Adjoint-Based Uncertainty Quantification with MCNP

This work serves to quantify the instantaneous uncertainties in neutron transport simulations born from nuclear data and statistical counting uncertainties. Perturbation and adjoint theories are used to derive implicit sensitivity expressions. These expressions are transformed into forms that are convenient for construction with MCNP6, creating the ability to perform adjoint-based uncertainty quantification with MCNP6. These new tools are exercised on the depleted-uranium hybrid LIFE blanket, quantifying its sensitivities and uncertainties to important figures of merit. Overall, these uncertainty estimates are small (< 2%). Having quantified the sensitivities and uncertainties, physical understanding of the system is gained and some confidence in the simulation is acquired.

[1]  Bradley T Rearden,et al.  Eigenvalue Contributon Estimator for Sensitivity Calculations with TSUNAMI-3D , 2007 .

[2]  J. F. Briesmeister.  MCNP-A General Monte Carlo N-Particle Transport Code , 1993 .

[3]  J. Lewins.  Importance, the adjoint function : the physical basis of the variational and perturbation theory in transport and diffusion problems , 1965 .

[4]  M. Salvatores,et al.  Uncertainty and target accuracy studies for the very high temperature reactor(VHTR) physics parameters. , 2005 .

[5]  Per F. Peterson,et al.  Adjoint-Based Uncertainty Analysis for Essential Reactions in a Laser Inertial Fusion Engine , 2011 .

[6]  J E Seifried.  Thermal Modeling and Feedback Requirements for LIFE Neutronic Simulations , 2009 .

[7]  Philip R. Page,et al.  ENDF/B-VII.0: Next Generation Evaluated Nuclear Data Library for Nuclear Science and Technology , 2006 .

[8]  Kevin James Kramer.  Laser Inertial Fusion-based Energy: Neutronic Design Aspects of a Hybrid Fusion-Fission Nuclear Energy System , 2010 .

[9]  Ho Jin Park,et al.  Uncertainty Propagation in Monte Carlo Depletion Analysis , 2011 .

[10]  M. Williams,et al.  Sensitivity and Uncertainty Analysis Capabilities and Data in SCALE , 2011 .

[11]  R P Abbott,et al.  Neutronics Design of a Thorium-Fueled Fission Blanket for LIFE (Laser Inertial Fusion-based Energy) , 2010 .

[12]  R. Chaplin.  NUCLEAR REACTOR THEORY , 2022 .

[13]  E. Greenspan,et al.  On the adjoint space in reactor theory , 1976 .

[14]  Ehud Greenspan,et al.  Sensitivity Functions for Uncertainty Analysis , 1982 .

[15]  R P Abbott,et al.  Neutron Transport and Nuclear Burnup Analysis for the Laser Inertial Confinement Fusion-Fission Energy (LIFE) Engine , 2008 .

[16]  Allan F. Henry,et al.  Nuclear Reactor Analysis , 1977, IEEE Transactions on Nuclear Science.

[17]  Mihai Anitescu,et al.  Nuclear data sensitivity, uncertainty and target accuracy assessment for future nuclear systems , 2006 .

[18]  R P Abbott,et al.  THE LASER INERTIAL FUSION ENGINE AS A WEAPONS GRADE PLUTONIUM FUEL BURNER , 2010 .

[19]  T. J. Downar.  Advanced depletion perturbation methods and waste transmutation in the IFR , 1991 .

[20]  C. R. Weisbin,et al.  Meeting cross-section requirements for nuclear-energy design , 1982 .

[21]  K. Shibata,et al.  JENDL-4.0: A New Library for Nuclear Science and Engineering , 2011 .

[22]  E. Greenspan,et al.  Optimal Neutron Source & Beam Shaping Assembly for Boron Neutron Capture Therapy , 2003 .

[23]  R. Iman,et al.  A distribution-free approach to inducing rank correlation among input variables , 1982 .

[24]  Bradley T Rearden,et al.  SCALE Sensitivity Calculations Using Contributon Theory , 2010 .

[25]  Kevin J. Kramer,et al.  Attainable Burnup in a LIFE Engine Loaded with Depleted Uranium , 2009 .

[26]  H.W. Kraner,et al.  Radiation detection and measurement , 1981, Proceedings of the IEEE.

[27]  N. García-Herranz,et al.  Propagation of statistical and nuclear data uncertainties in Monte Carlo burn-up calculations , 2008 .

[28]  Per F. Peterson,et al.  Explicit Uncertainty Analysis for Tritium Breeding in a Laser Inertial Fusion Engine , 2010 .

[29]  Mark L Williams,et al.  Development of Generalized Perturbation Theory Capability within the SCALE Code Package , 2009 .

[30]  J. Lewins.  DEVELOPMENTS IN PERTURBATION THEORY , 1968 .

[31]  Robert Hayes,et al.  Monte Carlo Parameter Studies and Uncertainty Analyses with MCNP5 , 2004 .

[32]  D. E Cullen,et al.  TART 2000: A Coupled Neutron-Photon, 3-D, Combinatorial Geometry, Time Dependent, Monte Carlo Transport Code , 1998 .

[33]  D. S. Selengut.  VARIATIONAL ANALYSIS OF MULTI-DIMENSIONAL SYSTEMS , 1959 .

[34]  Paul J. Turinsky,et al.  Uncertainty Quantification, Sensitivity Analysis, and Data Assimilation for Nuclear Systems Simulation , 2008 .

[35]  F. Brown,et al.  Adjoint-Weighted Tallies for k-Eigenvalue Calculations with Continuous-Energy Monte Carlo , 2011 .

[36]  Naoki Sugimura,et al.  Improvement on multi-group scattering matrix in thermal energy range generated by NJOY , 2006 .

[37]  M. J. Abbate,et al.  Methods of Steady-State Reactor Physics in Nuclear Design , 1983 .

[38]  W. M. Stacey,et al.  Variational Methods in Nuclear Reactor Physics , 1975, IEEE Transactions on Plasma Science.

[39]  Forrest B. Brown,et al.  MCNP Calculations of Subcritical Fixed Source and Fission Multiplication Factors , 2010 .

[40]  V. R. Cain,et al.  Adjoint and Importance in Monte Carlo Application , 1967 .

[41]  John S. Hendricks,et al.  MCNPX 2.7.0 extensions , 2011 .

[42]  Liu Ping,et al.  The updated version of the Chinese Evaluated Nuclear Data Library (CENDL-3.1) and China nuclear data evaluation activities , 2007 .

[43]  T. Cacoullos.  On Upper and Lower Bounds for the Variance of a Function of a Random Variable , 1982 .

[44]  Wayne R. Meier,et al.  Fusion-Fission Blanket Options for the LIFE Engine , 2010 .

[45]  R P Abbott,et al.  Thermal and Mechanical Design Aspects of the LIFE Engine , 2009 .

[46]  John C. Wagner,et al.  MCNP: Multigroup/adjoint capabilities , 1994 .

[47]  E. Lewis,et al.  Computational Methods of Neutron Transport , 1993 .