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Co-authored-by: GuySten <guyste@post.bgu.ac.il> Co-authored-by: Paul Romano <paul.k.romano@gmail.com>
133 lines
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133 lines
6 KiB
ReStructuredText
.. _kinetics:
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===================
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Kinetics parameters
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===================
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OpenMC has the capability to estimate the following adjoint-weighted effective
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generation time :math:`\Lambda_{\text{eff}}` and the effective delayed neutron
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fraction :math:`\beta_{\text{eff}}`. These parameters are calculated using the
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iterated fission probability (IFP) method [Hurwitz_1964]_ based on a similar
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approach as in `Serpent 2 <https://doi.org/10.1016/j.anucene.2013.10.032>`_. The
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implementation in OpenMC is limited to eigenvalue calculations and is described
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in more details in [Dorville_2025]_.
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----------------------------------
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Iterated Fission Probability (IFP)
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----------------------------------
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With IFP, additional information needs to be recorded during the simulation
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compared to a typical eigenvalue calculation. OpenMC stores an additional
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set of values (neutron lifetime or delayed neutron group number for
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:math:`\Lambda_{\text{eff}}` or :math:`\beta_{\text{eff}}`, respectively)
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for every fission neutron simulated. Each set of values corresponds to
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the values that are associated to the :math:`N_{\text{gen}}` direct ancestors
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of any given fission neutron.
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:math:`N_{\text{gen}}` is referred to as the number of generations in the
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IFP method and corresponds to the number of generations between the birth of
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a fission neutron and the time its score is added to the IFP tally. By default,
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OpenMC considers 10 generations but this value can be modified by the user via
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the ``ifp_n_generation`` settings in the Python API::
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settings.ifp_n_generation = 5
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``ifp_n_generation`` should be greater than 0, but should also be lower than
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or equal to the number of inactive batches declared for the calculation.
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The respect of these constraints is verified by OpenMC before any calculation.
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OpenMC will automatically detect the type of data that needs to be stored based
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on the tally scores selected by the user. This guarantees that only information
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of interest are stored during a simulation and avoids using extra memory when
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only one parameter is needed. The following table shows the tally scores that
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are needed to compute kinetics parameters in OpenMC:
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.. table:: **OpenMC tally scores needed to calculate adjoint-weighted kinetics parameters**
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:align: center
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=============================== ============================ ========================== ========
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OpenMC tally score \\ Parameter :math:`\Lambda_{\text{eff}}` :math:`\beta_{\text{eff}}` Both
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=============================== ============================ ========================== ========
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``ifp-time-numerator`` X X
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``ifp-beta-numerator`` X X
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``ifp-denominator`` X X X
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=============================== ============================ ========================== ========
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.. note:: Because the memory footprint of additional data is generally non-negligible
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with IFP, it is recommended to choose the value for ``ifp_n_generation`` carefully.
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For example, using one generation for both kinetics parameters corresponds to store
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one additional integer (for the delayed neutron group number used with
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:math:`\beta_{\text{eff}}`) and one floating point value (for the neutron lifetime
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used with :math:`\Lambda_{\text{eff}}`) for every fission neutron simulated once the
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asymptotic regime is reached.
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-----------------------------
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Obtaining kinetics parameters
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-----------------------------
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The ``Model`` class can be used to automatically generate all IFP tallies using
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the Python API with :attr:`openmc.Settings.ifp_n_generation` greater than 0 and
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the :meth:`openmc.Model.add_ifp_kinetics_tallies` method::
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model = openmc.Model(geometry, settings=settings)
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model.add_kinetics_parameters_tallies(num_groups=6) # Add 6 precursor groups
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Alternatively, each of the tallies can be manually defined using group-wise or
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total :math:`\beta_{\text{eff}}` specified by providing a 6-group
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:class:`openmc.DelayedGroupFilter`::
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beta_tally = openmc.Tally(name="group-beta-score")
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beta_tally.scores = ["ifp-beta-numerator"]
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# Add DelayedGroupFilter to enable group-wise tallies
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beta_tally.filters = [openmc.DelayedGroupFilter(list(range(1, 7)))]
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Here is an example showing how to declare the three available IFP scores in a
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single tally::
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tally = openmc.Tally(name="ifp-scores")
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tally.scores = [
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"ifp-time-numerator",
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"ifp-beta-numerator",
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"ifp-denominator"
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]
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The effective generation time :math:`\Lambda_{\text{eff}}` is calculated
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by dividing the result of the ``ifp-time-numerator`` score by the one obtained
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for ``ifp-denominator`` and by the :math:`k_{\text{eff}}` of the simulation:
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.. math::
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:label: lambda_eff
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\Lambda_{\text{eff}} = \frac{S_{\text{ifp-time-numerator}}}{S_{\text{ifp-denominator}} \times k_{\text{eff}}}
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The effective delayed neutron fraction :math:`\beta_{\text{eff}}` is calculated
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by dividing the result of the ``ifp-beta-numerator`` score by the one obtained
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for ``ifp-denominator``:
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.. math::
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:label: beta_eff
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\beta_{\text{eff}} = \frac{S_{\text{ifp-beta-numerator}}}{S_{\text{ifp-denominator}}}
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The kinetics parameters can be retrieved directly from a statepoint file using
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the :meth:`openmc.StatePoint.ifp_results` method::
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with openmc.StatePoint(output_path) as sp:
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generation_time, beta_eff = sp.get_kinetics_parameters()
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.. only:: html
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.. rubric:: References
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.. [Hurwitz_1964] H. Hurwitz Jr., "Naval Reactors Physics Handbook", volume 1, p. 864.
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Radkowsky, A. (Ed.), Naval Reactors, Division of Reactor Development, U.S.
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Atomic Energy Commission (1964).
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.. [Dorville_2025] J. Dorville, L. Labrie-Cleary, and P. K. Romano, "Implementation
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of the Iterated Fission Probability Method in OpenMC to Compute Adjoint-Weighted
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Kinetics Parameters", International Conference on Mathematics and Computational
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Methods Applied to Nuclear Science and Engineering (M&C 2025), Denver, April 27-30,
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2025.
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