No scores were obtained using a 3He beam for nuclear reactions with ErD2

Dear FLUKA expert,
I am simulating the interaction of a 3He beam with an ErD2 target. During this simulation, I noticed that when the incident energy of 3He is 1.5MeV, there is no proton production. However, when I use an energy of 5MeV, proton production is observed. The nuclear reaction involved in this process is D(3He,p)4He.

  1. What could be the reason for the observed behavior in this case?

  2. Is my target setup correct? Is the use of LOW-PWXS for neutron cross sections accurate? What do the labels in S(α,β) mean, and what do terms like “ortho” and “para” signify in relation to deuterium?

  3. Are my physics and transport settings configured correctly?

  4. When I use USRBIN to observe proton production from 3He at 5MeV, I noticed that if I set the region size larger (e.g., 21 bins), I can see its spatial distribution. However, if I set the region size very small (e.g., 23 bins, just within the target), I cannot observe the distribution. Could you explain the reason for this phenomenon and suggest a solution?

  5. When I use USRBIN to observe the spatial distribution of protons and alphas generated by the 5MeV 3He beam, I am puzzled by the significant difference in their distributions. Alphas seem to be concentrated at very low backscattering angles. Why is this difference occurring?


    proton

  6. When creating plots, such as 2D plots along the Z-axis, I notice that the resulting plots have an elliptical or rectangular aspect ratio. What methods can I employ to transform the ellipse into a circle or the rectangle into a square?

  7. When using USRBDX (24bin) for scoring, why are protons with energies as low as 5 MeV generated?

Thank you very much for your help and answers. Wish you the best of luck in everything.
yu
1.inp (3.1 KB)

Dear Yu,

Thank you for your question, and welcome to the forum! I apologize for the rather late reply.

(…) I noticed that when the incident energy of 3He is 1.5MeV, there is no proton production. However, when I use an energy of 5MeV, proton production is observed. (…) What could be the reason for the observed behavior in this case?

The discrepancy between the results obtained with incident 3He beams of 1.5 MeV and of 5 MeV is due to a kinetic energy cutoff for nuclear reactions in FLUKA at 1.1 MeV/n, below which no nuclear inelastic scattering happens (with a few exceptions, e.g. d+D and d+T). Your 1.5 MeV 3He beam corresponds to 0.5 MeV/n, falling below FLUKA’s cutoff and consequently not undergoing nuclear reactions.

This cutoff behavior may be revisited in the future.

Is my target setup correct?

If you refer to the material and compound definitions, they appear alright as far as they seem to respect the stoichiometry you may have in mind.

What do the labels in S(α,β) mean, and what do terms like “ortho” and “para” signify in relation to deuterium?

The thermal scattering law S(α,β,T) is applied for neutrons with energies below ~4 eV to account for the fact that neutron scattering at low energies is sensitive to the chemical/molecular/crystal binding environment in which the target nucleus finds itself. For more details you can consult the following materials: https://indico.cern.ch/event/1200922/contributions/5411865/attachments/2663551/4614953/13_Neutronics_2023_Advanced_ANL.pdf, and 7.22.43. LOW-PWXS — FLUKA Manual.

If by “labels in S(α,β)” you mean the various entries in the dropdown menu you see in Flair, these correspond to the 58 materials for which thermal scattering laws are available.

The ortho and para attributes denote different deuteron spin couplings in the D2 molecule, to which neutron scattering is sensitive. See e.g.: https://www.sciencedirect.com/science/article/pii/0168900294911746

Is the use of LOW-PWXS for neutron cross sections accurate?

No. The S(α,β) treatment has to be assigned to an individual isotope, not to a compound. If you choose to apply this treatment to deuterium you should also change the temperature in WHAT(3) since the available temperatures are from 19K to 23K.

Moreover, you should add an additional LOW-PWXS card without selecting any specific material in order to apply the point-wise treatment of neutrons to all materials involved in your geometry. Otherwise, the code resorts to the group-wise approach and, for example, Erbium is not accounted for in the group-wise database, leading to a crash.

Are my physics and transport settings configured correctly?

Yes, they appear fine for the problem you are studying, with the exception of the LOW-PWXS card outlined above.

(…) However, if I set the region size very small (e.g., 23 bins, just within the target), I cannot observe the distribution.

In logical unit 23 you are scoring, using an USRBIN, the spatial fluence of protons on a cylindrical grid inside target 1. Here are the results from this USRBIN that I get when running your input file:

Along R the particles are not extending much further than 0.25 cm due to the definition of the beam, which is annular and restricted up to R=0.25 cm.

Alphas seem to be concentrated at very low backscattering angles. Why is this difference occurring?

The spatial fluences of protons, as well as of alphas reveal both forward and backward emission. However, protons can be emitted at larger angles than alphas, since they are ligher.

What methods can I employ to transform the ellipse into a circle or the rectangle into a square?

The distortion you observe is a display artefact of gnuplot. Using the command “set size ratio 1” should solve the issue.

(…) why are protons with energies as low as 5 MeV generated?

The protons having energies as low as 5 MeV are produced in nuclear reactions of 3He on Erbium. In addition, these low-energy protons can also come from higher energy protons which were eventually slowed down.

Cheers,

Alexandra

1 Like

Dear Alexandra,

Thank you for your answers. I may still have some questions that need your help.

  1. You mentioned the nuclear reaction energy cutoff in FLUKA is 1.1 MeV/n, which means I cannot perform the calculation I want. So why does FLUKA need to set this cutoff, since nuclear reactions can actually occur below this energy value, is this related to the cross sections? By the way, where do the total and differential cross section data for the D(3He,p)4He nuclear reaction come from? Also, assuming I use some other Monte Carlo software, such as Geant4 or some you may know of, can they perform the related calculations?

  2. Assuming I do not choose S treatment for deuterium, does FLUKA have a default value for this, since our material is actually deuterium gas, is the related treatment still needed?

  3. In the spatial distribution of nuclear reaction protons, there is a red line along the transverse direction. This line is actually the incident direction of the 3He beam, does this mean some protons are generated during the 3He beam transport?

  4. I got no results when scoring DETEC1 to DETEC2 using USRBDX. I don’t know what went wrong. Also, for actual detector operation, is current more meaningful than flux?

  5. I wanted to try to get something like the output energy spectrum from a detector (Gaussian peak), so I chose to use DETECT, but it seems there are no results. I don’t know what errors occurred.

Thank you again for your patience in answering my questions. I wish you success at work and good health.
yu
1.inp (3.3 KB)

Dear Yu,

I apologize for the late reply.

You mentioned the nuclear reaction energy cutoff in FLUKA is 1.1 MeV/n, which means I cannot perform the calculation I want. So why does FLUKA need to set this cutoff, since nuclear reactions can actually occur below this energy value, is this related to the cross sections?

The 1.1 MeV/n cutoff serves as a general rule of thumb to roughly account for the fact that there is a Coulomb barrier energy below which nuclear reactions are not accessible. Unavoidably, for some situations (like in your specific case) this general recipe may have to be adapted.

By the way, where do the total and differential cross section data for the D(3He,p)4He nuclear reaction come from?

The reaction cross section comes from a parametrized expression fitted to experimental data.

The differential cross section, instead, is not parametrized. At your energies, for deuteron on 3He (above 1.1 MeV/n!) a compound nucleus is formed, which then passes through FLUKA’s Fermi break-up model to sample the possible final states.

Also, assuming I use some other Monte Carlo software, such as Geant4 or some you may know of, can they perform the related calculations?

You may need to address the question in the corresponding forum.

Assuming I do not choose S treatment for deuterium, does FLUKA have a default value for this, since our material is actually deuterium gas, is the related treatment still needed?

FLUKA does not activate S(α,β,T) thermal scattering laws by default, except for H bound in water (for which S(α,β,T) is activated automatically). Moreover, since there is no S(α,β,T) for D in the environment of your target (ErD2) in the databases, there is unfortunately nothing you may request. De facto, thermal neutron scattering will be on unbound D.

Instead, if your material is really D2 then you may request S(α,β,T) for 2H bound in D2_ortho and D2_para environments (see our previous discussion).

In the spatial distribution of nuclear reaction protons, there is a red line along the transverse direction. This line is actually the incident direction of the 3He beam, does this mean some protons are generated during the 3He beam transport?

Protons are generated from the D(3He,p)4He process.

In the plot attached below is the angular distribution of protons emitted from the interaction of the 3He beam with the ErD2 target:

As you can see, most of the protons are emitted in the forward direction, while there is also a small, but noticeable increase in the large emission angles (close to 180 degrees). The protons emitted at small angles are, however, entering the Molybdenum target, where they interact and exhaust their energy.

Removing the Molybdenum target and plotting the 2D fluence of protons you can observe clearly the effect described above: most protons are forward peaked, but there are also some protons emitted in the backward region, which were the ones you observed:

Setting the colorbox in linear scale, it is even more evident that there are less backscattered protons compared to the ones emitted in the forward direction:

I got no results when scoring DETEC1 to DETEC2 using USRBDX. I don’t know what went wrong.

There are two reasons why no results were obtained:

  1. There is a geometric effect due to the position and size of the detectors, which happen to cover a very narrow solid angle and in this way managing to capture only a limited number of particles. In the plot below you can see that from the proton fluence from Target 1 to Target 3 (in blue) only a very small amount of it arrives at Detector 1 (in dark green) where some of the protons interact in Aluminum and are stopped there, resulting in even less protons arriving at Detector 2 (in red).

  1. There is also a problem of low statistics. Given the aforementioned geometric argument, you will need to simulate a sufficiently large number of primary particles in order to generate enough protons which can make it to Detector 2.

Also, for actual detector operation, is current more meaningful than flux?

Possibly you mean current vs. fluence (time integral of the flux, readily accessible a la Monte Carlo).

If your detector is sensitive to the number of particles passing through it, you would need the current. Instead, if your detector is sensitive to the density of track lengths (e.g. if it measures energy deposition and related quantities), you would need to assess the particle fluence.

I wanted to try to get something like the output energy spectrum from a detector (Gaussian peak), so I chose to use DETECT, but it seems there are no results. I don’t know what errors occurred.

The lack of results comes from the two points detailed above: the geometric effect of the small solid angle covered by the detectors due to their position and size and relatively low statistics. Once you have enough statistics, you can proceed with the Gaussian broadening. However, be aware that event-by-event analyses are not recommended when using biasing techniques. See Note 2 in: 7.22.14. DETECT — FLUKA Manual.

Cheers,

Alexandra

1 Like

Dear Alexandra,
Thank you very much for your explanation. I have one more question regarding the angular distribution you mentioned. First, when you used USRYIELD to tally the proton angular distribution, you chose to hide the molybdenum target and have the ErD2 directly contact vacuum, right? Another question is, here I use the polar angle (angle with respect to the Z axis) to describe the angle (total range of 0-360°). When I use a perpendicular target (beam direction perpendicular to the target surface), because the proton emission is symmetric about the Z axis, tallying the 0-360° angular distribution corresponds to the 0-180° range used in USRYIELD (due to its direction relative to the beam). But when I use an inclined target (no longer perpendicular to the incident beam), the proton angular distribution is no longer symmetric about the Z axis. Tallying a certain angular range (e.g. 45°-225°) does not seem to be achievable with USRYIELD, right?
1.inp (3.8 KB)

Cheers,
yu

By definition of polar angle, it ranges only from 0 (forward along z) to 180 degrees (backward along z).
For a fixed polar angle, it’s the azimuthal angle (not filtered by USRYIELD) that spans from 0 (positive horizontal halfplane) through 90 degrees (positive vertical halfplane), 180 degrees (negative horizontal halfplane), 270 degrees (negative vertical halfplane), to 360 degrees (the same as 0).

Dear Yu,

(…) when you used USRYIELD to tally the proton angular distribution, you chose to hide the molybdenum target and have the ErD2 directly contact vacuum, right?

Exactly. I set the material of Target 2 to vacuum, instead of Molybdenum.

Cheers,

Alexandra

Dear Francesco,
I deeply apologize for the incorrect description of the polar angle. There may have been some misunderstanding here. Did you mean that USRYIELD cannot solve the problem of azimuthal angle of arbitrary ranges (such as the 45°-225° range I mentioned earlier)? If so, do you have any suggestions for calculating the angular distribution over the 45°-225° range?
cheers,
yu

Dear Alexandra,
Thank you very much for your patient response. I wish you the best in everything.
cheers,
yu