--Discussion
}
Two different sets of experimental measurements provided two
 beam spot sizes and two intensities. Specifically, one set of
 data recorded are for a larger spot accompanied by a higher
 beam intensity, while the other set provided data for a tighter
 spot but less protons in the pulse. These combinations provided
 an excellent matrix for purposes of verification of both the
 numerical predictions in terms of strain and in addition evidence
 of how well the energy deposition, predicted by different hadronic
 codes, is estimated. Specifically, energy deposition/distribution
 in the two ATJ rods were estimated using the codes MARS, GEANT
 and MCNPX. Figure [ ] depicts the mars calculations for the
 two different beam spots. Based on comparisons with the theoretically
 predicted strains, it was assessed that the codes MARS and GEANT
 generate better correlation of the energy deposition/distribution
 at these proton energies (24 GeV).

Figures [ ] through [ ]  depict recorded strain data along the
 two ATJ graphite rods. Shown is the out-of-phase strain response
 between gauges that are 180 degrees apart, a confirmation of
 the unimpeded response of the rod due to the pin support arrangement.
 Of importance is the confirmation of all modes of dynamic response
 of the target rod. Specifically, the axial mode, the bending
 and the radial mode are all confirmed with the analytical results.
 In summary, 
\begin{itemize}
\item Experimental strains in the middle of the ATJ graphite rod show
 a bending frequency mode somewhere between 380-390 Hz 
\item 
Predictions of the detailed model that implemented the supporting/holding
 fixtures of the target as close to the real setting as possible,
 predicts a bending frequency of 395 Hz
\item
The axial ``ringing'' of the target in the experimental data has
 a period of 260-265~$\mu$s. 
\item
The fundamental axial period T=2L/c (where L is target rod length
 and c is speed of sound) is approximately 261 microseconds
\item
The radial ``ringing'' (which from theory is calculated at 150
 KHz or 6.625~$\mu$s period), is visible only in the strain
 record filtered by the 500 KHz acquisition and is in agreement
 with the experimental data

\end{itemize}
Figure [] depicts the same strain record for the direct analog
 signal of 100 KHz and the specially filtered 500 KHz signal.
 Except for the ``radial'' ringing that can only be captured well
 by the 500 KHz-bandwidth, the rest of the record is coincident
 due to the fact that the involved frequencies are within even
 the analog bandwidth. Clearly, the need for a system with higher
 bandwidth capacity is not as serious as in the beam window experimental
 study.

Figures [ ] through [] represent experimental and prediction
 data for both ATJ graphite target rods and for the different
 beam spot/intensity combinations. The need to maintain a very
 small element size in the finite element model such that the
 smallest wavelength strain wave induced by the beam can propagate
 through the rod, combined with the very small step size, allowed
 the completion of only a few significant cycles. It is apparent,
 however, that both the amplitude of the strain as well as the
 structure of the response are predicted quite well for both
 beam settings.

As expected with the carbon-carbon composite, and shown in Figures
 [ ] and [ ], the strain levels that are seen by the rod are
 much lower than those seen in the ATJ rods. However, they are
 not totally insignificant (as claimed by various manufactures
 but for slow heating) and there appears to be a ``dynamic structure''
 in the response shown in Figure [].

For both solid target types, however, the beam intensity achieved
 during the experiment did not reach levels that would challenge
 the structural integrity of the targets, something that the
 experiment would have liked to see.

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