Dear FLUKA Experts,
I’m quite sure I’m missing something simple, but I cannot find an explanation for a result I get. A proton beam, generated with an external phase-space file, enters along Z a water target placed close to the beam source (Z=0). Fuence (BEAMPART) and dose (DOSE) are scored using an X-Y-Z USRBIN (6x6x5 cm^3). While the 1D projection of fluence along Z is equal to 1 (after normalization with the transverse USRBIN area of 36 cm^2) in Z=0, as expected, the 2D projection of fluence along Z in the first slice of the USRBIN from Z=0 to Z=0.02 cm has an integral value equal to about 0.0198, that is about 50 times less than what I expect. A similar result with the same factor of 50 is found for the dose. Can you please help me understand why this difference? Thank you in advance.
Kind regards,
Enrico

Ciao Enrico,
you are comparing two different physical quantities.

The 1D projection value, i.e. the average fluence [cm^-2] over the first z-bin, when multiplied by the transverse area [cm^2], gives you (roughly*) the number of particles [dimensionless] traversing that slice (* I say roughly because this is true only if the particles keep travelling perpendicularly to the slice, i.e. along z, while interactions may deviate them and make the multiplication result exceed the actual number of particles - remember that fluence is not current).

As for the 2D projection (giving the fluence [cm^-2] transverse distribution), its integral over the slice volume [cm^3] represents the particle tracklength [cm], which roughly corresponds to the z-bin width.

Coming to the dose, its volumetric integral [(GeV/g) cm^3] has no physical meaning, unless you multiply it further by the material density [g/cm^3], this way getting the total energy [GeV] deposited over the slice (while dose [GeV/g] and energy density [GeV/cm^3], as obtained by the USRBIN mesh, are local - intensive - quantities).

The 1D projection value, i.e. the average fluence [cm^-2] over the first z-bin, when multiplied by the transverse area [cm^2], gives you (roughly*) the number of particles [dimensionless] traversing that slice (* I say roughly because this is true only if the particles keep travelling perpendicularly to the slice, i.e. along z, while interactions may deviate them and make the multiplication result exceed the actual number of particles - remember that fluence is not current).

OK !

As for the 2D projection (giving the fluence [cm^-2] transverse distribution), its integral over the slice volume [cm^3] represents the particle tracklength [cm] , which roughly corresponds to the z-bin width.

Thanks for pointing this out. I misunderstood the meaning of Int in Flair by assuming it represented a 2D integral. Sorry for not having checked it with different Z-thicknesses, as I would have seen that Int changes accordingly.

Coming to the dose, its volumetric integral [(GeV/g) cm^3] has no physical meaning, unless you multiply it further by the material density [g/cm^3], this way getting the total energy [GeV] deposited over the slice (while dose [GeV/g] and energy density [GeV/cm^3], as obtained by the USRBIN mesh, are local - intensive - quantities).

Having understood the 3D-integral meaning of Int, now this point is clear too.

Thanks for your kindness and clear explanation, Francesco!
Ciao,
Enrico