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## Monte Carlo Methods for Isotopic Inventory Analysis

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### Tally. 11/20/2003. 2003 ANS Winter Meeting. 10 /19. Status. Early prototyping with Matlab ... Tally. Base. Current Tally. Population Tally. Main Application. SPRNG 2.0 ... – PowerPoint PPT presentation

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Title: Monte Carlo Methods for Isotopic Inventory Analysis

1
Monte Carlo Methods for Isotopic Inventory
Analysis
• Paul Wilson
• Phiphat Phruksarojanakun
• David Paige
• 2003 ANS Winter Meeting

2
Overview
• Motivation
• Basic Algorithm Simple 0-D
• Details Extensions
• Status Observations
• Code Development
• Early benchmarks
• Summary Future directions

3
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

f1
f2
4
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
5
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
• Else, end history and repeat

6
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

7
Comparison to Monte Carlo Transport
Neutral particles Individual atoms
Length of geometric cell
Residence time in control volume
Mean free paths between reactions (macroscopic
cross-section)
Mean times between reactions (effective total
transmutation decay rate)
Energy Isotopic identity
8
Details - Sources
• Single fixed source
• Sample discrete PDF of initial atoms
• Single continuous source
• Sample time dependent function representing
in-flow of atoms
• Multiple sources
• Sample between magnitude of sources
• Sample each source appropriately

9
Details - Tallys
• Atom current Tally
• Atom population Tally

10
Status
• Early prototyping with Matlab
• Current development under C

SPRNG 2.0 Scalable Pseudo-Random Number Generator
Atom
Control Volume
Main Application
MCTools
PRNG Wrapper
Nuclear Data Access
Current Tally
Discrete PDF Template
Tally Base
Population Tally
11
Analytic Benchmark Pure Decay
• 14O ?14N ? t1/2 70 s ? 1010 particles
? error 0.001

12
Computational Benchmark 56Fe Steady-state
Activation vs ALARA
• 10 yr ? 10-9 ALARA tolerance ? 108 particles
? 18 missing products

13
Variance Improvements - Parallelism
14
Variance Reduction Techniques
• Forced reaction
• Require a reaction (or many) to take place in
each control volume
• Uniform branching
• Select reaction path uniformly to enhance
pathways with low probability
• Uniform source sampling
• Select initial atoms uniformly to enhance role of
trace isotopes

15
Analog Extensions
• 0-D Calculation
• Simple Flow
• Complex Flow
• Loop

16
Flow Benchmarking Equivalents to 0-D Steady State
• Simple flow tests
• Create systems with multiple control volumes
(CVs) but same total residence time and uniform
neutron flux
• 2 CVs vs 1 CV
• 10 CVs vs 1 CV
• Complex flow tests
• Create systems with well-defined flow splitting
uniform neutron flux
• 5050 flow split
• 9010 flow split

17
Flow Benchmarking Case Comparison
• 10 yr ? 10-9 ALARA tolerance ? 108 particles

5050 Complex Flow
1 CV Steady- State
2 CV Simple Flow
9010 Complex Flow
10 CV Simple Flow
18
Summary
• Concept works well
• Analog precision limit worse than
• 1/ particles for single initial isotope
• 1/(M particles) for uniform mixture of M
isotopes
• Needs parallel performance and
• Needs variance reduction
• Variance reduction
• Early results are promising

to precision limit
19
Future Work
• Implement test variance reduction
• Investigate options for pulsed irradiaton systems
• Probably inefficient to model pulses as separate
control volumes
• Pulse frequencies and flow frequencies may not be
synchronized
• Opportunities based on delta-tracking transport
analog
• Production calculations for fission fusion
systems
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