USRYIELD output normalisation

Scoring
1

Hello FLUKA user forum,

My question today is regarding the normalisation of the results given by a USERYIELD scoring card.

The case I am interested in is a particle yield through a surfce (d^2N/dx1dx2) for x1=\theta the polar angle distribution (respect to the beam axis), and x2 not really important (particle charge between -0.5 and 0.5 since i am interested in neutrons), so basically scoring dN/d\theta for \theta between 0 and \pi (ie=14 in WHAT(1)).

From what I understand out of note 6 in the USERYIELD card’s documentation, the results is always given normalised per sr, thus in units of [particles/sr]. So even though x1=\theta, what I am getting back is dN/d\Omega (with \Omega the solid angle) as a function of the polar angle \theta (i.e. for each polar angle bin given in radians). Is that right?

If so, then I do not understand the option ie=17 in WHAT(1), where x1 = ‘1/(2πsinθ) weighted angle in the lab frame’. If I understad correctly, since d\Omega = 2πsin(θ)dθ, this would mean that the output is once again dN/d\Omega like the previous case but this time as a function of the solid angle \Omega (i.e. for each solid angle bin in sr). Is that right?

Any help is appreciated. Thanks!

Cheers,

Joaquin

3

Dear Joaquin,

Yes, that’s right, it’s always a solid angle.

And as you pointed out:

So, per solid angle normalisation is applied for bins of different widths (since sin(θ))..
If θ bins are non-uniform in solid angle, a uniform θ binning, ie = 14`, concentrates too many bins near the beam axis (small θ), which biases the visual impression and analysis.

Instead, ie = 17 option applies a correction that gives you a distribution per unit solid angle with uniform bin weighting, suitable for isotropy checks.

If you want dN/dθ, you have to manually modify the output file by multiplying bin edges by 2πsin(θ).

Cheers,
Volodymyr

4

Dear Volodymyr,

Awesome, thank you for your help !

Best,

Joaquin