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Added description of method of successive generations.

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Paul Romano 2012-08-03 12:25:40 -04:00
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32
docs/source/methods/criticality.rst
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@ -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