Questions about USRBDX spectra, log-energy plotting, and interpretation of dΦ/d(logE)

Scoring
1

Dear FLUKA and FLAIR experts,

I am trying to understand the correct interpretation and plotting of a neutron spectrum scored with USRBDX, especially when using logarithmic/linear energy bins and when plotting the results in FLAIR.

From the FLUKA forum and the scoring material, my understanding is the following: USRBDX fundamentally gives a quantity differential in energy, i.e. dΦ/dE. In addition, for a logarithmic energy representation, the recommendation is to use the lethargy plot < X >*Y = dΦ/d(log⁡E) = E dΦ/dE with [cm-2] as its units. Confusion regarding USRBDX - #2 by ceruttif

  1. My first question is about the meaning of the x-axis. If the proper logarithmic representation is dΦ/d(log⁡E)= E dΦdE. Why is the horizontal axis in plots usually still shown as E instead of log⁡E? Should I think of this as “plotting against energy E, but on a logarithmic axis”, or more rigorously as “representing the spectrum per unit logarithmic interval”? I want to understand whether the usual label E is just a practical convention.

  2. My second question is about the integral of dΦ/d(log⁡E). Is the expression: ∫dΦ/d(logE) ​dE physically meaningful at all? or is it inconsistent because dΦ/d(logE) should instead be integrated with respect to d(log⁡E), i.e. ∫dΦ/d(log⁡E) d(log⁡E)? Sampling from energy spectra - #4 by ctheis

  3. Related to that, I would also like to understand what the linear/logarithmic tick option in FLAIR really means. If I set the x-axis or y-axis to logarithmic in FLAIR, does this only change the graphical scale of the axis and the spacing of the ticks, or does it imply any transformation of the physical quantity being plotted? In other words, if I plot dΦ/dE versus E and simply select a logarithmic x-axis in FLAIR, am I still plotting the same physical quantity dΦ/dE vs E, only with log-spaced ticks? or automatically switching to dΦ/d(logE)? The neutronics slides seem to suggest that, regardless of what I choose (linear or log E) in my USRBDX card https://indico.cern.ch/event/1352709/contributions/5824030/attachments/2839838/4963557/14_Neutronics_2024_INTA.pdf (SLIDES 43+)

  4. My fourth question is why USRBDX looks completely different when I try to interpret it in a linear-style way over many orders of magnitude in energy. I initially thought that, if I set the x-axis to use logarithmic ticks in FLAIR and then use < X >*Y as the y-axis, the resulting spectrum should look similar to the usual log-style representation. However, the shape I obtain looks very different from what I would physically expect.

  5. Finally, I would appreciate some clarification on why the USRBDX examples in the scoring lectures:
    https://www.fluka.eu/Fluka/www/htmls/free_download/course/jlab2012/Lectures/07_Scoring_0412.pdf (Slide 18-19) and https://indico.cern.ch/event/656336/contributions/2729627/attachments/1552510/2439699/Scoring.pdf (Slide 10)
    Even when logarithmic energy intervals are used, the y-axis is still reported in units of [GeV−1 cm−2]. I would like to understand why those units remain unchanged in that case, and what exactly should be plotted if one wants to preserve those same y-axis units in one’s own spectrum plots.

Thank you very much for your time and for any clarification you may be able to provide.

Best Regards,
Carlos

3

Dear Carlos,

Right, in general, your understanding of the USRBDX scoring output is correct. You just need to figure out important technical details. Log scale in scoring is not recalculating the energy function in the simulation algorithm. It’s a selection of the change in the increment of the discrete bin for data scoring, so energy is constant within the bin.

1 - Logarithmic scoring in the USRBDX determines selection of the scoring bins. It does not affect plotting. Plotting will be adjusted separately in GNUPlot settings.

2 - As it has been mentioned, energy is constant within the bin, so d(log(E)) = 1/E*dE = const*dE, Hence, equations are meaningful for the numerical algorithm. Analytically, it will also be meaningful in the case of a linear energy function, but one should be consistent with the energy scale over all calculations. But sure, yes, your notation mathematically is correct and necessary if we omit the assumption of linearity of the energy function.

3 - The same as (1), you will have a Matrix of calculated output, and then you change plotting preferences, with a change only in visualization, it will not recalculate the scoring output.

4 - This is actually why the logarithmic scoring option exists in Fluka. Switch from log to linear binning over the large range aggects statistic discribution and significantly improves accuracy (error bars) in the small bins at the beginning of the range. This tool will significantly improve the accuracy in one bin over the total number of primaries in MC simulation.

Hope it helps you.

Kind regards,

Illia

1 Like
4

Dear Illia,

Thank you very much. Your reply was very helpful.

Best regards,
Carlos