From b4617a9c42b835dc94792864be21ac1cfbffd10c Mon Sep 17 00:00:00 2001 From: Paul Romano Date: Fri, 3 Aug 2012 12:25:40 -0400 Subject: [PATCH] Added description of method of successive generations. --- docs/source/methods/criticality.rst | 32 +++++++++++++++++++++++++---- 1 file changed, 28 insertions(+), 4 deletions(-) diff --git a/docs/source/methods/criticality.rst b/docs/source/methods/criticality.rst index b9cd472b70..5e141cd565 100644 --- a/docs/source/methods/criticality.rst +++ b/docs/source/methods/criticality.rst @@ -21,6 +21,30 @@ calculations in a Monte Carlo code. Method of Successive Generations -------------------------------- +The method used to converge on the fission source distribution in a criticality +calculation, known as the method of successive generations, was first introduced +by [Lieberoth]_. In this method, a finite number of neutron histories, +:math:`N`, are tracked through their lifetime iteratively. If fission occurs, +rather than tracking the resulting fission neutrons, the spatial coordinates of +the fission site, the sampled outgoing energy and direction of the fission +neutron, and the weight of the neutron are stored for use in the subsequent +generation. In OpenMC, the array used for storing the fission site information +is called the *fission bank*. At the end of each fission generation, :math:`N` +source sites for the next generation must be randomly sampled from the :math:`M` +fission sites that were stored to ensure that the neutron population does not +grow exponentially. The sampled source sites are stored in an array called the +*source bank* and can be retrieved during the subsequent generation. + +It's important to recognize that in the method of successive generations, we +must start with some assumption on how the fission source sites are distributed +since the distribution is not known *a priori*. Typically, a user will make a +guess as to what the distribution is -- this guess could be a uniform +distribution over some region of the geometry or simply a point +source. Fortunately, regardless of the choice of initial source distribution, +the method is guaranteed to converge to the true source distribution. Until the +source distribution converges, tallies should not be scored to since they will +otherwsie include contributions from an unconverged source distribution. + ------------------------- Source Convergence Issues ------------------------- @@ -78,12 +102,12 @@ at plots of :math:`k_{eff}` and the Shannon entropy. A number of methods have been proposed (see e.g. [Romano]_, [Ueki]_), but each of these is not without problems. ------------------------ -Fission and Source Bank ------------------------ - .. _Shannon entropy: https://laws.lanl.gov/vhosts/mcnp.lanl.gov/pdf_files/la-ur-06-3737_entropy.pdf +.. [Lieberoth] J. Lieberoth, "A Monte Carlo Technique to Solve the Static + Eigenvalue Problem of the Boltzmann Transport Equation," *Nukleonik*, **11**, + 213-219 (1968). + .. [Romano] Paul K. Romano, "Application of the Stochastic Oscillator to Assess Source Convergence in Monte Carlo Criticality Calculations," *Proc. International Conference on Mathematics, Computational Methods, and