Neutron Transport Calculations for a
Solid Oxygen Based UCN Source at
Indiana University
Chris Lavelle
Chen-yu Liu
Yunshang Shin
Indiana University
Postdoctoral Fellow
IU Cyclotron Facility
Faculty
Indiana University
Graduate Student
The Indiana University Cyclotron Facility (IUCF) is a
multidisciplinary laboratory performing research and
development in the areas of accelerator physics,
nuclear physics, materials science, and medical
applications of accelerators.
The Indiana University Cyclotron Facility (IUCF) is a
multidisciplinary laboratory performing research and
development in the areas of accelerator physics,
nuclear physics, materials science, and medical
applications of accelerators.
Proton and Neutron
Radiation Effects
200 MeV Cyclotron
Proton Therapy
Klystron RF System
7-13 MeV Radio Frequency
Quadruple (RFQ) and
Drift Tube Linac (DTL)
Proton Therapy
Target/Moderator/Reflector
(TMR) and Shielding
Outline
• IUCF and the Low Energy Neutron Source
(LENS) Project
• Ongoing experimental program developing
a solid oxygen UCN source
• Neutron transport calculations for
expected UCN yield and heat load on a
solid oxygen source at LENS.
LENS provides cold neutrons for materials
research and innovation in neutron scattering
techniques.
•7 (and later 13) MeV
Be(p,xn) reactions for
neutron production
using long proton
pulses (up to ~1 msec).
•Low radiation loads
from target present new
opportunities for very
low temperature
cryogenic moderators
(<10K).
LENS provides cold neutrons for materials
research and innovation in neutron scattering
techniques.
•7 (and later 13) MeV
Be(p,xn) reactions for
neutron production
using long proton
pulses (up to ~1 msec).
•Low radiation loads
from target present new
opportunities for very
low temperature
cryogenic moderators
(<10K).
Cold neutron beams and long pulse operation has
been demonstrated at low accelerator power in
Phase I of the project.
If scattering thermal treatment is valid, the MCNP
model returns very accurate results. Here we
compare water moderated neutron yield with a
calibrated detector.
Cold neutron beams and long pulse operation has
been demonstrated at low accelerator power in
Phase I of the project.
Solid oxygen’s absorption MFP is 4-5 times longer
than deuterium, and the UCN production by
magnon excitation is potentially more intense than
solid deuterium.
Sources can be
larger and UCN
have longer
lifetimes than
solid deuterium.
Crystal growth is technically challenging. A wide
variety of crystals can be grown depending on the
methods used. A slow (~0.017K/min) cool down
appears to produce highest UCN yields.
γ – β phase
transition
β phase via vapor
deposition
β phase via slow
cooldown
A UCN source at LENS would be
a demonstration of a solid oxygen
superthermal source, as well as
a test bed for new methods for
UCN sources.
Magnetic phase of converter
can be probed with external
fields.
The UCN conversion is very
sensitive to phase and how
crystal is prepared, for example
critical scattering may have
been seen enhancing the UCN
yield.
Images and Data taken by Y. Shin et. al @ PSI
We did not see superthermal
enhancement at low
temperature. Experimental
study ongoing at Los Alamos…
Scattering Probability in O2
1
0.8 Liquid O @55K
Probability
2
0.6
γ −O @ 50K
2
0.4
α −O2 @ 8K
0.2
β −O @ 30K
2
0 −4
10
−3
−2
10
10
−1
10
Energy (eV)
Neutron attenuation experiments at PSI suggest that
different oxygen phases have different neutron
transport properties, beyond a simple density
dependence.
Our core approach is
based on the flux
trap configuration
pioneered at Los
Alamos.
4K
Polyethylene
Cold Flux Trap
However, a LENS
implementation has
lower heat loads and
potentially similar
cold neutron fluxes
from the proton long
pulse.
Water
cooled
production
target
(Phase II
LENS)
Solid Oxygen
UCN Converter
Beryllium
Reflector
The Neutron Production Target
MCNP
model
MCNP
Model
Water cooled beryllium proton target
Peak current:
Time averaged current:
Average Power:
20 mA
1 mA
~30 kW
The cold flux (0-5 meV) in a cryogenic polyethylene flux
trap is a function of incident neutron energy and trap
geometry. We simulate the response of a trap with a pencil
beam of neutrons from 10 meV to 10 MeV.
Variables:
Monoenergetic Incident
Neutron “Pencil” Beam
Inner Radius
Thickness
Height
The cold flux (0-5 meV) in a cryogenic polyethylene flux
trap is a function of incident neutron energy and trap
geometry. We simulate the response of a trap with a pencil
beam of neutrons from 10 meV to 10 MeV.
Response Function of the Cold Flux Trap
100 meV drop
off in neutron
transmission
from phonon
scattering
No phonon scattering drop off
with free gas models
The thickness of the cold trap walls sets the
coupling energy for the production of cold
flux. 2.0-3.0 cm – Strong epithermal response and good mean
0-5 meV Flux in Trap (n/cm2/src)
response over all energies.
4x10-3
3x10-3
1.0 cm thick
2.0 cm thick
4.0 cm thick
5.0 cm thick
2x10-3
1x10-3
0
10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 101
Source Energy (MeV)
<1.5 cm –
Moderate
thermal
response
0-5 meV Flux in Trap (n/cm2/src)
Walls must be thick enough to thermalize the incident
neutrons inside the trap walls, but thin enough to allow
those cold neutrons to diffuse into the UCN converter
region without absorbing.
4x10-3
3x10-3
1.0 cm thick
2.0 cm thick
4.0 cm thick
5.0 cm thick
2x10-3
>4.0 cm –
Weak Fast
neutron
response
1x10-3
0
10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 101
Source Energy (MeV)
A neutron reflector can shape the energy, time,
and spatial characteristics
r of the neutron flux
φ ( E, t, r )
How do you choose the right material?
Localized thermal
neutron flux…is there a
spot where UCN
production is strongest?
A neutron reflector can shape the energy, time,
and spatial characteristics
r of the neutron flux
φ ( E, t, r )
How do you choose the right material?
•Hydrogenous materials thermalize very rapidly, localizing the
thermal flux near the target…indicating a thin trap might do well by
coupling to the thermal flux.
•High A reflector materials have longer fast neutron random walk
(more collisions required to thermalize)…and so a thicker trap
might do well since the fast neutrons have higher probability of
encountering the trap during slowing down.
•A Beryllium would have a sizeable (n,2n) reaction…leading to
increased neutron yield of ~10-15%
•Heavy water reflector would have very low absorption, so a thin
trap might do well…
RT (E )
0-5 meV Flux in Trap (n/cm2/src)
Convolute the response of a trap of thickness T
with the spatial and energy distribution of the flux
in a reflector of material M. (beryllium reflector pictured here)
4x10-3
3x10-3
1.0 cm thick
2.0 cm thick
4.0 cm thick
5.0 cm thick
2x10-3
1x10-3
0
10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 101
Source Energy (MeV)
Convolute the response of a trap of thickness T with the spatial and
energy distribution of the flux in a reflector of material M.
r
φM ( E , r )
(beryllium reflector pictured here)
Convolute the response of a trap of thickness T
with the spatial and energy distribution of the flux
in a reflector of material M. (beryllium reflector pictured here)
∞
r
r
Φ T , M (r ) = ∫ RT ( E )φM ( E , r )dE
0
This simple estimate allows one to quickly search
materials, positions, trap thicknesses, and tells us
beryllium reflected 2-3 cm thick traps have highest
cold neutron flux.
If the trap is thin, thermal
flux dominates its cold
flux response.
However, a thicker trap
produces more cold flux
by directly converting
high energy source flux
as well as thermal flux
This simple estimate allows one to quickly search
materials, positions, trap thicknesses, and tells us
beryllium reflected 2-3 cm thick traps have highest
cold neutron flux.
If the trap is thin, thermal
flux dominates its cold
flux response.
However, a thicker trap
produces more cold flux
by directly converting
high energy source flux
as well as thermal flux
The simple estimate indicates we should place the trap as
close as possible to the target.
The peak cold flux is
n
n
10
→1.8 ×10
3.8 ×10
2
cm ⋅ src
cm2 ⋅ s ⋅ mA
−4
0-5 meV Flux (n/cm^2/src)
4.50E-04
4.00E-04
3.50E-04
3.00E-04
2.50E-04
2.00E-04
1.50E-04
1.00E-04
5.00E-05
0.00E+00
-20
-15
-10
-5
0
Y Position (cm)
5
10
15
20
Using a 2.0 cm thick trap, 1000 cc solid oxygen source
we can model the volume average cold flux in the
oxygen as a function of position. 1 cm left of center is
optimal.
n
n
10
→1.8 ×10
3.8 ×10
2
cm ⋅ src
cm2 ⋅ s ⋅ mA
−4
However…
0-5 meV Flux (n/cm^2/src)
4.50E-04
4.00E-04
3.50E-04
3.00E-04
2.50E-04
2.00E-04
1.50E-04
1.00E-04
5.00E-05
0.00E+00
-20
-15
-10
-5
0
Y Position (cm)
5
10
15
20
We will measure total neutron cross-section,
S(q,ω), and UCN conversion cross-sections at Los
Alamos this summer. In the mean time, we can try
different MCNP models…
Solid Oxygen
Thermal Treatment
Reflector
Neutron Flux
(10-4 n/cm2/src)
300 K Free Gas
None
0.50±0.01
300 K Free Gas
300 K Beryllium
reflector
3.81± 0.08
No Solid Oxygen
300 K Beryllium
reflector
7.11±0.14
4 K Free Gas
300 K Beryllium
reflector
9.12±0.36
77K Beryllium, includes
coherent scattering
effects
300 K Beryllium
reflector
9.45±0.09
We will measure total neutron cross-section,
S(q,ω), and UCN conversion cross-sections at Los
Alamos this summer. In the mean time, we can try
different MCNP models…
Solid Oxygen
Thermal Treatment
Reflector
Neutron Flux
(10-4 n/cm2/src)
300 K Free Gas
None
0.50±0.01
300 K Free Gas
300 K Beryllium
reflector
3.81± 0.08
300 K Beryllium
2/src
7.4x10-4 n/cm
reflector
7.11±0.14
No Solid Oxygen
Mean Flux:
30035%!!!
K Beryllium
4Standard
K Free Gas Deviation:
9.12±0.36
reflector
77K Beryllium, includes
coherent scattering
effects
300 K Beryllium
reflector
9.45±0.09
−8
−1
Solid Oxygen
UCN Conversion Rate:
≈ 3 ×10 cm
0-5 meV Neutron Flux:
n
≈ 1.8 ×10
2
cm ⋅ s ⋅ mA
10
UCN
UCN Production Rate: ≈ 5 × 10
cc ⋅ s ⋅ mA
2
UCN Current:
UCN
≈ PUCN × V = 5 ⋅10
s ⋅ mA
5
(~1 mA current)
We expect 500 UCN/cc/mA in the solid oxygen.
Only ~½ watt/mA total heating in 1000 cc of solid
oxygen.
Cell
Photon
Heat
Target
Neutron Photon
Heat
Heat
Total
So2
0.20
0.08
0.12
0.39
SO2 Al
0.09
0.01
0.04
0.15
Poly
0.39
1.58
0.17
2.13
Poly Al
0.20
0.03
0.09
0.32
Guide
0.07
0.00
0.01
0.09
0.54
2.54
We expect 500 UCN/cc/mA in the solid oxygen.
Only ~½ watt/mA total heating in 1000 cc of solid oxygen.
The solid oxygen will be cooled by flowing liquid helium.
The other elements will be cooled by separately via mechanical
pulse tube helium cryostat.
Cell
Photon
Heat
Target
Neutron Photon
Heat
Heat
Total
So2
0.20
0.08
0.12
0.39
SO2 Al
0.09
0.01
0.04
0.15
Poly
0.39
1.58
0.17
2.13
Poly Al
0.20
0.03
0.09
0.32
Guide
0.07
0.00
0.01
0.09
0.54
2.54
Closing Remarks
• LENS is a a small, long pulsed source with
good potential to test new ideas.
• We will develop solid oxygen
experimentally at Los Alamos and IUCF.