Advanced Mathematical Methods for

Gamma Ray Based Nuclear Safeguards

Measurements

Ram Venkataraman

Canberra Industries (AREVA BDNM)

Presented at the IAEA Symposium on International Safeguards

October 20 – 24, 2014, Vienna, Austria

The contributions of the co-authors is gratefully acknowledged

Canberra

Andrey Bosko (now with the IAEA)

Frazier Bronson

Nabil Menaa

Gabriela Ilie

William Russ

IAEA

Ludovic Bourva (now with Canberra)

Alain Lebrun

Vladimir Nizhnik

Andrey Berlizov

Seokryung Yoon

Introduction Mathematical methods for computing gamma ray efficiencies such as

In Situ Object Calibration Software (ISOCS) are very attractive for

gamma ray based Nuclear Safeguards applications.

Accuracy of quantitative results will depend on how closely does the

efficiency calibration match the item being assayed.

ISOCS Uncertainty Estimator

Many of the characteristics of

items encountered in the field

are “Not Well Known” (NWK)

The matrix composition, density and

fill height

Weight fraction of U in matrix is not

known.

Container dimensions

ISOCS Uncertainty Estimator

(IUE) software tool can be used

to estimate uncertainties due to

NWK

Advanced-IUE

Advanced ISOCS (or Advanced IUE) takes it one step further.

Automated determination of efficiency calibration most consistent with gamma ray

spectrum measured in the field.

A-IUE developed by Canberra in close collaboration with the IAEA

A-IUE Algorithm Flow:

Container with Unknown

distribution of radioactive

material

Platform (could be rotating)

Radiation Sensor

High Voltage Power Supply

Collimator & Shield

Pre-Amplifier Amplifier

Analog to Digital

Convertor

Multi-Channel Analyzer for Signal

Processing

Pre-loaded Software and

Set up Files for Data

Acquisition & Automated

Analysis

Pre-Analysis with initial efficiency

(using guesstimated

geometry parameters)

Best Efficiency solution and Uncertainty Estimation

Final Analysis with Best Efficiency.

Nuclide Identification and

Activity Quantification

Report Nuclide Activities and Uncertainties

EXECUTE AUTOMATED

ANALYSIS

Benchmarks/Figure of Merits - Isotopics,U or Pu Mass

Isotopic analysis results of U or Pu Gamma ray spectra of items using codes

MGAU, MGA, & FRAM

MGAU (U measurements): U Enrichment used as benchmark

MGA: (Pu measurements): Relative efficiencies used as benchmark

FRAM: (U or Pu measurement): Enrichment for U, Relative efficiency for Pu

User-defined enrichment

MGAU and MGA are distributed as Canberra products and therefore are

seamlessly integrated with Genie2000 software.

Isotopic results are stored by Genie2000 directly in the measured spectrum; results

can be extracted without having to access an external file.

Isotopic results are representative of the shape of the efficiency curve; not

the magnitude (because of the “infinitely thick” sample conditions).

Isotopic benchmark used in combination with U (or Pu) mass benchmark

U (or Pu) mass in the ISOCS model compared with measured mass

Measured mass: obtained using measured peak areas, the gamma ray yields and the ISOCS

calculated peak efficiencies at U or Pu gamma ray energies of interest. Activity is converted to

mass by using the specific activities of the nuclides.

Benchmarks/Figure of Merit - Line Activity Consistency Evaluation (LACE),

- Multiple Counts of same item

LACE Benchmark:

Useful in measurements of a

nuclide emitting multiple

gamma lines.

Works best when gamma lines

span a wide energy range (e.g. 152Eu)

Multi-Count: A given item

counted at multiple

geometries

Source parameters that give a

consistent mass results with

the multiple-count data

Powerful benchmark that

boosts confidence in the

verification.

UNIFORM

SOURCE

DISTRIBUTION

A-IUE

CALIBRATION

PO

SIT

ION

1

PO

SIT

ION

2

Count 1

Count 2

Routines used in IUE to search for Efficiency Solution

Best Random Fit (BRF)

large number of random ISOCS models by varying the NWK parameters

within the range indicated by the user

Efficiencies from each trial model is compared against one or more

benchmarks, and the FOMs are calculated.

Individual FOMs obtained for each benchmark are then combined

together into a single Composite FOM.

Models are then ranked from the best to worst according to their

Composite FOM values.

Computes the mean efficiency and standard deviation based on the best

models; user defines the number of best models to be used

The mean efficiencies which represent the most consistent solution are

used in the analysis of the gamma ray spectrum.

Search is carried out until the user-set convergence is reached for

various energy ranges, or when the max. no. of models is reached

(default is 2000 models).

Routines used in IUE to search for Efficiency Solution

Smart search using Downhill

Simplex

involves continuously improving the

FOMs of models represented by

points in the solution space at the

vertices of a multidimensional form,

or simplex.

An initial simplex is established with

one vertex more than the number of

free parameters, and all of these

point models are evaluated.

The points are sequentially improved

by simultaneously adjusting all of

the free parameters in the point with

the worst FOM.

After the worst point is improved

and is no longer the worst point, the

new worst point is improved

Simplex vs. Best Random Fit

Simplex

Advantage: Short computation

times; tens of minutes; < 1 hour

even for highly attenuating

geometries

Disadvantage: Solution could

fall into local minimum

Mitigation: Convergence Check

option implemented. Perturbs

the solution space and confirms

convergence with original

results

Best Random Fit

Disadvantage: For highly

attenuating geometries, could

take several hours.

Advantage: If one is willing to

tolerate long computation

times, BRF will give a good

solution

Mitigation: Option to speed up

BRF; the software automatically

narrows down the specified

variation ranges for NWK

parameters based on the

results of the initial batch of

random ISOCS models.

Verification and Validation

Measurement spectra provided by the IAEA – mostly U but

also some Pu spectra.

Canberra sources were also measured.

U measurements (IAEA spectra):

Uranyl Nitrate solutions in High Density PolyEthylene vials with various

fill heights and concentrations; 15 – 30 g of U

“CBNM” standard with 169.7 g of low enriched uranium (LEU: 2.95%,

4.46%) in U3O8

“SU-135” standard with 848 g LEU (3.105%) in U3O8

Uranium Carbide samples similar to what is encountered in the field;

mixture of graphite and U; known matrix weight (2 to 3 kg), but unknown

U weight fraction; HEU: 20%-50; U mass range of 800 g – 1600 g

Example: Uranium Carbide Spectrum, and measurement geometry

Count 1

Count 2

Uranium Measurement Results

Each U spectrum analyzed using the

following benchmarks:

MGAU + U mass

FRAM + U mass

User-defined enrichment + U

mass

LACE + U mass

CBNM & SU-135 standards counted

at 2 different geoms.

Majority of the A-IUE results are

within ±20%of expected mass

Simplex agrees with BRF to within

±10%

Outlier: U Carbide spectrum with

LACE + U mass benchmark and

Simplex

Plutonium Measurements

Except for Plutonium 1,

expected masses were not

available for other Pu items.

One could only draw

conclusions based on the

consistency of results among

various benchmarks

Plutonium 1 is a spectrum

measured at Canberra (CRM). Pu

mass known

A-IUE results were between 8%-10%

of the expected Pu mass.

0.1

1

10

100

0 5 10 15 20

Op

tim

ize

d p

luto

niu

m

ma

ss

, g

Optimization case

Plutonium 1

Plutonium 2

Plutonium 2 (no Pu)

Plutonium 3

Plutonium 4 (no Pu)

Results from Best Random Fit

Results from Simplex

241Am + 152Eu Point source inside 208 liter drum matrix

Efficiency model Activity for

Position 1, mCi

Activity for

Position 2, mCi

Weighted

average activity,

mCi

Measured

/Expected

Uniform source

distribution 9.20 +/- 0.17 1.22 +/- 0.03 1.38 +/- 0.02 0.351

Point source in the middle 10.60 +/- 0.20 1.53 +/- 0.03 1.74 +/- 0.03 0.442

BRF (LACE) 3.70 +/- 0.06 4.42 +/- 0.14 3.81 +/- 0.06 0.966

BRF (Multi) 3.88 +/- 0.13 3.78 +/- 0.13 3.82 +/- 0.09 0.969

BRF (Multi + LACE) 3.73 +/- 0.04 4.15 +/- 0.04 3.94 +/- 0.03 0.998

Simplex (LACE) 3.50 +/- 0.07 4.60 +/- 0.09 3.88 +/- 0.05 0.983

Simplex (Multi) 4.36 +/- 0.08 4.36 +/- 0.09 4.36 +/- 0.06 1.106

Simplex (Multi + LACE) 4.09 +/- 0.08 4.04 +/- 0.08 4.06 +/- 0.03 1.029

Efficiency model Activity for

Position 1, mCi

Activity for

Position 2, mCi

Weighted

average activity,

mCi

Measured

/Expected

Uniform source

distribution 17.22 +/- 1.73 0.55 +/- 0.06 0.57 +/- 0.06 0.145

Point source in the middle 23.27 +/- 2.34 0.75 +/- 0.08 0.77 +/- 0.08 0.196

BRF (LACE) 4.15 +/- 0.31 4.30 +/- 0.54 4.19 +/- 0.27 1.069

BRF (Multi) 4.45 +/- 0.94 2.97 +/- 0.78 3.57 +/- 0.60 0.910

BRF (Multi + LACE) 4.28 +/- 0.29 3.71 +/- 0.12 3.79 +/- 0.11 0.967

Simplex (LACE) 3.86 +/- 0.39 4.57 +/- 0.46 4.15 +/- 0.30 1.058

Simplex (Multi) 22.49 +/- 2.26 4.04 +/- 0.41 4.62 +/- 0.40 1.179

Simplex (Multi + LACE) 4.87 +/- 0.49 3.55 +/- 0.36 4.02 +/- 0.29 1.025

152Eu results

241Am results

Field ISOCS Utility

This utility is focused on the ease of use by IAEA inspectors in the field

and was designed to fully support the Expert-Inspector concept.

Conclusions

The A-IUE prototype software was developed by Canberra in

close collaboration with the IAEA.

The A-IUE automatically determines the efficiency calibration

that is consistent with the gamma ray spectrum measured in

the field.

A-IUE was thoroughly tested using the measurement spectra

provided by the IAEA, and measurements done at Canberra’s

factory.

Acknowledgement: The A-IUE project was funded by the U.S.

Support Program: USSP Task USA A 1607 "Development of

ISOCS Self Modeling Capabilities" A.267. The authors

gratefully acknowledge the support from USSP.

Thank You!