Re: USRBDX for FLUENCE scoring

From: Alfredo Ferrari (
Date: Fri Feb 28 2003 - 11:31:29 CET

You have found a subtle rounding effect. In your case, neutrons
are scored when they cross the boundary with an angle with respect to the
normal at the point of crossing which is in the interval [0,pi/2] (or better,
with a cosine in the interval [0,1]).
Since in your case the angle is always exactly 0 (cosine = 1), of course all
neutrons should be scored. However, due to computer rounding accuracy
the dot product of the particle direction and the normal is always somewhat
different from 1. The difference is tiny and consistent with the expected
machine accuracy (order 1E-16), with random sign. Even if the difference
is extremely small, the check against =< 1 can fail and the program will
consider the neutron to be outside the allowed angular scoring interval.
The amount of rounding is also architecture dependent (not unexpected), ie
my old DEC Alpha doesn't score only 1/4 of the neutrons rejected
running Linux on an Intel PC.
We have now added a protection to take care of rounding in these "extreme"
cases. This modification will be available only in the next FLUKA release,
since it is not an issue in any real life problem. Indeed this problem has
no effect in any "real" situation, where of course "exact" alignment with
no scattering never occurs: already if you move the source point by
1.E-4 cm (a micrometer), the artifact disappears. Only in an artificial test
like yours, it is possible to have all particles crossing with a cosine
exactly identical to 1.

              Thanks for finding this problem.

                    Alfredo Ferrari

On Wed, 26 Feb 2003, Chin-Cheng, CHEN wrote:

> Dear FLUKA users
> We encounter a problem when using the USRBDX for FLUENCE scoring.
> The input file is simple:
> 1. A point source is located at the center of a void sphere.
> 2. Mono-energetic neutrons are emitted isotropically.
> I would like to estimate the FLUENCE acrossing the sphere.
> The result was expected to be exactly 1.0 and with zero variance
> (assuming the area of the sphere is1.0 cm2).
> The USRTRACK indeed gives the right answer
> but the USRBDX gives the answer 0.8045805 +/- 0.1547585%.
> Does anybody know what happens?
> The input and output files are attached.
> Thank you very much.
> Sincerely yours,
> C. C. Chen and R. J. Sheu
> National Tsing-Hua University, Taiwan, R.O.C.

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