Monte Carlo Methods for Isotopic Inventory Analysis

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Monte Carlo Methods for Isotopic Inventory
Analysis

• Paul Wilson
• Phiphat Phruksarojanakun
• FTI Meeting January 28, 2003

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Outline

• Introduction
• Motivation
• Project Details
• Basics
• Status
• Matlab
• C
• Issues/Challenges
• Future work

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Motivation

• Some classes of problems are not handled well by
  traditional isotopic inventory analysis codes
• Material flowing in complex geometries
• Common fusion blanket designs
• Constant addition/removal of materials to the
  system
• Symbiotic fuel cycles with transmuters
• Liquid fueled fission cycles
• Chemical reaction steps in material life cycle

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Project Details

• 2002 NEER Project
• 3 Years
• Started July 2002
• 260k
• PPHW, DLH One graduate student
• Phiphat Phruksarojanakun

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Simple 0-D Problem Definition
Control Volume

• Sample Atom
• Atomic
• Isotopic

• Control Volume
• neutron flux, f
• residence time, tR

Mean reaction Time tm1/leff
Nuclear Data
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0-D Analog MC Sampling

• Convert residence time to number of mean reaction
  times for this isotope

• Randomly sample number of mean reaction times
  before next reaction

• If nR gt n, reaction occurs

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When Reaction Occurs

• Randomly sample which reaction occurs
• Determine new isotope
• Update remaining residence time
• tR ? tR n ? tm
• Repeat with new isotope
• Therefore new tm

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Obvious Extensions to 0-D

• Multi-D
• Simultaneous independent 0-D problems
• Simple flowing systems
• If no reaction in one volume, atom moves into
  next volume
• Complex flowing systems
• If no reaction in one volume, randomly sample
  which volume the atom moves into
• Pulsing
• Variety of techniques (analog non-analog)

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Outline

• Introduction
• Motivation
• Project Details
• Basics
• Status
• Matlab
• C
• Issues/Challenges
• Future work

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MATLAB Prototyping Status

• MATLAB provides rapid prototyping of
  ideas/concepts
• Built-in random number generator
• Built-in plotting capability
• Effort to read nuclear data
• Two tests so far
• Basic proof-of-principle
• Variance reduction investigation

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Proof-of-principle

• Purpose
• Develop basic test bed for future ideas
• Gain understanding of statistics of this type of
  problem
• Investigate different tallying options
• Problem Definition
• 15 isotopes in chain
• Identical effective half-lives
• Simulation time is 10 half-lives
• Two types of tallies
• Qualitative results available
• Quantitative comparison still under development

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Proof-of-principle Results
Qualitative Results

• Unit Tally
• Tallied at 11 discrete points
• Each contributing particle has same contribution

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Proof-of-principle Results
Qualitative Results

• Partial Tally
• Tallied in 10 bins
• Each contributing particle has contribution
  related to time spent in bin

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Variance Reduction Prototype

• Purpose
• Investigate exponential transform VR
• This problem is analogous to deep penetration
  shielding problems
• Problem definition
• Modify previous problem by reducing effective
  half-life of 2nd isotope by 2 orders of magnitude

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VR Results

• Expectations
• Without VR expect very small tallies after 2nd
  isotope
• High relative error
• With VR expect same tally values but
• based on more particles
• lower relative error
• Still under development

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C Object-Oriented Design

• Classes
• Atom
• Which isotope
• Remaining time to sampled next reaction
• In which control volume currently resident
• ControlVolume
• Total residence time
• Map of simplified nuclear data
• FoldedData
• Effective reaction rate constants
• Reaction lists

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Modular Design

• Provide standard services from MCTools library
• PRNG run-time changing of random number
  generator
• Base RNG is SPRNG (ASCI project)
• DiscretePDF run-time selection of methods for
  sampling discrete PDFs
• Provide standard data access from DataTools
• Under development

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Outline

• Introduction
• Motivation
• Project Details
• Basics
• Status
• Matlab
• C
• Issues/Challenges
• Future work

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Issues/Challenges

• Variance reduction will be important
• In addition to exponential transform, there are
  inventory analogues to many transport VR methods
• Splitting/Roulette/Weight Windows
• Forced reaction
• Source biasing
• Next reaction estimator
• Flow-loop smearing
• Tally development
• Which tallys will be meaningful?

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Outline

• Introduction
• Motivation
• Project Details
• Basics
• Status
• Matlab
• C
• Issues/Challenges
• Future work

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Project Timeline

• Year 1
• 0-D analog MC development benchmarking
• Year 2
• Flowing system development
• Source/Sink development
• Application to nuclear systems
• Year 3
• Tally function development
• Variance reduction development
• Application to future nuclear systems

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Near Term Developments

• Demonstrate exponential transform VR
• Demonstrate 0-D with real nuclear data
• Software developments
• Abstracted generic tally service
• Input file formatting XML?
• Begin test suite development

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Questions?