# Chapter II: E951 R & D Effort

## 

## 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.

Figure 1 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 2 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 quadropoles.

***[Window Study]{.underline}***

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
\[...\]. 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 \[..\]. 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.

***[Carbon Targets]{.underline}***

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.

***[CERN Mercury Trough Target]{.underline}***

Part of the experimental matrix of E951 was the CERN mercury target
configuration. This passive target arrangement, shown in Figure \[\],
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.

######### Mercury Jet Target

The active mercury target of E951 consisted of a mercury jet
intercepting the AGS proton beam as shown in Figure \[ \]. In this first
phase of the experiment, no magnetic solenoid field was integrated with
the experiment.

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.

## E951 -- Beam Window Study

### 

### 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 4 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:

-   Survivability of windows based on a single beam pulse

##### Survivability of windows to a series of pulses

-   Assessment of the effects of irradiation on the mechanical
    properties of the candidate materials

Detailed dynamic analyses that capture the window structure response
helped guide the selection of materials to be tested. These analyses
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
(1mm and 6mm).

### 

### 

### Goals of Experimental Effort

The goals of the first phase of the window experiment effort are
summarized below:

-   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"

-   "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

-   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

-   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.

### 

###  

### Theoretical Predictions on Beam Window Response - Background

Consider a thin window structure of radius ***R*** and thickness ***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.

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 \[6\]
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^ secs.

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.

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 Figure \[\]. 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 3 shows the temperature rise in the
stainless steel window as a result of a single pulse.

Also depicted in Figure 4 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 \[\] 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 8 presents similar results in a
Havar window and shows that under such beam parameters the peak stresses
are approaching the yield stress limit.

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.

# 

# E951 EXPERIMENT

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.

## 

## *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.

## 

## *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 Fig. \[\] 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.

# 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:

-   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 analyses 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.

-   Because of the lower than anticipated intensity and possibly larger
    beam spot, the failure conditions for the weakest window (aluminum)
    were never approached.

-   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.

-   Given the nature of shock waves in the materials, a further increase
    in the measuring system bandwidth is desirable.

### 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:

-   Close examination of the exposed windows and especially of the
    directly affected area for possible micro-structural failure

-   Properties of materials having the most promise of long-term
    survival should be evaluated from the point of view of radiation
    exposure and degradation

-   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.

## E951 -- Mercury Jet Target Study 

### 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 μs, 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 below, lists some of the physical
properties of mercury that were used in the various estimations

#### *[Physical Properties of Mercury]{.underline}*

Density: ρ = 13.5 x g/cm^3^

Compressibility: κ = 0.45 x 10^-10^ m^2^/N

Volumetric Thermal expansion: α~v~ = 18.1 x 10^-5^ K^-1^

Specific Heat: c~v~ = 140 J/Kg K

Velocity of Sound = 1300 m/s

Critical Point Temperature: T~cr~ = 1593^o^ C

Critical Point Pressure: P~cr~ = 185 MPa

## *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
d**V** experiencing a change of temperature **ΔT** and pressure **ΔP**
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

K.E. = ½ ρ dV **U**~r~^2^ = ΔP δ(dV)

ΔP ≈ α~v~ ΔT/k

α~v~ = (∂V/∂T)~P~

δ(dV) = α~v~ dV ΔT

**U**~r~^2^/**c**^2^ = 2 α~v~^2^ ΔT^2^

**U**~r~ = √2 \[α~v~ ΔT\] **c**

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.

***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 μs 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.

### E951 Set-Up

## A schematic of the mercury jet target chamber is shown in Figure \[ \]. Also shown is the location of the array of fiberoptic 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 μs and 2) 16 frames at speeds up to 1 MHz and exposure time of 150 ns per frame. 

## 

## 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/μs revealed that the initiation of jet dispersion occurred at a
time of \~ 40μs.

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 **U**~r~ = √2 \[α~v~ ΔT\] **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.

## 

## 

## 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.

## E951 -- Graphite & Carbon-Carbon Target Study

### 

### 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:

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

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

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

### 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 fiberoptic 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.

### 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,

-   Experimental strains in the middle of the ATJ graphite rod show a
    bending frequency mode somewhere between 380-390 Hz

-   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

-   The axial "ringing" of the target in the experimental data has a
    period of 260-265 microseconds.

-   The fundamental axial period T=2L/c (where L is target rod length
    and c is speed of sound) is approximately 261 microseconds

-   The radial "ringing" (which from theory is calculated at 150 KHz or
    6.625 microsec period), is visible only in the strain record
    filtered by the 500 KHz acquisition and is in agreement with the
    experimental data

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 Fgures \[ \]
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.

### 

### 

# II. REFERENCES

M. Zisman, Status of Neutrino Factory and Muon Collider R&D, PAC2001,
WOAB008

S. Osaki et al., eds., Feasibility Study-II of a Muon-Based Neutrino
Source,

<http://www.cap.bnl.gov/mumu/studyii/FS2-report.html>

H. Kirk et al., "Target Studies with BNL E951 at AGS," PAC2001, TPAH137

K. Brown, et al., "First Beam Tests of the Muon Collider Target Test
Beam Line at the AGS," PAC2001, TPAH129

N. Simos, et al., "Thermal Shock Analysis of Windows Interacting with
Energetic, Focused Beam of the BNL Muon Target Experiment," PAC2001,
TPAH085

R.B. Oswald, et al., " One-Dimensional Thermoelastic Response of Solids
to Pulsed Energy Deposition," Journal of Applied Physics, Vol. 42, No.
9, pp. 3463-3473, 1971

D. Burgreen, "Thermoelastic Dynamics of Rods, Thin Shells and Solid
Spheres", Nucl. Sc. And Eng., 12, 203-217, 1962

P. Sievers, "Elastic Stress Waves in Matter due to Rapid Heating by
Intense High-Energy Particle Beam," LAB.II/BT/74-2, CERN, 1974

H. Conrad, "On Elastic Stress Waves in Targets", Institut fur
Festkorperforschung, 1994

N.V. Mokhov, "The MARS Code System User Guide, Version 13 (95)", 1995

ANSYS Engineering Analysis of Systems, Swanson Analysis Systems Inc.