Scoring small geometries and low proton energies

Scoring
1

Dear FLUKA users,
I hope you are doing well.

I am running in various problems in the FLUKA simulations, and I would like to discuss them with you. Just to give a background, I am looking at irradiating Ti6Al4V with proton beams of 3 MeV or 15 MeV for 10 mins with a current of 30 uA (1.875x10^14 p/cm^2/s). In my simulations I would like to measure the DPA, dose rate and decay as well as various nuclei produced during irradiation.

  1. Are my simulations set up correctly for the relatively “low” proton energies? Or is there something that I am missing? As the dose rate results for the 15MeV are a factor of 10000 out at 60s cooling compared to other simulations considering the same irradiation settings. And, the 3 MeV simulations are not even producing results, but just giving a dose rate of 0.
  2. Are there limits to how small the geometries can be? I would need a target that is 50um thick for the 3 MeV irradiation, but at the moment FLUKA is not producing results for a target with thickness of 100um.

You can find the FLUKA files attached to this message.
Thank you for your time.
Kind regards,
Jatinder

Ti6Al4V-proton-15MeV-30uA-10min.flair (6.4 KB)
Ti6Al4V-proton-15MeV-30uA-10min.inp (5.5 KB)

Ti6Al4V-proton-3MeV-30uA-10min.inp (5.5 KB)
Ti6Al4V-proton-3MeV-30uA-10min.flair (6.4 KB)

3

Dear Jatinder,

Thank you for your questions, welcome to the forum, and sorry for the slight delay.

the 3 MeV simulations are not even producing results, but just giving a dose rate of 0.

The parametrization employed in FLUKA for proton reaction cross sections has a threshold effect (loosely intending to account for Coulomb barrier effects), typically in the order of a few MeV. However, this threshold is at times a bit too high, and it may well block otherwise open low-energy nuclear reaction channels at lower energies, normally (p,n) and (p,γ).

The following plot shows the FLUKA reaction cross section parametrization for protons on Ti, Al, and V (the constituents of your Ti6Al4V compound). At 3 MeV the FLUKA proton reaction cross section vanishes and this explains why you do not score any ambient dose rates:

1793×1024 60.1 KB

Note, however, that this is an artefact of the FLUKA reaction cross section parametrization. As you can see in the following plot with experimental data from EXFOR, for various isotopes of Ti there are open channels at 3 MeV, indeed (p,γ) and (p,n):

1750×1051 88.3 KB

In previous versions of the code, local fixes to remedy this artefact were done on an isotope-by-isotope basis. See, e.g. Low energy Cu(p,x) cross section - #3 by cesc. This aspect may be revisited in future versions of the code.

Are there limits to how small the geometries can be?

Yes, but in your case, the problem is not the geometry and its dimensions, but rather the low energy of the incident proton beam (3 MeV), falling a bit below the spurious threshold in the FLUKA proton reaction cross section parametrization, as outlined above.

Are my simulations set up correctly for the relatively “low” proton energies? Or is there something that I am missing? As the dose rate results for the 15MeV are a factor of 10000 out at 60s cooling compared to other simulations considering the same irradiation settings

For this observation, could you provide any reference you used in your comparison of the dose rates? Upon a first look at your input, all employed conversion factors look alright (both in the input and in the Flair plot tab).

I have some additional remarks regarding your input files:

  • You may want to revisit your COMPOUND card. If you express the composition in terms of the atom content, you are indicating the stoichiometry, i.e. you need to indicate the number of atoms of each element. In your case that would rather be: 6 atoms of Ti, 4 atoms of Al, and 1 atom of V. For more details, you can consult the following material:
    https://indico.cern.ch/event/1012211/contributions/4247792/attachments/2256347/3828711/06_Materials_2021_online.pdf.

  • In the MAT-PROP card with SDUM = DPA-ENER, the default values of b_arcdpa and c_arcdpa are both 0, which means that you are not scoring ARC-DPA, but DPA-NRT, as per Note 7 in: 7.22.44. MAT-PROP — FLUKA Manual

  • One comment regarding the following statement:

    with proton beams (…) with a current of 30 uA (1.875x10^14 p/cm^2/s)

    The beam intensity that you indicate in WHAT(2) of the IRRPROFI card is expressed in particles/s. Your conversion was alright, except that there are no units of cm^(-2).

  • It may be wise not to set the beam starting position exactly on the boundary between two regions as you do now (between the black hole and the void).

Cheers,

Alexandra

4

Dear Alexandra,
Thank you very much for your informative and very useful reply.

I am comparing the FLUKA simulations to the FISPACT-II results, please see the images below. The first picture contains the detail of the activity and dose rate of the FISPACT-II results.
FISPACT-Simulation-Results

FISPACT-Dose-Rate
FISPACT-Dose-Rate1278×815 46.9 KB

As you can see from both the table and the dose rate graph, they do not match with the overall dose rate seen in FLUKA. To be clear, for the FISPACT dose rate calculations, the dose rates were calculated for a point source of 1 g at a distance of 1 m. This was assumed due to the target mass, which is 0.2215 g (for a 1x1x0.05 cm Ti6Al4V sample with a density of 4.43 g/cm^3). Hence, using the default assumption of a semi-infinite slab approximation might not be correct.

Is there a way of excluding the target from the detector and just measuring the dose rate around the target? As that might replicate the FISPACT-II results.

Thank you very much for your time.
Kind regards,
Jatinder

5

Dear Jatinder,

for the FISPACT dose rate calculations, the dose rates were calculated for a point source of 1 g at a distance of 1 m.

Two points worth highlighting:

  • In your FLUKA simulation you are scoring the ambient dose rate with a USRBIN (coupled to various cooling times with the DCYSCORE card), legitimately. However, the USRBIN extends within ±2 cm of the target. This does not match the setting you mentioned for your FISPACT calculation, where you are looking 1 m away! The fluence from a point isotropic source (like what one has in a radioactive decay) scales with the distance (r) as 1/r^2. Therefore, you can expect a factor of (2/100)^2 = 4E-4 difference when comparing any fluence-related quantity (such as the ambient dose rate, indeed) between these two distances. This is a purely geometric effect which may easily explain the bulk of the order of magnitude discrepancy you observe.
  • Next, the target definitions from FLUKA and FISPACT are possibly not one-to-one comparable. In FLUKA you define a slab of a certain thickness (essentially exceeding the proton range), implying transport, slowing down by ionization, as well as nuclear reactions of protons. As a result, the production of radioactive isotopes is smeared on a certain material mass thickness, involving various proton energies from 15 MeV down to a few MeV. You will have to tread carefully in order to compare this (physical) simulation setup, where the resulting radioisotopes distribution is smeared over some mass thickness and involves various transport effects, with results from a point source of 1 g.

On the other hand, what drives the ambient dose rate is the activity in the target. Once you have sufficiently cleared up for yourself the different target definitions and the comparison procedure, if you find reasonably close values of the activity in FISPACT and in FLUKA, the rest should be just the 1/r^2 geometric aspect outlined above.

I went ahead and examined the activity, e.g. after a cooling time of 60s, running your original FLUKA input file and I obtained ~1.9E9 Bq, which is rather close to what you report (1.04E9). If I set the right material composition in FLUKA as per my previous reply, I get an activity of ~1.2E9 Bq. Finally, if I make the target 0.035 cm thick, I get an activity of ~1.0E9 Bq. All of these assessments were done with very low statistics due to lack of time, but they illustrate the point: target definition matters!

Finally, one detail which eluded me in my previous reply: in order to estimate ambient dose rates you need the fluence in air, not in vacuum. Please change the material surrounding your target to air. Be aware that it may now matter whether your proton source is placed immediately in front of the target or further away (as you had it originally), so please adapt as needed.

Cheers,

Alexandra

6

Dear Alexandra,
Thank you very much for the reply, that would explain the large difference between the two.

However, I am struggling to understand how the binning would work for this case. Would something like the image below be accurate?

Geometry-Binning
Geometry-Binning2050×1286 231 KB

Or do I want to have bins of 1x1x1 m? Because I tried both bins in the top image and a single 1x1x1 m and I do not get results that are closer to what you mentioned in your reply. Especially, I am not able to get anywhere close to the activity in Bq. However, the dose rate was drastically reduced compared to what I was getting originally. I would just like to confirm if I have understood things correctly.
Please find attached the FLAIR and input files at the end of the reply.

I tested for the beam distance, and it seems that keeping the beam at the edge of the sample produces a much higher dose rate than the beam starting 1 m away from the target.

Thank you very much for your time and help.
Kind regards,
Jatinder
Ti6Al4V-proton-15MeV-30uA-10min.flair (8.4 KB)
Ti6Al4V-proton-15MeV-30uA-10min.inp (7.2 KB)

7

Dear Jatinder,

I apologize for the late reply.

I am struggling to understand how the binning would work for this case. (…) Or do I want to have bins of 1x1x1 m? Because I tried both bins in the top image and a single 1x1x1 m (…)

You are now scoring activity in two different ways:

  1. Using a USRBIN (associated with a cooling time via the DCYSCORE card) extending up to ±50 cm on the x and y axes, and ±50.05 cm on the z axis. The number of bins is 99, thus the bin size is approximately 1 cm. This is relevant because the results have dimensions of Bq/cm^3, meaning that the activity is divided by the volume of the bin. Since in your case the volume of the bin is roughly 1 cm^3, you are de-facto scoring the activity (in Bq). However, in order to get the precise value of the activity you have to multiply by the volume of your bin (especially if the bin size is not 1 cm).

    One remark here is that since you are scoring the activity in the target, you can define a USRBIN covering exactly the dimensions of your target (being careful with the bin size as described above) or a USRBIN scoring per region.

  2. Using the RESNUCLEI card (again associated with a cooling time via the DCYSCORE card). Scoring in this way, you can extract the value of the activity from the *_28_sum.lis output file. Taking your latest input file I get:

729×412 9.5 KB

Here, the volume is taken by the code as 1 cm^3, and what you are reading as “Tot. response” is directly the value of the activity in Bq.

Because I tried both bins in the top image and a single 1x1x1 m and I do not get results that are closer to what you mentioned in your reply. Especially, I am not able to get anywhere close to the activity in Bq.

The way in which you are scoring the activity is not the cause of the numerical differences that you observed.

In my previous reply I suggested to put air around the target instead of vacuum, considering the fluence-to-dose conversion done by the code to evaluate ambient dose (the involved coefficients assume fluence in air).

The closing remark “adapt as needed”, related to the starting position of the beam, was not an innocent one: now you have air everywhere, and your beam starts 1 m before the target. This 1 m of air leads to a substantial drop in target activity (this can be attributed to the fact that protons lose energy on their way to the target resulting then in fewer nuclear reactions / at lower energies). I suggest you adapt the beam position as needed.

For example, if I place the beam at 1 cm in front of the target and keep all the other settings in your input file as they are, I get an activity of the same order of magnitude as what you report from FISPACT-II:

726×407 9.66 KB

However, the dose rate was drastically reduced compared to what I was getting originally.

The reduction that you witness is due to two factors:

  1. You went from scoring the ambient dose rate at 2 cm (in your original reply) to scoring at 50 cm (now). What you are observing is a reduction factor of geometric origin (as you increase the distance at which you score, the ambient dose rate drops). Still, if you want to score at 1 m away from the target, you should extend your USRBINs up to ±100 cm.

  2. The beam has now a whole meter of air before the target, leading to a lower activity as outlined in the foregoing point.

Cheers,

Alexandra

8

Dear Alexandra,

Thank you very much for your help and time. I extended the USRBIN to ±100, and I was able to replicate the results following your suggestions.

Thank you again.
Kind regards,
Jatinder