**Moving Solid Metallic Targets for Pion Production in the Muon Collider
/ Neutrino Factory Project**

P. Thieberger^\*^, H.G. Kirk, R.J. Weggel, BNL, Upton NY, USA

and K. McDonald, Princeton University, Princeton, NJ, USA

*Abstract*

The production of large fluxes of pions and muons using high-energy,
high-intensity proton pulses impinging on solid or liquid targets
presents unique problems which have not yet been entirely solved. We
investigate the possibilities of using solid targets by choosing a metal
of either extremely low thermal expansion coefficient or exceptionally
high mechanical strength. Candidates are respectively Super-Invar and
Vascomax 350 or Inconel 718. Moving targets in the form of chains or
cables would be required for cooling purposes. These materials seem
easily capable of surviving the beam pulses required for the largest
beam power contemplated. Questions regarding radiation damage effects
are being investigated.

**INTRODUCTION**

[^1]The new frontier of multi-megawatt accelerators offers important new
physics opportunities as well as interesting technical challenges. In
particular, the production of large fluxes of pions and muons using
high-energy, high- intensity proton pulses impinging on solid or liquid
targets \[1, 2\] presents unique problems which have not yet been
entirely solved. The large required power and power density deposited in
the material as well as the short pulse duration produce large, almost
instantaneous local heating, and the resulting sudden thermal expansion
can result in damage-causing stresses in solids and in the violent
disruption of liquid jets. We concentrate on solutions based on solid
metallic targets which, through their motion, carry the deposited power
from the interaction region to a cooling bath.

The conditions created by the short beam pulses (rms width \~50 ns
during recent experiments \[3\] and \<5 ns for a final system \[1, 2\]
are very unusual. Intense, almost instantaneous, beam heating causes a
fraction of the target volume to suddenly be in a highly compressed,
inertially confined state. Subsequently this volume expands initiating
strong vibrations in the material. The amplitude of these oscillations
is such that large negative pressures (tensile stresses) or shear
stresses can be generated exceeding the strength of the material and
thus causing mechanical failure.

For a preliminary screening of possible materials, we assume that
tensile and sheer stresses will arise in the oscillations which are
similar in magnitude to the initial compression. In fact, the natural
tendency in most cases will be for the energy initially concentrated in
a fraction of the target volume to rapidly spread over the entire volume
thus reducing subsequent peak values. However, vibration focusing
effects can lead to unexpected stress concentrations. Computer modeling
will be required once a candidate material is selected, and target
geometries can then, if necessary, be modified.

**CANDIDATE MATERIALS**

Two possible approaches to avoid stress induced failures are to either
select extremely strong materials that may withstand the large stresses,
or materials with extremely low coefficient of thermal expansion for
which the thermal shock stresses will be minimized. In the present study
we consider the alloys Vasco Max C-350 and Inconel 718 in the first
category and Super Invar in the second one. For comparison, we also
include data for pure iron. Table 1 lists the thermal and mechanical
properties of these materials.

For all these materials and for target radii ranging down to a few mm,
the radial sound transit times are orders of magnitude larger than the
energy deposition times of nanoseconds or even tens of nanoseconds. Heat
diffusion times are longer still by several orders of magnitude. The
initial compression is therefore inertially confined to good
approximation and the subsequent oscillations are nearly adiabatic.

**STRESS ESTIMATES**

To determine the initial compression we must first find maximum values
of the energy density deposited by the beam. This was done by using the
MARS code \[4\] for a number of different target radii, and by assuming
a proton beam rms radius, σ, 2.5 times smaller than the target radius in
each case. An example of such a calculation for iron is shown in Fig. 1
for a target radius of 7.5 mm, a beam rms radius of 3 mm and a 24 GeV
proton pulse of 16 × 10^12^ protons. Table 2 lists maximum energy
density values for a range of radii. Once the maximum value ε~max~ of
the energy density (per unit mass) is found from these calculations for
each case, we calculate the corresponding maximum compression P~max~ for
each material:

P~max~ = 3 × ε~max~ × Β × α / c~v~

where B is the bulk modulus, α the linear expansion coefficient, and
c~v~ the specific heat at constant volume. The factor 3 is, for an
isotropic material, the ratio between volumetric and linear relative
expansions. These stress values are then appropriately scaled for the 1
MW and the 4 MW options of the Muon Collider/ Neutrino Factory project
\[1, 2\] the first of which calls for 15 pulse per second with 17.3
× 10^12^ protons per pulse, with both these numbers doubled for the
second one.

Table 1. Mechanical and thermal characteristics.

<table style="width:100%;">
<colgroup>
<col style="width: 13%" />
<col style="width: 10%" />
<col style="width: 9%" />
<col style="width: 10%" />
<col style="width: 8%" />
<col style="width: 9%" />
<col style="width: 10%" />
<col style="width: 11%" />
<col style="width: 7%" />
<col style="width: 9%" />
</colgroup>
<tbody>
<tr class="odd">
<td></td>
<td>Density</td>
<td>Linear Exp. Coeff.</td>
<td>Young Modulus</td>
<td>Bulk Modu-lus</td>
<td>Poisson Ratio</td>
<td>Specific Heat @ constant pressure</td>
<td>Thermal Conducti-vity</td>
<td>Yield Stren-gth</td>
<td><p>Fatigue Endu-</p>
<p>rance Limit</p></td>
</tr>
<tr class="even">
<td>Symbol</td>
<td>ρ</td>
<td>α</td>
<td>Y</td>
<td>B</td>
<td>μ</td>
<td>C<sub>P</sub></td>
<td>λ</td>
<td>σ<sub>0.2</sub></td>
<td>σ<sub>−1</sub></td>
</tr>
<tr class="odd">
<td>Unit</td>
<td>g/cm<sup>3</sup></td>
<td>10<sup>-6</sup> / <sup>0</sup>K</td>
<td>G Pa</td>
<td>G Pa</td>
<td></td>
<td>J/(g <sup>0</sup>K)</td>
<td>W/(m <sup>0</sup>K)</td>
<td>M Pa</td>
<td>M Pa</td>
</tr>
<tr class="even">
<td>Iron</td>
<td>7.87</td>
<td>12.5</td>
<td>205</td>
<td>171</td>
<td>0.30</td>
<td>0.478</td>
<td>80</td>
<td>170</td>
<td>~85</td>
</tr>
<tr class="odd">
<td>Inconel 718</td>
<td>8.19</td>
<td>13.1</td>
<td>200</td>
<td>158</td>
<td>0.29</td>
<td>0.435</td>
<td>11.2</td>
<td>1034</td>
<td>586</td>
</tr>
<tr class="even">
<td>VascoMax C-350</td>
<td>8.08</td>
<td>15.0</td>
<td>200</td>
<td>167</td>
<td>0.30</td>
<td>0.450</td>
<td>25.2</td>
<td>2242</td>
<td>758</td>
</tr>
<tr class="odd">
<td>Super Invar</td>
<td>8.15</td>
<td>0.63</td>
<td>144</td>
<td>88.9</td>
<td>0.23</td>
<td>0.515</td>
<td>10.5</td>
<td>276</td>
<td>~138</td>
</tr>
</tbody>
</table>

![](media/image1.png)**Fig. 1** Three-dimensional view of energy
deposition MARS values for a 3 mm rms radius 24 GeV, 16 × 10^12^ proton
beam pulse on a 7.5 mm radius iron target.

![](media/image2.wmf)**Fig. 2** Maximum initial stress as % of yield
stress for the 24 GeV, 17.3 × 10^12^ proton beam pulses required for the
1 MW option

In Figs. 2 and 3, we apply our criterion to both options of the Muon
Collider/Neutrino Factory proposal \[1, 2\] by plotting these maximum
stresses as percentages of the respective

![](media/image3.wmf)**Fig. 3** Maximum initial stress as % of yield
stress for the 24 GeV, 34.7 × 10^12^ proton beam pulses required for the
4 MW option

yield stresses for the different materials and for a range of rms beam
radii, with target radii 2.5 times larger. We see, for example, that for
Vascomax 350 our criterion wouldn\'t be exceeded even for the 4 MW
option down to a \~4 mm radius target which is smaller than envisaged.
Super-Invar, while being further from reaching the yield stress is
limited to larger radii due to the fact that its low expansion
coefficient characteristic disappears at temperatures higher than \~120
^o^C. Also, results from radiation damage studies, reported elsewhere in
these proceedings \[5\], indicate that Super-Invar may not be an
appropriate choice.

A somewhat more stringent criterion for estimating the resiliency of
these materials is to compare the maximum initial stresses to the
fatigue limit instead of the yield stress. In that case the results for
Vascomax 350 and for Inconel 718 become similar, and indicate that
target radii equal or larger than 4.5 mm and than 7.5 mm would be viable
for the 1 MW and the 4 MW option respectively. Using fatigue limits is
probably overly conservative since these limits, which are specified at
low repetition rates, are known to increase substantially with
frequency. We also see that iron or other alloys much weaker than the
ones considered here would be inadequate even for the 1 MW option using
either criterion.

**Table 2. Maximum energy densities deposited by 16** ×10^12^ **24 GeV
proton beam pulses**

in iron targets. Values for the other materials considered here will be
nearly identical.

  ---------------------------- ------ ----- ------ ------ ------ ------ ------
  Proton beam rms radius       .5     1     1.5    2      2.5    3      3.5
  \[mm\]                                                                

  Target radius \[mm\]         1.25   2.5   3.75   5      6.25   7.5    8.75

  Maximum energy density       305    105   55.6   36.0   26.5   22.1   16.5
  \[J/g\]                                                               
  ---------------------------- ------ ----- ------ ------ ------ ------ ------

**POSSIBLE IMPLEMENTATIONS**

Finally we show some schematic representations of possible chain
configurations for moving targets as alternatives to the previously
proposed \"Band Saw\" system \[6\] or the use of a metallic cable \[7\]
.

![](media/image4.png)

Fig. 4 Examples of metallic chain links configurations showing rather
compact designs with large metal to gap volume ratios.

![](media/image5.png)

Fig. 5. Schematic of a chain with long links which, if surrounding
hardware such as magnet coils permit, would allow each beam pulse to be
coaxial with the target.

Cooling requirements dictate in each case the minimum velocity as well
as the length for a chain of a given material and a given geometry. An
estimated required velocity for a Vascomax C-350 chain for the 4 MW
option would, for example, be 3 m/s and the total length would be \~35 m
to transfer the power deposited by the beam to a 20 ^o^C cooling bath
without exceeding an internal target temperature of 300 ^o^C and thus
largely preserving the strength of the material.

**DISCUSSION AND CONCLUSIONS**

We conclude that solid moving metallic targets with very large tensile
strength are viable candidates for a 1 MW and even a 4 MW Muon
Collider/Neutrino Factory system and should therefore also be considered
for other multi megawatt high energy proposals. It was also shown that
more conventional solids such as iron can not be expected to work.

The choice between Vascomax C350 and Inconel 718 (or perhaps Inconel
750) may be influenced by the fact that Inconel isn\'t ferromagnetic and
will therefore not be subjected to the rather large forces Vascomax
chains will experience when entering and exiting a high solenoidal
field. A disadvantage of Inconel is its low thermal conductivity which
makes cooling slower and will thus require longer chains. It may be
possible to improve this situation by providing cooling channels through
the chain links.

The present stress and temperature estimates are thought to be
conservative since no credit was taken for the advantageous frequency
dependence of fatigue tolerance, nor for the possibility of using
non-Gaussian beam profiles to reduce the peak energy density if
necessary. Uncertainties about the survival of high-temperature
stationary carbon targets and about the possibility of rapidly clearing
large quantities of dispersed mercury for liquid jet targets \[8\] makes
these moving solid targets a safer choice.

**REFERENCES**

1.  N. Holtkamp and D. Finley, eds., A Feasibility Study of a Neutrino
    Source Based on a Muon Storage Ring, Fermilab-Pub-00/108-E (2000),
    http://www.fnal.gov/projects/muon\\\_collider/nu-factory/nu-factory.html}.

2.  S. Ozaki, R. B. Palmer, M. S. Zisman, and J. Gallardo,Editors,
    Feasibility Study-II of a Muon-Based Neutrino Source, BNL-52623
    (June 2001); http://www.cap.bnl.gov/mumu/studyii/FS2-report.html.

3.  H. G. Kirk, et.al. Target Studies with BNL E951 at the AGS,
    Proceedings of the 2001 Particle Accelerator Conference, Chicago,
    Il., March 2001, p.1535.

4.  N. V. Mokhov et.al., Fermilab-Conf-98/379LANL Report
    LA-UR-98-5716(1998); http://www-ap.fnal.gov/MARS/

5.  H. G. Kirk et.al., SUPER-INVAR AS A TARGET FOR A PULSED
    HIGH-INTENSITY PROTON BEAM}, Proceedings to this Conference, PAC03,
    Portland, OR., May 2003.

6.  B. J.King et.al. A Rotating Metal Band Target for Pion Production at
    Neutrino Factories and Muon Colliders, Proceedings of the 2001
    Particle Accelerator Conference, Chicago, Il., March 2001, p.1532.

7.  R. B. Palmer, Private Communication.

8.  P. Thieberger, MUC note \# 212:
    http://www-mucool.fnal.gov/mcnotes/public/pdf/muc0212

[^1]: ^\*^ PT@BNL.GOV