[Feature] Forced collision variance reduction technique

[nglaser3]

Is your feature request related to a problem? Please describe.

Optically thin regions are hard to simulate with analog monte carlo. Low collision probabilities lead to poor statistics in the region for collision estimators.

Describe the feature you'd like.

A standard solution is the method of forced collisions. Forced collisions is a variance reduction technique that works by splitting a particle in a region of interest into two: a collided and a transmitted particle. The collided particle is then forced to undergo a collision event in the region of interest, while the transmitted particle is moved to the nearest surface along its incoming direction. The collided particle is moved a distance between its current position and the next surface, and this distance is sampled via:

$$ d = -\frac{1}{\Sigma_T} \log\left(1 - \xi \cdot \left(1 - e^{-\Sigma_T d_s}\right)\right) $$

where $\xi$ is the randomly generated number and $d_s$ is the distance to the next surface.

To conserve weights, the collided and transmitted weights are adjusted as:

$$ \begin{align} W_{collide} &= W_0 \cdot \left(1 - e^{-\Sigma_T d_s}\right)\\ W_{transmit} &= W_0 \cdot e^{-\Sigma_T d_s} \end{align} $$

How can this issue be closed?

This issue can be closed when forced collisions are a variance reduction technique in MCDC