Re: [fluka-discuss]: Re: Boundary crossing artefacts: Fano test

From: Francesco Cerutti <Francesco.Cerutti_at_cern.ch>
Date: Thu, 16 Jun 2016 19:32:03 +0200

   Dear Ana,

   it took us a bit of time to reproduce the artefact you pointed out, since
   the sudden local decrease in your flat dose profile was of the order of few
   per mil. The problem is due to the fact that, at scoring level, the proton
   energy loss by ionization is distributed uniformly along the particle step,
   so each bin traversed by the latter gets a dose value proportional to the
   respective step fraction. In reality, the stopping power's change - normally
   increase - along the step implies that the energy loss is larger towards the
   step end. This variation is fully taken into account during the
   evaluation of the energy loss suffered by a particle in a given step,
   however when that loss is scored it is uniformly distributed in the step
   itself. Therefore, if the simulated step length is too large with
   respect to the input scoring grid, one sees the artefacts also shown here:
   https://indico.cern.ch/event/489973/contributions/2000430/attachments/1269537/1881112/04_AdvancedSettings2016.pdf
   slide 28

   We would like to stress that this is purely an artefact due to the scoring,
   which is already complex enough in "apportioning" the step length among the
   possibly several bins crossed by it. The physics is "exact" in the limit
   of the accuracy of our stopping power models and of the integration
   algorithm used to compute the average energy loss over a step accounting
   for dE/dx variations.

   Coming to your specific case, the introduction of a geometry boundary
   shortens the nearby particle steps (which are forced to end on the
   boundary). This actually means that the respective scored dose value will be
   lower than the one of a 'normal' longer step starting from the same
   initial point, due to the smaller increase of the stopping power along the
   step, BUT the consequent local dose decrease is not compensated by larger
   dose values that should in principle come from the final fraction of
   particle steps ending where the shortened steps start.

   To visualize it, think about a 2 cm step, starting 1 cm prior to the
   boundary, over which there is an overall 2% dE/dx variation (numbers are
   purely fictitious). In absence of the boundary, the SCORED dose along
   the 2 cm step will be 1% higher than the one at the starting point and
   1% lower that the one at the end point. If the step is split into two substeps
   by the boundary, the first half will score a dose 0.5% higher than the
   one at the initial point (and 0.5% lower than the one at the
   sub-step final point which is also the median point of the initial 2 cm
   long step). The second half also scores a dose 0.5% higher than the one at
   its initial point and 0.5% less than the one at its final point, but now
   its initial point is the median point of the original step, and it is easy to
   verify that the second half will produce a SCORED dose 1% higher than
   the one of the 1st half.
   Actually life is significantly more complex because dE/dx does not vary
   linearly with x, step lengths corresponding to the same fractional loss
   are varying wildly with energy, multiple scattering plays a role, and,
   in FLUKA, particles moving from a boundary are restarted with short
   steps becoming progressively longer, which somehwat washes out the "up"
   effect on the right side of the boundary (that in fact you do not see).

   The solution is to properly shorten (ALL) transport steps down to =<1mm by
   STEPSIZE. Since this is going to have a huge CPU penalty, you may want to
   apply it only to the geometry regions of interest, e.g. creating a new
   boundary somewhat upstream (we used 2 cm upstream) of the boundary you are
   interested in. This way you can apply STEPSIZE only to the regions
   downstream of this new boundary, assuming that you do not care about the
   small scoring artefact that you will obviously see at the position of
   the latter.

   Another more complex solution would be to alter the scoring algorithm to
   take into account the stopping power gradient along the step, in order to
   calculate accordingly the dose values in the scoring bins traversed by the
   track step. This is something we have discussed internally already some
   time ago, we are a bit scared by the complexity of the implementation in
   the already very complex "track apportioning" scoring scheme. Also, if
   it turns out to be as CPU expensive as shortening the steps, there would
   be no advantage...
   Maybe we will implement something like that in the future.

   As a side remark, not really relevant but with still some impact, in your
   input you forgot to apply FLUKAFIX to the 1st material (WATER), which
   stayed at the larger - default - fractional energy loss.

Kind regards

Alfredo, Anton, Francesco and friends

   **************************************************
   Francesco Cerutti
   CERN-EN/STI
   CH-1211 Geneva 23
   Switzerland
   tel. ++41 22 7678962
   fax ++41 22 7668854

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Received on Thu Jun 16 2016 - 21:16:02 CEST

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