eMC - Why do FADDs and the curves from Beam Analysis not necessarily match?

Comment from Varian Finland regarding the KFJ beam data:

"The fitted curve in Beam Data and the calculated in Beam Analysis were looking quite different in some cases. I found that very surprising and my question now is, how come? Don't they have to be more or less the same?

They might not match, even within statistical error. The reason is the following:

Precalculated Monte Carlo data is fitted to measurements.  This gives weights for each of the precalculated data sets.  The fitted curve is just an optimally weighted average of the precalculated data sets.
In the calculation, the weights for monoenergetic e- beams are interpreted as a spectrum.  When generating particles, this spectrum is sampled _continuously_.  In other words, even in the precalculated data has only monoenergtic beams 0.5, 1.0, 1.5, 2.0 MeV, etc..,  an electron in the calculation mights still have the energy 1.3445217423 MeV, which does not exist in the precalculated simulations.

This gives rise to the difference between fitted and calculated curves. As an extreme example, suppose that just between 4.2 and 4.4 MeV, there would be very strong interactions for electrons in water (this is not the case in reality!).  This would NOT be taken into account in configuration, but would still be modeled in calculation, and the curves would be very different.

One option would be to sample only the same discrete energies that were used in the precalculated simulations.  But it was concluded that more accurate results would be obtained by using a continuous source spectrum; the drawback is the difference between fitted vs. calculated. The difference could also be reduced by having a finer energy spacing in the precalculated data. This requires some amount of work (new simulations), however.

The difference will be bigger in cases where the real spectrum does not fit well to the discrete model, e.g., when the maximum of the spectrum is at 5.75 (halfway between 5.5 and 6.0). I believe this is just the case here, because of the following observation:

Regarding the other differences that you see: because the measured curve always falls off more rapidly than the calculated one, this suggests that the real energy would be slightly lower than the nominal energy.  I tested this and, in fact, if I use 5.5 MeV instead of 6.0 MeV as the nominal energy, the fit gets somewhat better. (This is something the user cannot do by himself, because the standard eMC only allows certain, discrete nominal energies.)  Even I cannot test 5.75, because this configuration data does not exist."

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