4. Radiation Shielding

Introduction by D. E. Peplow and B. T. Rearden

The Monaco with Automated Variance Reduction using Importance Calculations (MAVRIC) fixed-source radiation transport sequence is designed to apply the multigroup and continuous energy fixed-source Monte Carlo code Monaco to solve problems too challenging for standard, unbiased Monte Carlo methods.i The intention of the sequence is to calculate fluxes and dose rates with low uncertainties in reasonable times even for deep penetration problems. MAVRIC is based on the Consistent Adjoint Driven Importance Sampling (CADIS) methodology, which uses an importance map and biased source that are derived to work together. MAVRIC generates problem-dependent cross section data and then automatically performs a coarse mesh 3D discrete ordinates transport calculation using Denovo to determine the adjoint flux as a function of position and energy. MAVRIC then applies the information to optimize the shielding calculation in Monaco. In the Forward-Weighted CADIS (FW-CADIS) methodology, an additional Denovo calculation is performed to further optimize the Monaco model to obtain uniform uncertainties for multiple tally locations. Sources can be input using many spatial and energy distributions, or they can be imported from a previously generated mesh file. Responses can be generated from cross section reaction rates, flux-to-dose conversion factors, or user-defined functions; responses are tallied on geometry regions, Cartesian or cylindrical grids, or as point detectors.

MAVRIC enables users to import spent fuel isotopics from ORIGEN binary concentrations files such as those generated with ORIGAMI and to import gamma emission spectral data directly from the ORIGEN nuclear data files to streamline analysis and reduce the opportunity for human error.

Several utility modules are also provided for data introspection and conversion.

• 4.1. MAVRIC: Monaco with Automated Variance Reduction using Importance Calculations
  • 4.1.1. Introduction
  • 4.1.2. CADIS Methodology
    • 4.1.2.1. Overview of CADIS
    • 4.1.2.2. Multiple sources with CADIS
    • 4.1.2.3. Multiple tallies with CADIS
    • 4.1.2.4. Forward-weighted CADIS
    • 4.1.2.5. MAVRIC Implementation of CADIS
      • 4.1.2.5.1. Denovo
      • 4.1.2.5.2. Monaco
      • 4.1.2.5.3. Running MAVRIC
  • 4.1.3. MAVRIC input
    • 4.1.3.1. Composition block
    • 4.1.3.2. SGGP geometry blocks
    • 4.1.3.3. Other blocks shared with Monaco
    • 4.1.3.4. Importance map block
      • 4.1.3.4.1. Constructing a mesh for the S_N calculation
      • 4.1.3.4.2. Macromaterials for S_N geometries
        • 4.1.3.4.2.1. Ray Tracing
        • 4.1.3.4.2.2. Point Testing
        • 4.1.3.4.2.3. Example
      • 4.1.3.4.3. Optimizing source/detector problems
      • 4.1.3.4.4. Multiple adjoint sources
      • 4.1.3.4.5. Options for Denovo \(S_n\) calculations
      • 4.1.3.4.6. Starting with an existing adjoint flux file
      • 4.1.3.4.7. Forward-weighting the adjoint source
      • 4.1.3.4.8. Forward weighting with an existing forward flux file
      • 4.1.3.4.9. Using the importance map
      • 4.1.3.4.10. Other notes on importance map calculations
  • 4.1.4. MAVRIC output
    • 4.1.4.1. Main text output file
    • 4.1.4.2. Additional output files
  • 4.1.5. Sample problems
    • 4.1.5.1. Graphite shielding measurements with CADIS
      • 4.1.5.1.1. Input file
      • 4.1.5.1.2. Output
    • 4.1.5.2. Dose rates outside of a simple cask
      • 4.1.5.2.1. Geometry and materials
      • 4.1.5.2.2. Sources and responses
      • 4.1.5.2.3. Analog calculation
      • 4.1.5.2.4. SAS4 calculations
      • 4.1.5.2.5. Calculations using CADIS
      • 4.1.5.2.6. MAVRIC input files
      • 4.1.5.2.7. Neutron source/neutron response results
      • 4.1.5.2.8. Photon source/photon response results
    • 4.1.5.3. Gamma-ray litho-density logging tool using FW-CADIS
      • 4.1.5.3.1. Input file
      • 4.1.5.3.2. Output
    • 4.1.5.4. AOS-100 using FW-CADIS and continuous-energy transport
      • 4.1.5.4.1. Input file
      • 4.1.5.4.2. Output file
    • 4.1.5.5. Independent spent fuel storage installation
      • 4.1.5.5.1. Source term
      • 4.1.5.5.2. Input file
      • 4.1.5.5.3. Output
    • 4.1.5.6. TN24-P spent fuel cask
      • 4.1.5.6.1. Input file
      • 4.1.5.6.2. Output
• 4.2. MAVRIC CAAS Capability
  • 4.2.1. Introduction
  • 4.2.2. Methods
  • 4.2.3. User Input
    • 4.2.3.1. KENO-VI input
    • 4.2.3.2. Mesh tally to mesh source conversion
    • 4.2.3.3. MAVRIC input
  • 4.2.4. Example problem
    • 4.2.4.1. KENO-VI criticality and fission source distribution
    • 4.2.4.2. MAVRIC transport calculations
      • 4.2.4.2.1. Detector doses using CADIS
      • 4.2.4.2.2. Dose map using FW-CADIS
  • 4.2.5. Summary
• 4.3. MAVRIC Utilities
  • 4.3.1. Introduction
  • 4.3.2. Utilities working with Monaco mesh tally (3DMAP) files
  • 4.3.3. Utilities for working with DENOVO binary flux (*.dff) files
  • 4.3.4. Utilities for working with DENOVO *.varscl (a TORT format) files
  • 4.3.5. Miscellaneous utilities
• 4.4. MAVRIC Advanced Features
  • 4.4.1. Alternate normalization of the importance map and biased source
  • 4.4.2. Importance maps with directional information
    • 4.4.2.1. Approaches incorporating directional information
    • 4.4.2.2. Directionally dependent weight windows without directional source biasing
    • 4.4.2.3. Directionally dependent weight windows with directional source biasing
    • 4.4.2.4. Using space/energy/angle CADIS in MAVRIC
    • 4.4.2.5. Example problem
      • 4.4.2.5.1. CADIS
      • 4.4.2.5.2. Angular CADIS 1 - without a biased source angular dist.
      • 4.4.2.5.3. Angular CADIS 2 - with a biased source angular dist.
  • 4.4.3. University of Michigan methods for global variance reduction
    • 4.4.3.1. Weight windows using only forward estimates of flux
      • 4.4.3.1.1. Global flux weight windows
      • 4.4.3.1.2. Global response weight windows
      • 4.4.3.1.3. Implementation in MAVRIC
    • 4.4.3.2. Methods using forward and adjoint estimates
      • 4.4.3.2.1. Source/detector problems
      • 4.4.3.2.2. Source-region problems
      • 4.4.3.2.3. Global response problem
    • 4.4.3.3. Implementation in MAVRIC
      • 4.4.3.3.1. Example problems
      • 4.4.3.3.2. CADIS
      • 4.4.3.3.3. Becker 1 - flux optimization
      • 4.4.3.3.4. Becker 2 - response optimization
      • 4.4.3.3.5. A global problem
      • 4.4.3.3.6. FW-CADIS
      • 4.4.3.3.7. GRWW
      • 4.4.3.3.8. Becker source/region
      • 4.4.3.3.9. Becker - global
    • 4.4.3.4. Other special options for the importance map block input
  • 4.4.4. Using MAVRIC to run fixed-source Denovo calculations
    • 4.4.4.1. Optional Denovo parameters
    • 4.4.4.2. Forward source preparations
    • 4.4.4.3. Adjoint source preparation
    • 4.4.4.4. Other notes
    • 4.4.4.5. MAVRIC utilities for Denovo
    • 4.4.4.6. Example problem
      • 4.4.4.6.1. Forward
      • 4.4.4.6.2. Adjoint