Monte Carlo neutron slab model

[The_shadow]

Hi All,

Trying to write a simple Monte Carlo code for mono energetic neutrons in a steady state slab geometry in one-dimension. Their is an incident source on the left hand side of the slab and its of length L.

I understand how to work out the path length and scattering angles based on the pseudo-random numbers, as well as the type of scattering the particle undergoes, however I wish to calculate the flux and current and compare it to the deterministic model. I'm struggling to find much on this topic (that's useful).

For example the deterministic solutions for flux and current depend upon the source term (directly proportional), by contrast the Monte Carlo depends upon the initial numbers of particles, and a sufficiently large number is required to get good statistics - so presumably some scaling/normalization is required to compare directly to the deterministic equations? anyone know what that scaling factor is?

 

[mathman]

Divide by the number of particles in the Monte Carlo to get results per particle. You should have a conversion factor for source strength to number of particles.

 

[The_shadow]

Hi Mathman! many thanks, I'm working on an Event-based Monte Carlo code - i.e the tracking of individual particles in a medium so I'm not sure where/how I derive the conversion factor for source strength to number of particles in order to compare it to the deterministic equations.

For example the current at a given surface is just the sum of net particles passing through that particular surface divided by the surface area and the flux is just the sum of track lengths divided by the volume of the element. The number of particles needs to be high enough (millions) to get good statistics - however that makes the flux and current completely arbitrary so how exactly would one compare this to the standard analytical solution for a neutron diffusion in a slab? i.e say:

{d^2\phi(x) \over d x^2} -\Sigma_a\Sigma_t\phi(x) + S = 0

Where S is the incident source. This source would produce N particles say, but given a source of say unity, what is N? Many thanks again,

 

[mathman]

What is your definition of source strength? When I was working in this area (a long time ago), the source strength was simply the number of neutrons, usually in the form of an energy spectrum.

Note:the equation looks like a Latex expression, without saying Latex.

 

[Aaronvan]

Not sure if this will help but here you are.

http://people.sc.fsu.edu/~jburkardt/c_src/reactor_simulation/reactor_simulation.html