Novel hybrid Monte Carlo/deterministic technique for shutdown dose rate analyses of fusion energy systems
Introduction
Accurate predictions of dose rate estimates from activated structural materials during shutdown, referred to as shutdown dose rate (SDDR), are critical to support operation, maintenance, and waste disposal planning and to guide possible design changes of critical components in fusion energy systems. For example, accurate SDDR calculations are needed to find the balance between an adequate performance and the nuclear shielding necessary for the diagnostics, the electron cyclotron heating, the ion cyclotron heating, the neutral beam injection, the pellet injection, and the disruption mitigation systems in ITER. In the preliminary design phase of ITER, SDDR analyses must be accurately performed to ensure that these systems can still perform adequately even with the necessary amounts of shielding [1].
Because the SDDR is caused by decay photons emitted by radioisotopes generated during irradiation, an SDDR calculation involves three steps:
- 1.
a neutron transport calculation for the space and energy neutron flux distributions,
- 2.
an activation calculation for the photon source distribution, and
- 3.
a photon transport calculation for SDDR estimation.
The rigorous 2-step (R2S) computational system, developed for calculating SDDR in full 3-D geometries, entails Monte Carlo (MC) neutron and photon transport calculations coupled with a comprehensive activation step using a dedicated inventory code and library [2]. Accurate R2S estimation of the SDDR is impractical for large and geometrically complex problems because it requires calculating space- and energy-dependent neutron fluxes everywhere inside the structural materials. Biasing the neutron transport calculation using an importance function [3] is not straightforward because of the difficulty of explicitly expressing the response function of the neutron calculation, which depends on the next calculation steps.
The use of global MC variance reduction techniques [4], [5], [6] was suggested for accelerating the R2S neutron transport calculation [7]. These techniques, which attempt to calculate MC tallies with nearly uniform relative uncertainties in the low-flux space-energy regions as well as in the high-flux space-energy regions, do not preferentially focus the MC computational efforts toward space-energy regions of high importance to the final decay dose. The prohibitive computational costs of these approaches, which increase with the overall problem size and amount of shielding materials, inhibit their ability to accurately predict the SDDR in fusion energy systems using full-scale modeling of an entire fusion plant.
This paper describes a novel hybrid MC/deterministic technique that uses the Consistent Adjoint Driven Importance Sampling (CADIS) method, which has been successfully used for more than a decade in shielding calculations [8] but focuses on multi-step shielding calculations such as the R2S calculations of SDDR. This technique, referred to as Multi-Step CADIS (MS-CADIS), speeds up the R2S MC neutron transport calculations using an importance function that represents the importance of the neutrons to the final SDDR.
Section snippets
Theory and implementation
The importance sampling technique [3] uses an importance function—the expected score to a detector from a particle at some point in phase space—to modify the MC sampling process. In the CADIS method [8], this function is used in modifying both the sampling of particles emitted from the source and the sampling of particles being transported. If the exact importance function is known, the detector response R can be expressed aswhere is the source
Problem description
The simple system shown in Fig. 2 was used to verify the effectiveness of the proposed MS-CADIS method. The system consists of a rectangular parallelepiped of a homogenous mixture of 98Mo and water. The square base of the system had a side length of 150 cm and the height was 250 cm.
A monoenergetic (1 MeV) point neutron source with total source strength of 1012 neutron/s was positioned 15 cm above the center of the base. After a very long irradiation time at which the maximum activity of 99Mo was
Conclusion
A novel hybrid MC/deterministic technique has been proposed to speed up the MC transport simulations in multi-step shielding analysis such as the R2S calculations of the SDDR. Using an importance function that represents the importance of the neutrons to the final SDDR, the MS-CADIS method develops the weight-windows and source biasing parameters for the neutron MC simulations of the SDDR R2S calculations. The MS-CADIS method has been tested with a simplified example. The preliminary results
Acknowledgments
This manuscript has been authored by UT-Battelle, LLC, under contract DE-AC05-00OR22725 with the US Department of Energy. The US Government and the publisher, by accepting for publication, acknowledges that the US Government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript, or allow others to do so, for US Government purposes.
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