Sunday, February 17, 2008

Tech Review - 1

Per my own goals and aspirations, I'm jumping into the Sunday morning tech review. For my first tidbit, I revisit an article I've read at least once before entitled "An Automated Deterministic Variance Reduction Generator for Monte Carlo Shielding Applications" by J. Wagner, a former mentor at ORNL.

In the article, Wagner notes that Monte Carlo methods are widely believed the best tool for solving radiation transport problems, but at the same time, are extremely computationally-intensive for difficult, "deep penetration" problems. The work described aims to provide a way in which to cut down on this computer time via variance reduction.

The method does two key things. First, it produces for the problem a so-called biased source, which is defined essentially as the space- and energy-dependent source, s(x,E) weighted over the entire detector response function via the adjoint flux, A, i.e.

--> s'(x,E) = A(x,E)s(x,E)/R

where R is just the integral of the numerator over all energy space. What this source does is that it gives to us those particles most important to the detector response of interest. If, for example, we had a fission source (think the Chi-spectrum) and detector separated by a thick concrete wall, we imagine our detector response is largely dependent on the fastest of those neutrons; as such, we bias the source to give more of those particles while simultaneously decreasing the per-particle weight to maintain "fair" biasing.

The method uses weight-windows for transport biasing. WW's are essentially a superficial grid placed on the problem geometry. The various superficial regions are assigned a range of particle importance that it will let enter; for those particle outside the range, either Russian roulette or splitting occurs (i.e. if the particle 'weighs' too much, it is split into two or more particles of appropriate weight, and if the particle 'weighs' too little, a game is played to see whether it can enter; if so, its importance is raised a consistent amount; if not, it is destroyed).

The lower bounds of the WW's are inversely proportional to the importance function, A. and proportional to the overall detector response. That is to say

--> wl(x,E) = R/(Ak)

where k is some constant I won't explain here. Suffice it to say, wl(x,E) is defined such that biased-source particle weights are in (wl,wu) to remain consistent; this reduces unnecessary splitting or rouletting straightaway.

The article goes on to apply these methods to difficult problems, namely a nuclear well-logging simulation (which I've done before!). Time is saved by several orders of magnitude, which makes this theory a very valuable one indeed.

In the future, I would like to couple the idea with charged-particle problems, namely with proton beam therapy facility shielding analysis in mind.

2 comments:

Johan said...

This is certainly going to be a interesting blog to follow.

I myself am a swedish physics student that have devoted my last year to nuclear engineering and Im just about to start my masters thesis work on molten salt reactors. So far I am clueless on computational tools, for some reason physics educations in sweden includes almost only analytical problems.

Keep on blogging and Il defenetly be reading :) I hope you enjoy living in Finland!

Jeremy said...

Thanks for the support. I intend as best I can to continue updating this regularly.