I would like to calculate the dpa as an average quantity over a region of an IRON sphere of 1 cm radius. As an attempt to reproduce the neutrons in a tally of a reactor, I employed the FLOOD BEAMPOS option for a neutron source of 15 MeV that is considered homogeneously distributed and isotropic in the volume of the 1 cm sphere. I run the attached input firstly at vacuum and had a look at the fluence of neutrons. When I set the R = 1.00001 cm, the projection in XY shows that the fluence in [-1, 1] is not flat. At R = 2.5 cm, the fluence becomes flatter as well as at R = 4 cm. But in all cases the DPA (region scoring) is very different. Since Fluence = 1/(pi x R^2) in case FLOOD is employed, for R = 1, 2.5, 4 cm we get F = 0.32, 0.051, 0.02 n/cm2/pr. In the case of R = 1 cm (Just outside the sphere) the value of the fluence according the formula does not showed in the 1st left plot. I have the impression that the dpa is scalled with the Fluence value as it could be seen in the middle and right plot of the attached figure… BUT what is the correct R to be set? FloodDPA.inp (3.7 KB)
Another test I did, was to use a cube centred at (0,0,0) with 1 cm half-side instead of the sphere. For the same BEAMPOS R = 2.5 cm, the DPA is 55% greater than the one of the sphere. That also puzzled me, since I was expecting that the DPA as an intensive quantity, does not depend on the shape of the Fe volume when I am invoking a flat source distribution with an isotropic fluence, thus as a volume containing particle tracks oriented in all directions with the same probability.
The last question I have has to do with the DPA calculation in FLUKA. As far as I read, it uses M444 from NJOY2006 and that results to an NRT corrected estimation based on a fit from MD (Stoller)? Thus, the result that it provides should be between MD and NRT values and certainly smaller than NRT. Is it correct?
Thank you very much in advance, I am looking forward to hearing from you concerning what would be the correct radius to set in BEAMPOS with FLOOD option, in order to calculate the DPA on an IRON sphere.
Dear Georgios,
your calculations with FLUKA are correct and the fluence is always flat in the given spherical volume, it’s just a matter of how you generate the plot. When you make the 1D projection you have to select a meaningful range for X and Y otherwise flair will average over the scoring volumes and value plotted (which is an average) will be lower. The same is true if you have an R-Phi-Z scoring and in that case you should adjust the Z range and look at the fluence as function of R. For the case TARGET set to VACUUM and R=1.00001cm this is what I obtain with your scoring cards
Of course, if you increase the radius for the source volume the fluence will appear flat even if you average.
For the FLUKA implementation of the DPA calculations, please have a look at this article that is quoted as reference in the official FLUKA Manual: A. Fasso, A. Ferrari, G. Smirnov, F. Sommerer, V. Vlachoudis, FLUKA Realistic Modeling of Radiation Induced Damage, Proceedings of a Joint International Conference on Supercomputing in Nuclear Applications and Monte Carlo 2010 (SNA + MC2010), Tokyo, Japan, October 17-21, 2010.
Thanks so much for your reply. So, as far as I understand, you select manually a range in X, Y in order to find out the limits in the projection to have a rather flat fluence. Thus, should I set the same limits for the DPA in the sphere when now I am setting IRON instead of VACUUM as a material?
As it looks for R=1.00001cm in:
Therefore, the value of the DPA is actually the 9.77E-22 instead of the 3.41E-21 that is achieved via region scoring? By increasing the R of the FLOOD surface, is it logical that the DPA is decreasing?
yes I select the ranges to avoid averaging outside the sphere.
For the DPA scoring it depends what you need and with what granularity. DPA is an intensive quantity and remember that, for DPA, the result from USRBIN mesh is the number of displacements per atom per unit primary, averaged over the bin volume.
In case of USRBIN region scoring you will get a global value which you must divide by the region volume to get back an average value over the region, a meaningful quantity: this is because FLUKA can calculate the volume of each bin in case of a mesh but cannot calculate volumes for a region. So from the output of 3.41E-21, dividing by the target volume, you would get 8.14E-21 dpa per primary weight as an average over the TARGET region.
Yes it is logical that the number that you get are decreasing: the neutron fluence is not the same when you change the radius since the fluence inside the sphere goes as 1/(pi R^2). But you can check that the average dpa per unit fluence is, within the uncertainty, the same in the three cases (just take the dpa per primary and divide by the fluence which is primary/cm2). If you are making a comparison with calculation from another code I would use the same value for R that was used in your reference. Otherwise there should be almost no difference except in the computation time: with large radii particles are less likely to cross your region and the time needed for convergence is longer.
I am really grateful for your very detailed explanations. The factor of the volume of the sphere that I did not take into account in my calculations was the missing one and only reason that there was a factor of 4 overestimation in the results compared with MCNP. Now both studies agree with each-other thanks to you!
