The document discusses thermal load optimization of spherical targets for use in neutrino oscillation experiments. Such experiments deposit around 20 kW of heat in the target from 2.3 MW proton beams. Spherical targets are proposed to better dissipate this heat compared to cylindrical targets. Simulation results are presented showing spherical targets have lower peak stresses than cylinders under off-center beam impacts. Preliminary modeling also indicates an array of spheres could be effectively cooled with circulating helium to handle the 2.3 MW beam power. The research aims to enable higher power neutrino beams through improved target designs.

1. Thermal Load Optimization of “Spherical” Targets in Neutrino Oscillation Experiment
Ryan Goode (Mentor) Dr. Lionel Pittman
August 2015
INTRODUCTION
The Long Baseline Neutrino Facility (LBNF, formerly the Long Baseline Neutrino Experiment) is a
next generation neutrino oscillation experiment, with primary objectives to search for CP violation in
the leptonic sector, to determine the neutrino mass hierarchy and to provide a precise measurement of
θ23. The facility will generate a neutrino beam at Fermilab by the interaction of a proton beam with a
target material, which must dissipate the c.20 kW heat load that will be deposited at the ultimate
anticipated proton beam power of 2.3 MW. Currently various cooling schemes are implemented to
alleviate these thermal loads and to ensure the health of the target.
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• http://www.fnal.gov/pub/resources/index.html
TARGET MATERIALS
The energy deposited in the target depends on the specific
beam parameters and target material. Graphite is an
obvious candidate target material due to its excellent high
temperature properties and resilience to radiation damage.
Graphite has been used in most, if not all conventional
neutrino facilities so far [CNGS, NuMI, T2K refs]. Beryllium
was selected for this study as a comparative material
because of its similarly low atomic number, (thus low energy
deposition) mechanical properties and successful
application for beam windows.
Figure 4. Comparison of stress patterns in a
cylindrical beryllium rod and sphere both of the
same diameter
Figure 6 Is the peak Von Mises
stress (including thermal stress
and all inertial effects) for simply
supported beryllium cylindrical
rods and spheres with a two
sigma off-center beam across the
range of radii and power levels.
Also shown on the figure is a
plausible design stress assumed
as two thirds of the nominal yield
strength. As can be seen in Figure
6, at 2.3 MW only a segmented
beryllium target could survive an
off-center focused beam without
yielding. Note also that in normal
operation a segmented target
would experience lower stresses
than a cylinder hence offering a
longer life expectancy.
RESEARCH ABSTRACT
A fully optimized target could enable higher-power neutrino beams where
there is, at present, no demonstrably survivable target. Furthermore, this
type of target could increase the yield of usable neutrinos from a given
beam power by allowing smaller proton beam sizes and more efficient
focusing through the horn systems.
Figure 1 shows Using Fermilab's
Main Injector accelerator as a
proton source, the Long-Baseline
Neutrino Facility's beamline is
expected to make the highest-
intensity neutrino beam in the
world.
ACKNOWLEDGMENTS
Fermilab’s Accelerator Division
Target Systems Department
Robert Zwaska, & Patrick Hurh
Figure 5 Segmented target concept
Figure 2 LBNFFigure 1 The Neutrino beam line
Figure 4 Pressurized
recirculating helical flow
helium cooling of target
spheres
Figure 3 The NuMI Horn
Figure 6. Peak stress across Task A parameter space for a 2 sigma off center beam .
In the equaiotn, E is the kinetic energy of
the pions leaving the target (with
transverse momentum 𝑝 having an
acceptance of ( 0.4 𝐺𝑒𝑉
/c) and is scored in
21 intervals between 1.5 and 12 GeV. N is
the number of pions of both signs
emerging from the target per primary
particle. The energy at the center of each
interval was calculated as
𝐸𝑐𝑒𝑛=
(𝐸𝑚𝑖𝑛+𝐸𝑚𝑎𝑥2)
2
Preliminary ANSYS modelling indicates that both a cylinder and an array of spheres could be effectively cooled with
helium at the 2.3 MW beam power. Figure 8 shows the peak temperatures expected when cooling the array with helium
at 10 bar with an expected peak velocity of around 180 m/s and a pressure drop of 1 bar.
Preliminary Thermal Modelling of Array of Spheres
Conclusions
1. Simulation of baseline target thermal load -Improved
2. Parametric study on the effect of varying thermal boundary conditions and material properties of
spheres on the thermal load now simulated.
3. Parametric study on the effect of varying thermal boundary conditions and geometric properties
of cooling system associated with spherical target experiment observed.
Figure 4 shows how the concept would
fit within a magnetic horn employing
an annular feed path for the coolant
similar to that employed for a
cylindrical target.
The largest amplitude oscillation
period corresponds to 2L/c. On the
other hand, the dynamic component
in a sphere (of equal diameter to the
cylinder) appears negligible.