Fluence Rate Calculation Theory
The fluence rate E0 (SI unit: W/m2) is a volume quantity that indicates potential exposure to radiation. The fluence rate at any point in a domain is the total incident power that would hit a small spherical target at that location, from all directions, divided by the cross sectional area of the sphere (Ref. 16).
For the purpose of defining fluence rate the “small sphere” is an opaque detector whose radius is much smaller than any geometry details in the model, but substantially larger than the wavelength of radiation. Thus, the absorption cross section of the sphere is equal to its geometrical cross section and it is not necessary to consider Mie scattering theory.
In the path of a collimated beam of uniform intensity I (SI unit: W/m2), the fluence rate is simply I; however, the fluence rate distribution may be more complicated if there are multiple beams intersecting at a point (since fluence rate takes contributions from radiation arriving in all directions), or if the radiation is diffusely emitted or reflected.
The Fluence Rate Calculation node is a special type of Accumulator (Domain) that can be added to a model when the ray power is solved for, meaning that one of the options Compute power, Compute intensity and power, or Compute intensity and power in graded media should be selected from the physics interface Intensity Computation list. This feature defines an accumulated variable in each domain mesh element that gets the following contribution from rays as they propagate through the element:
where the sum is taken over the rays within each mesh element, Qi (SI unit: W) is the ray power, and ci (SI unit: m/s) is the speed of light of the ray. The division by the mesh element volume meshvol compensates for the tendency of a larger domain element to intersect a greater number of rays. Rather than a time integral, the above can be thought of as a path integral of ray power from the entrance point to the exit point as each ray traverses the mesh element.
The key distinction between fluence rate and deposited power is that fluence rate can be nonzero even if the medium is not absorbing; it represents the potential for a small object to be irradiated even if that object can only block a tiny fraction of the radiation in the domain.