**Argon scattering in the Hyspec detector vessel**

**Vinita J. Ghosh**

**August 9, 2006.**

**Executive Summary**

At the Hyspec IDT meeting (April 7, 2006) concern was expressed that
scattering by the argon gas in the detector vessel could create an
unacceptable background. The specific issue that needs to be addressed
is as follows: Some small part of the neutrons in a Bragg peak beam
passing through the detector bank will inevitably be scattered by argon
atoms. They will lose or gain energy in the scattering process and, in
addition, their paths to the detector bank will be longer than those of
the unscattered, Bragg-peak neutrons. Argon gas scattering will
therefore generate a beam-related, time-dependent background that will
spread over the entire detector array. This background, if too large,
could negatively impact on instrument sensitivity.

In general, inelastic peaks can be expected to have integrated
intensities roughly four orders of magnitude smaller than their Bragg
equivalents. To be clearly identified and quantified it is obviously
important that they not be significantly obscured by scattering from the
argon gas. What would be acceptable in the way of gas-scattered
background will depend on the specific experimental situation and is to
some extent a matter of opinion but a consensus view would probably be
that it should be least one and preferably two orders of magnitude
smaller than a typical inelastic signal.

In order to asses the impact of argon scattering several sets of
simulations were performed. First the time-integrated neutron intensity
was mapped for a representative set of neutron energies assuming a
collimated, monochromatic source of neutrons located at the sample
position. These results are presented in Figs 2-7.

In making a definitive evaluation of the effect of the gas-scattered
background, however, it is important to keep in mind that what is
important is not only its magnitude but the range of energy transfers
that it would obscure. Thus it is also necessary to simulate the \"times
of arrival\" of these neutrons relative to the unscattered Bragg-peak
neutrons. The time-dependent neutron flux at the detector bank was
therefore simulated as realistically as possible, taking into account
the energy, angle and time distribution of neutrons at the
sample-source. This model and its results are presented in Figs 8-15.
Representative simulations of unscattered and scattered neutron arrival
times are plotted in figs. 12 and 14 and the simulation results are
replotted in terms of \"apparent energy transfers\" in figs. 13 and 15.

In addition, the argon scattering results were compared with scattering
by helium and air (figs 16 and 17). If the HYSPEC detector vessel were
evacuated it would require 3.6mm Al windows according to W.J.
Leonhardt's calculations. When the detector vessel is filled with argon
it would require an Al window which is 0.81mm thick. These two scenarios
were simulated and the simulation results are presented in Fig 18.

It was found that the maximum time-integrated flux due to argon
scattering on the non-Bragg peak detector cells was a few times 10^-5^
of the flux in the Bragg peak near the Bragg peak detector. The
background flux decreased to \~10^-6^ as the distance from the Bragg
peak detector was increased (see Fig 17). The impact of adding a thin Al
window (0.81mm thick) is negligibly small. If the HYSPEC detector vessel
were evacuated it would require 3.6mm Al windows. The scattering from
the thicker (3.6mm) Al window (see Fig 18) is a background flux \~10^-6^
times the flux of the Bragg peak.

Given these results, the question to be addressed is whether a
time-integrated background flux due to scattering from the argon in the
detector vessel which is five to six orders of magnitude smaller than
the Bragg peak flux is 'small enough' to resolve low-intensity,
small-energy-transfer peaks in near-neighbor detectors.

**Simulation model**

In order to map the time-integrated Bragg-peak induced gas-scattered
background at the HYSPEC detector bank some simple MCNPX simulations
have been performed, For simplicity the detector vessel was represented
as a rectangular box rather than a segment of a cylinder as shown in the
following figure. (The effect of this is to slightly increase the path
lengths of the gas-scattered atoms and thus slightly increase their time
of arrival at the detector bank).

Figure 1. Layout of the simulation model

For the first set of simulations a perfectly collimated monoenergetic
beam of neutrons enters the detector vessel at the middle of the z = 70
cm face. The z = 450cm face represents the extended detector bank. For a
sample-detector distance of 450 cm the box had a length of (450-70) =
380 cm, the width of the detector bank was 450\*2\*tan30 = 2\*260 cm,
and the height of the detector bank was 2\*450\*tan7.5 = 2\*60 cm. A
mesh tally was performed on the extended detector bank. The pixel size
was 2cm by 2cm. The intensity in the Bragg peak was set equal to one. A
10^9^ neutron simulation was performed for some representative neutron
energies.

**Results:**

The mesh plots showing the time-integrated distribution of the
argon-scattered neutrons at the detector bank are shown in figures 2-7.
The neutron intensity in each 2cm by 2cm detector pixel obviously
depends on the size of the pixel.

![](media/image1.wmf)

Fig. 2. Integrated intensity distribution for a Bragg peak energy of
3.5meV

![](media/image2.wmf)

Fig 3. Integrated intensity distribution for a Bragg peak energy of 5meV

![](media/image3.wmf)

Fig 4. Integrated intensity distribution for a Bragg peak energy of
15meV

![](media/image4.wmf)

Fig 5. Integrated intensity distribution for a Bragg peak energy of
30meV

![](media/image5.wmf)

Fig 6. Integrated intensity distribution for a Bragg peak energy of
60meV

![](media/image6.wmf)

Fig 7. Integrated intensity distribution for a Bragg peak energy of
90meV

In these figures the blue region represents integrated intensities less
than 10^-6^, and the green regions represent integrated intensities less
than 10^-5^. Around the Bragg peak there is a small area of higher
intensity. Parts of the detector bank where the integrated intensity was
less than 10^-6^ have not been shown. It is obvious from a comparison of
Figs. 2-7 that lower energy neutrons are more effectively scattered by
argon than those of higher energy. This is consistent with the values of
the argon scattering cross-sections shown in Appendix 1. It is obvious
from figure A1 that the absorption cross-section of argon decreases from
\~3 to 0.3 barns as the neutron energy increases from 1 to 100meV, and
from figure A2 that the elastic scattering cross-section of argon
decreases from \~1 to 0.7 barns as the neutron energy increases from 1
to 100meV. Since the magnitude of the argon scattering cross-sections
decreases as the neutron energy increases, the integrated intensity of
the argon scattering background is expected to decrease as the neutron
energy increases (as is evident in fig 2-7).

**Time dependence of the argon scattering**

The time dependence of the argon-scattered Bragg peak neutrons was next
explored using MCNPX. For this simulation the model of the extended
detector bank was modified and only one array of detector cells centered
at the scattering plane was examined in detail (see Fig 8). These cells
were either 2.5 or 5cm wide and 10cm high. The central cell (cell 1) and
the Bragg peak are centered at x=0 y=0. For the time-dependent
simulations the cell width was chosen to be twice the actual width of a
detector tube. In addition to that the outputs of symmetrical cells on
both sides of the Bragg peak were combined to reduce statistical errors.
These large cell sizes had to be used to make the time bins equal to 10
microseconds.

Figure 8: Location of the detector pixels

To make the time-dependent simulations as realistic as possible the
energy and time dependence of the neutron beam at the sample position
were taken into account. The energy (see Fig 9) and time distribution
(see Fig 10) of the 15meV (nominal energy) neutrons at the sample
position was obtained from HYSPEC McStas simulations.
![](media/image7.wmf)

Fig 9. Energy distribution of the 15meV (nominal incident energy)
neutrons immediately downstream of the wavelength selecting chopper.
These are McStas results for a simulation with a moderator-monochromator
distance of 37m.

![](media/image8.wmf)

Fig 10. Time distribution of the 15meV (nominal incident energy)
neutrons immediately downstream of the wavelength selecting chopper, at
the sample position and at the detector bank provided there was no air
or argon scattering. These are McStas results for a simulation with a
moderator-monochromator distance of 37m.

The energy spectrum shown in Fig 9 was used as input for MCNPX. The time
distribution of the neutrons at the sample position is illustrated in
Fig 10. To simplify the calculations it was assumed that the time pulse
was triangular and had a FWHM of 50 microseconds at the sample. This
triangular distribution was convoluted with the time dependence of the
scattered neutrons at the detector bank to obtain the results presented
in Fig 12.

![](media/image9.wmf)

Fig 11. The time-integrated flux on each detector cell normalized to the
flux in the Bragg peak cell as a function of the distance from the Bragg
peak cell.

The normalized time-integrated flux is plotted in Fig 11 for each
detector cell in the scattering plane. We see from Fig 11 that the Bragg
peak typically spreads out over two detector cells. This spreading is
almost entirely due to the 20 minute divergence of the source neutron
beam at the sample position. The third cell (whose center is 10 cm from
the Bragg peak center) has a neutron flux of \~10^-5^ of the flux in the
Bragg peak cell. The flux in the detector cells decreases as the
distance from the Bragg peak increases. This flux is entirely due to
argon scattering. When a simulation was done with no gas in the detector
vessel the flux in detector cells 3 and larger was zero (as expected).
It is relevant to note that the simulation of Fig 11 has the same space
dependence as that in Fig 4.

![](media/image10.wmf)

Fig. 12. The time dependence of the argon scattered neutrons in various
detector cells.

![](media/image11.wmf)

Fig 13. The apparent energy of the argon-scattered neutrons in various
detector cells calculated from the time of arrival of the neutrons at
these cells.

The time dependence and the apparent energy dependence of the
argon-scattered neutrons for a nominal energy of 15meV are plotted in
figures 12 and 13. For these simulations the sample-source neutrons had
an energy distribution shown in Fig 9 and angular divergence of 20
minutes. In order to simulate the time dependence of the neutrons
incident on the sample a triangular time pulse with a FWHM of
50micrseconds was convoluted with the time dependence of the
argon-scattered neutrons at the detector. The apparent energy plots of
Fig13 are very informative. They show that because of the finite size of
the sample and the divergence of the sample-source the Bragg peak
spreads out onto adjacent detectors. Because of the energy and time
width of the source pulse the smallest energy loss that could be
measured would be approximately 0.75meV (energy resolution \~5%). One
should remember that for this simulation the time width at the
wavelength-selecting chopper was \~50μs. The time and hence the energy
width of the incident neutron pulse can be changed (both increased and
decreased) by changing the rotation rate of the T2 chopper.

The figure also shows that for detectors that are more than 35cm from
the Bragg peak

detector the argon-scattering flux is less than 10^-6^. Detectors that
are closer than 35cm have an argon-scattering flux that is higher than
10^-6^ but lower than 10^-5^.

The time and apparent energy dependence of the argon-scattered neutrons
for a nominal energy of 5meV are plotted in figures 14 and 15. The
apparent energy plots in Fig 15 show the same qualitative behavior as
those of the 15meV neutrons plotted in Fig 13. For a nominal incident
energy of 5meV the smallest energy loss that could be resolved would be
\~(5-4.85) = 0.15meV (energy resolution \~3%) because the incident beam
has a finite time and energy width. One should remember that for this
simulation the time width at the wavelength-selecting chopper was
\~50μs. The time and hence the energy width can be changed (both
increased and decreased) by changing the rotation rate of the chopper.

![](media/image12.wmf)

Fig 14. The time dependence of the argon scattered neutrons in various
detector cells.

![](media/image13.wmf)

Fig 15. The apparent energy of the argon-scattered neutrons in various
detector cells calculated from the time of arrival of the neutrons at
these cells.

The figure also shows that for detectors that are more than 35cm from
the Bragg peak detector the argon-scattering flux is less than 10^-6^.
Detectors that are closer than 35cm have an argon-scattering flux that
is higher than 10^-6^ but lower than 10^-5^.

These time-dependent simulations were not performed for higher neutron
energies. Since the scattering cross-section of argon decreases as the
neutron energy increases (see Appendix 1) the background time-dependent
flux due to argon scattering is expected to decrease as the neutron
energy increases.

**Background generated by argon, helium and air scattering**

Simulations were performed to compare the impact of the scattering due
to argon, ^4^He, and air (80% N, 20% O) on the Bragg peak. The detector
vessel was filled with the selected gas at room temperature and one
atmosphere pressure. The normalized time-integrated flux on the various
detectors is plotted in Fig 16. The control simulation with vacuum in
the detector vessel has not been plotted because the neutron flux on the
non-Bragg peak detectors was zero. It is obvious from this figure why
detector vessels are evacuated -- the scattering due to air is much
larger than the scattering due to argon or ^4^He. The scattering
cross-sections for ^4^He, N and O are plotted in Appendix 1.

![](media/image14.wmf)

Fig 16. Comparison of the background neutron flux when the detector
vessel is filled with argon, helium or air. In this simulation the space
between the sample and the detector vessel is a vacuum.

![](media/image15.wmf)

Fig. 17. Comparison of the background neutron flux when the detector
vessel is filled with argon, helium or air. In this simulation it is
assumed that the sample is surrounded by an evacuated dewar with a
radius of 10cm. The space between the sample dewar and the detector
vessel is filled with air.

It is clear from comparing figs 16 and 17 that the impact of the
scattering due to 60cm of air upstream of the detector vessel is
insignificant compared to the scattering due to the gas in the detector
vessel.

**Scattering due to Al windows**

W.J. Leonhardt has estimated the thickness of the upstream aluminum
window for the HYSPEC detector vessel. According to his calculations the
thickness of the Al window would have to be 3.6mm if the HYSPEC detector
vessel were evacuated. If the detector vessel is filled with argon the
thickness of the Al window could be reduced to 0.81mm. This of course
suggested a comparison between the scattering due to the Al window and
the scattering due to the argon in the detector vessel.

In order to study the impact of the Al scattering two simulations were
performed:

1.  The Al window thickness was 3.6mm and there was a vacuum in the
    detector vessel.

2.  The Al window thickness was 0.081mm thick and the detector vessel
    was filled with argon at 1bar.

In both cases the space between the sample dewar and the detector vessel
was filled with air. MCNPX treats all materials as dense gases with no
positional order and therefore does not separate the scattering into
coherent elastic Bragg and temperature diffuse (phonon) components.  Al
is a polycrystalline material and the greatest part of the scattering
from it will be Bragg scattering (most of which will be intercepted and
stopped by the radial collimator in the detector tank).  The simulations
therefore significantly overestimate the scattering from the Al windows.
The results of these simulations are presented in Fig. 18.

![](media/image16.wmf)

Fig 18. Impact of the Al window on the Bragg peak neutrons. The blue
triangles represent the scattering due to the 3.6mm Al window when the
detector vessel is evacuated. The red circles represent the scattering
due to the 0.81mm Al window when the detector vessel is filled with
argon.

It is clear from this figure that the background due to argon scattering
is somewhat larger than that due to the thicker Al window near the Bragg
peak. The contribution of the very thin (0.81mm) Al window to the argon
scattering background is very small.

**Summary and conclusions**

In order to asses the impact of argon scattering several sets of
simulations were performed. First the time-integrated neutron intensity
was mapped for a representative set of neutron energies assuming a
collimated, monochromatic source of neutrons located at the sample
position. These results are presented in Figs 2-7.

In making a definitive evaluation of the effect of the gas-scattered
background, however, it is important to keep in mind that what is
important is not only its magnitude but the range of energy transfers
that it would obscure. Thus it is also necessary to simulate the \"times
of arrival\" of these neutrons relative to the unscattered Bragg-peak
neutrons. The time-dependent neutron flux at the detector bank was
therefore simulated as realistically as possible, taking into account
the energy, angle and time distribution of neutrons at the
sample-source. This model and its results are presented in Figs 8-15.
Representative simulations of unscattered and scattered neutron arrival
times are plotted in figs. 12 and 14 and the simulation results are
replotted in terms of \"apparent energy transfers\" in figs. 13 and 15.

In addition, the argon scattering results were compared with scattering
by helium and air (figs 16 and 17). If the HYSPEC detector vessel were
evacuated it would require 3.6mm Al windows according to W.J.
Leonhardt's calculations. When the detector vessel is filled with argon
it would require an Al window which is 0.81mm thick. These two scenarios
were simulated and the simulation results are presented in Fig 18.

It was found that the maximum time-integrated flux due to argon
scattering on the non-Bragg peak detector cells was a few times 10^-5^
of the flux in the Bragg peak near the Bragg peak detector. The
background flux decreased to \~10^-6^ as the distance from the Bragg
peak detector was increased (see Fig 17). The impact of adding a thin Al
window (0.81mm thick) is negligibly small. If the HYSPEC detector vessel
were evacuated it would require 3.6mm Al windows. The scattering from
the thicker (3.6mm) Al window (see Fig 18) is a background flux \~10^-6^
times the flux of the Bragg peak.

Given these results, the question to be addressed is whether a
time-integrated background flux due to scattering from the argon in the
detector vessel which is five to six orders of magnitude smaller then
the Bragg peak flux is 'small enough' to resolve low-intensity,
small-energy-transfer peaks in near-neighbor detectors.

Appendix 1

Scattering and absorption cross-sections of argon, helium, nitrogen and
oxygen generated using MCNPX. The x axis in Figs A1-A8 is incorrectly
labeled meV. The energy units should be MeV

![](media/image17.png){width="4.122916666666667in" height="3.1875in"}

Fig A1. Absorption cross-section of argon as a function of energy

![](media/image18.png){width="4.122916666666667in" height="3.1875in"}

Fig A2. Elastic scattering cross-section of argon as a function of
energy

It is obvious from figures A1 and A2 that the absorption cross-section
of argon decreases from \~3 to 0.3 barns as the neutron energy increases
from 1 to 100meV, and from figure 9 that the elastic scattering
cross-section of argon decreases from \~1 to 0.7 barns as the neutron
energy increases from 1 to 100meV. Since the magnitude of the argon
scattering cross-sections decreases as the neutron energy increases the
integrated intensity of the argon scattering background is expected to
decrease as the neutron energy increases, as shown by the simulation
results in figures 2-7.

![](media/image19.png){width="4.375in" height="3.379861111111111in"}

Fig A3. Elastic scattering cross-section of ^4^He.

![](media/image20.png){width="4.5in" height="3.477777777777778in"}

Fig A4. Absorption cross-section of ^4^He.

The elastic scattering cross-section of ^4^He is somewhat but not much
larger than that of argon. However, the absorption cross-section is
negligibly small.

![](media/image21.png){width="4.125in" height="3.1881944444444446in"}

Fig A5. The elastic scattering cross-section of nitrogen

![](media/image22.png){width="4.375in" height="3.38125in"}

Fig A6. The elastic scattering cross-section of nitrogen.

The scattering cross-sections of nitrogen and oxygen are \~ 13-15 times
the scattering cross-sections of argon and 4He.

![](media/image23.png){width="4.5in" height="3.477777777777778in"}

Fig A7. The elastic scattering cross-section of oxygen.

![](media/image24.png){width="4.625in" height="3.5743055555555556in"}

Fig A8. The absorption cross-section of oxygen.

A comparison of the scattering cross-sections of argon, helium, nitrogen
and oxygen explains why detector vessels are evacuated. Filling the
detector vessel with argon or helium will result in a small
time-dependent background due scattering by these gases.