As a start to implementing a somewhat more general “Finite Detector Estimator” I am trying to implement a Point Detector Estimator. After some thinking about it I am going to break this post into three pieces. In the first piece I want to describe my understanding of the estimator both as a refresher to myself and for anyone who knows more to correct any misunderstandings I might have. Second, I wanted to describe my approach to the implementation in hopes of constructive criticism. Finally, I will ask a couple of questions that I have come up with as I have been working on this problem.
If this you just want to see the questions, please see the third post.
Part 1: Point Detector Estimator
A Point Detector Estimator is a method for estimating the flux of some particle at a point in space and can be written as:
This equation is evaluated for every source particle and collision event throughout the random walk.
The first term is the “source term” where:
r_i is the position of the particle source
W_i is the particle weight when it is created at the source
P_i is the probability that the particle is emitted in some solid angle towards the detector r_i
The second term is the “interaction term” which is summing across every collision j in the history of particle i.
r_j is the position of the interaction
W_j is the particle weight prior to it’s interaction
P_j is the probability that some particle is emitted in some solid angle towards the detector from r_j
For both terms:
r_d is the position of the point detector
Beta(x, y) is the number of attenuation lengths (optical path length) between x and y for the particle which for gamma-rays can be expressed as:
s is each different geometry segment between x and y.
d_s is the length of that geometry segment
lambda_s is the attenuation length of the material in that geometry segment
So you can estimate the scalar flux at a point detector by summing some “Direct term” of the source with a “Scattering term”. The direct term (how much of the source shines directly through to the detector without collision) is calculated using beam attenuation to the detector from the source point chosen for that event multiplied by a solid angle correction and multiplied by a probability of the particle being emitted in that direction from that point (for non-isotropic sources). The scattering term is (how much of the source reaches the detector at some reduced energy due to scattering from surroundings) is calculated using beam attenuation to the detector from the source point chosen for that event multiplied by a solid angle correction and multiplied by a probability of some process emitting a particle towards the detector.
If I have made any errors so far, subtle or egregious, in this, please let me know.