diff --git a/docs/source/methods/introduction.rst b/docs/source/methods/introduction.rst index 508ac9919..7e4f94633 100644 --- a/docs/source/methods/introduction.rst +++ b/docs/source/methods/introduction.rst @@ -8,7 +8,7 @@ The physical process by which a population of particles evolves over time is governed by a number of `probability distributions`_. For instance, given a particle traveling through some material, there is a probability distribution for the distance it will travel until its next collision (an exponential -distribution). Then, when it collides with a nucleus, there is associated +distribution). Then, when it collides with a nucleus, there is an associated probability of undergoing each possible reaction with that nucleus. While the behavior of any single particle is unpredictable, the average behavior of a large population of particles originating from the same source is well defined. @@ -45,10 +45,15 @@ following steps: - Initialize the pseudorandom number generator. - - Read ACE format cross sections specified in the problem. + - Read the contiuous-energy or multi-group cross section data specified in + the problem. - If using a special energy grid treatment such as a union energy grid or - lethargy bins, that must be initialized as well. + lethargy bins, that must be initialized as well in a continuous-energy + problem. + + - In a multi-group problem, individual nuclide cross section information is + combined to produce material-specific cross section data. - In a fixed source problem, source sites are sampled from the specified source. In an eigenvalue problem, source sites are sampled from some initial @@ -95,6 +100,10 @@ proceed. The life of a single particle will proceed as follows: P(i) = \frac{\Sigma_{t,i}}{\Sigma_t}. + Note that the above selection of collided nuclide only applies to + continuous-energy simulations as multi-group simulations use nuclide + data which has already been combined in to material-specific data. + 8. Once the specific nuclide is sampled, the random samples a reaction for that nuclide based on the microscopic cross sections. If the microscopic cross section for some reaction :math:`x` is :math:`\sigma_x` and the total @@ -105,13 +114,20 @@ proceed. The life of a single particle will proceed as follows: P(x) = \frac{\sigma_x}{\sigma_t}. + Since multi-group simulations use material-specific data, the above is + performed with those material multi-group cross sections (i.e., + macroscopic cross sections for the material) instead of microscopic + cross sections for the nuclide). + 9. If the sampled reaction is elastic or inelastic scattering, the outgoing - energy and angle is sampled from the appropriate distribution. Reactions - of type :math:`(n,xn)` are treated as scattering and the weight of the - particle is increased by the multiplicity of the reaction. The particle - then continues from step 3. If the reaction is absorption or fission, the - particle dies and if necessary, fission sites are created and stored in the - fission bank. + energy and angle is sampled from the appropriate distribution. In + continuous-energy simulation, reactions of type :math:`(n,xn)` are treated + as scattering and any additional particles which may be created are added + to a secondary particle bank to be tracked later. In a multi-group + simulation, this secondary bank is ont used but the particle weight is + increased accordingly. The original particle then continues from step 3. + If the reaction is absorption or fission, the particle dies and if + necessary, fission sites are created and stored in the fission bank. After all particles have been simulated, there are a few final tasks that must be performed before the run is finished. This include the following: diff --git a/docs/source/methods/tallies.rst b/docs/source/methods/tallies.rst index 65a0989ac..60a2b9a63 100644 --- a/docs/source/methods/tallies.rst +++ b/docs/source/methods/tallies.rst @@ -32,8 +32,9 @@ OpenMC: flux, total reaction rate, scattering reaction rate, neutron production from scattering, higher scattering moments, :math:`(n,xn)` reaction rates, absorption reaction rate, fission reaction rate, neutron production rate from fission, and surface currents. The following variables can be used as filters: -universe, material, cell, birth cell, surface, mesh, pre-collision energy, and -post-collision energy. +universe, material, cell, birth cell, surface, mesh, pre-collision energy, +post-collision energy, polar angle, azimuthal angle, and the cosine of the +change-in-angle due to a scattering event. With filters for pre- and post-collision energy and scoring functions for scattering and fission production, it is possible to use OpenMC to generate @@ -55,9 +56,9 @@ be scored to for each value of the filter variable. If a particle is in cell :math:`n`, the mapping would identify what tally/bin combinations specify cell :math:`n` for the cell filter variable. In this manner, it is not necessary to check the phase space variables against each tally. Note that this technique -only applies to discrete filter variables and cannot be applied to energy -bins. For energy filters, it is necessary to perform a binary search on the -specified energy grid. +only applies to discrete filter variables and cannot be applied to energy, +angle, or change-in-angle bins. For these filters, it is necessary to perform +a binary search on the specified energy grid. ----------------------------------------- Volume-Integrated Flux and Reaction Rates @@ -196,8 +197,9 @@ One important fact to take into consideration is that the use of a track-length estimator precludes us from using any filter that requires knowledge of the particle's state following a collision because by definition, it will not have had a collision at every event. Thus, for tallies with outgoing-energy filters -(which require the post-collision energy) or for tallies of scattering moments -(which require the scattering cosine), we must use an analog estimator. +(which require the post-collision energy), scattering change-in-angle filters, +or for tallies of scattering moments (which require the scattering cosine of +the change-in-angle), we must use an analog estimator. .. TODO: Add description of surface current tallies @@ -430,7 +432,7 @@ analytically. For one degree of freedom, the t-distribution becomes a standard .. math:: :label: cauchy-cdf - c(x) = \frac{1}{\pi} \arctan x + \frac{1}{2}. + c(x) = \frac{1}{\pi} \arctan x + \frac{1}{2}. Thus, inverting the cumulative distribution function, we find the :math:`x` percentile of the standard Cauchy distribution to be diff --git a/docs/source/usersguide/beginners.rst b/docs/source/usersguide/beginners.rst index 9ecffe3f6..2487e9c41 100644 --- a/docs/source/usersguide/beginners.rst +++ b/docs/source/usersguide/beginners.rst @@ -65,7 +65,7 @@ Now let's look at the pros and cons of Monte Carlo methods: - **Pro**: Running simulations in parallel is conceptually very simple. -- **Con**: Because they related on repeated random sampling, they are +- **Con**: Because they rely on repeated random sampling, they are computationally very expensive. - **Con**: A simulation doesn't automatically give you the global solution