Skip to main content
SpringerLink
Log in

Deterministic Design I: Conceptual Formulation

  • Chapter
The Assay of Spatially Random Material

Part of the book series: Mathematics and Its Applications ((MAIA,volume 20))

  • 149 Accesses

Abstract

In this Chapter we shall develop a powerful analytical aid for the design of assay systems which are intended to measure materials which are randomly distributed in space. We learned in Chapter 1 that the design procedure must be based on a quantitative measure of performance which guides the designer to the best from among alternative realizable designs. This performance-measure must evaluate the accuracy of the assay system in the face of two main challenges. First of all, the measure must assess how well the assay system confronts the challenge of spatial uncertainty: the spatial randomness of the assayed material. Second, the measure of performance must evaluate the degree to which the assay system is sensitive to the statistical uncertainty arising from randomness of the radiation-measurement process. Not only must the measure encompass these diverse and complex aspects of an arbitrary assay system, it must also be practicable. That is, it must be computationally feasible to evaluate the performance measure for a wide range of alternative proposed designs.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. The relative mass resolution is by no means the only concept which may be used to define a measure of performance. In much design work of nuclear assay systems the degree of “flatness” of the response function has been used as a measure of performance. An additional useful and widely employed design concept is the resolving power. See:

    Google Scholar 

  2. A. Notea and Y. Segal, A General Approach to the Design of Radiation Gauges, Nucl. Tech., 14: 73 – 80 (1974).

    Google Scholar 

  3. Y. Segal, A. Notea and E. Segal, A Systematic Evaluation of Nondestructive Testing Methods, in Research Techniques in Nondestructive Testing, Vol. Ill, R. S. Sharpe, ed., Academic Press, 1977.

    Google Scholar 

  4. N. Shenhav, Y. Segal and A. Notea, Application of Neutron Count Moment Analysis Method to Passive Assay, Nucl. Sci. Eng., 80: 61 – 73 (1982).

    Google Scholar 

  5. The concept of the response function does not require that the detector be localized at a single point. It is meaningful for well‐ type counters which entirely surround the sample and for calori‐ metric measurements. For an interesting exploitation of the sensitivity of a Nal well‐type counter to the spatial distribution within the well of a gamma source see

    Google Scholar 

  6. F. Cejnar, L. Wilhelmova and I. Kovar, Determination of Radionuclide Two‐phase Distribution by Well‐Type Nal(Tl) Detectors, Int. J. Appl. Rad. Isotopes, 32: 1 – 4 (1981).

    Article  Google Scholar 

  7. For a discussion of calorimetric measurements see

    Google Scholar 

  8. J. D. Nutter, F. A. O’Hara and W. W. Rodenburg, The Use of Calorimetry in Nuclear Materials Management, Inst. NucL Mat. Mgt. r 11‐th annual conf., May 1970, Gatlinburg, Tenn., pp. 101– 121.

    Google Scholar 

  9. See G. Knoll, Radiation Detection and Measurement, John Wiley, 1979, for a discussion of mean free paths.

    Google Scholar 

  10. The probability of shadowing can readily be evaluated analytically in certain circumstances. For a discussion of free paths in a Poisson ensemble of disks or spheres see:

    Google Scholar 

  11. W. Feller,An Introduction to Probability Theory and its Applications,Vol. II, John Wiley, 1971.

    MATH  Google Scholar 

  12. Many examples may be found in

    Google Scholar 

  13. T. Gozani, Active Nondestructive Assay of Nuclear Materials, U.S. Natl. Tech. Inf. Serv., NUREG/CR‐0602, 1981.

    Google Scholar 

  14. A. N. Kolmogorov and S. V. Fomin, Introductory Real Analysis, Dover, 1970.

    Google Scholar 

  15. P. Kelly and M. L. Weiss, Geometry and Convexity, Wiley Interscience, 1979.

    Google Scholar 

  16. S. R. Lay, Convex Sets and Their Applications, John Wiley, 1982.

    Google Scholar 

  17. Y. Ben‐Haim and N. Shenhav, The Measurement of Spatially Random Phenomena, S.I.A.M. J. Appl. Math., 44: 1150 – 63 (1984).

    Article  MathSciNet  MATH  Google Scholar 

  18. Y. Ben‐Haim and N. Shenhav, The Design of Nondestructive Assay Systems, Int. J. Appl. Rad. Isotopes, 34: 1291 ‐ 1299 (1983).

    Article  Google Scholar 

  19. N. E. Holden and M. S. Zucker, Plutonium Nuclide Nuclear Data Standards of Safeguards Interest, 6‐th Ann. Symp. Safeguards and Nuclear Mat. Mgt., ESARDA, Venice, May 1984.

    Google Scholar 

  20. T. Gozani and D. G. Costello, Isotopic Source Assay System for Nuclear Materials, Trans. Am. Nuc. Soc., 13: 746 – 7 (1970).

    Google Scholar 

  21. T. Gozani and D. G. Costello, On the Reduction of Gamma Self‐Shielding Using the Fission Multiplicity Detector, Trans. Am. Nuc. Soc14:809–10 (1971).

    Google Scholar 

  22. . M. S. Zucker and E. Karpf, Absolute Calibration of Spontaneous Fission Neutron Sources, 6‐th Ann. Symp. Safeguards and Nuclear Mat. Mgt., ESARDA, Venice, May 1984.

    Google Scholar 

  23. See ref. [5] and

    Google Scholar 

  24. T. Gozani, Fission Multiplicity Detectors, Trans. Am. Nuc. Soc., 24: 127 – 8 (1976).

    Google Scholar 

  25. I. S. Panasyuk, On Measurements of Disintegration Rates of Radioactive Sources by Coincidence Methods, Nucl. Inst. Meth., 31: 314 – 6 (1964).

    Article  Google Scholar 

  26. T. Gozani, Reduction of Geometry and Matrix Effects by Fast Coincidence Non‐Destructive Assay, Proc. Inst. Nucl. Mat. Mgt., 12: 195 – 206 (1983).

    Google Scholar 

  27. The material in this section is discussed from various points of view in ref. [8] and in

    Google Scholar 

  28. N. Shenhav and Y. Ben‐Haim, A General Method for the Design of Nondestructive Assay Systems, Nucl. Sci. Eng., 88: 173 – 83 (1984).

    Google Scholar 

  29. L. D. Y. Ong et. al., A Look at SNM Measurement Errors Based on Safeguards Inventory Verification Duplicate Samples, Inst. Nucl. Mat. Mgt. 11‐th annual conf., May 1970, Gatlin‐ burg, Tenn., pp. 177–89.

    Google Scholar 

  30. J. Lieblein, Generalized Propagation of Error Using a New Approach, ibid, pp. 190–211.

    Google Scholar 

  31. T. E. Sampson and R. Gunnink, Propagation of Errors in the Measurement of Plutonium Isotope Composition by Gamma‐Ray Spectroscopy, J. Inst. Nuclear Mat. Mgt., 12: 39 – 48 (1983).

    Google Scholar 

  32. For thorough discussion of the fundamentals of the Poisson process see

    Google Scholar 

  33. W. F. Feller, An Introduction to Probability Theory and its Applications, Vol. I, John Wiley, 1968.

    MATH  Google Scholar 

  34. A. Papoulis, Probability Random Variables and Stochastic Processes, McGraw‐Hill, 1965.

    MATH  Google Scholar 

  35. For a discussion of how the Poisson process arises in electronic systems see

    Google Scholar 

  36. S. O. Rice, Mathematical Analysis of Random Noise, in Noise and Stochastic Processes,ed. by N. Wax, Dover Pub., 1954.

    Google Scholar 

  37. For a discussion of how Poisson processes arise in neutronic systems see

    Google Scholar 

  38. M. M. R. Williams, Random Processes in Nuclear Reactors, Pergamon Press, 1974.

    Google Scholar 

  39. J. W. Kormuth, J. F. Gettings, D. B. James, Nondestructive Assay of Plutonium Fuel Plates, Inst. Nucl. Mat. Mgt. 11‐th annual conf., May 1970, Gatlinburg, Tenn., pp. 266–79.

    Google Scholar 

  40. T. W. Packer, R. Howsley and E. W. Lees, Measurement of the Enrichment of Uranium Deposits in Centrifuge Pipework, 6‐ th Ann. Symp. Safeguards and Nuclear Mat. Mgt., ESARDA, Venice, May 1984.

    Google Scholar 

  41. T. Dragnev, Spectrometric Gamma Absorption Measurements, ibid.

    Google Scholar 

  42. N. Hayano, et. al., Evaluation of Leached Hull Monitoring System as the Tokai Reprocessing Plant, ibid.

    Google Scholar 

  43. For a good discussion of several passive neutron techniques see

    Google Scholar 

  44. J. L. Parker et. al., Passive Assay ‐ Innovations and Applications, Inst. Nucl. Mat. Mgt., 12‐th ann. conf., June 1971, Palm Beach, Fla, pp. 514–47.

    Google Scholar 

  45. M. Despres et al, Analysis Code for Plutonium Isotopic‐ Composition Measurements, Int. J. Appl. Rad. Isotopes., 34: 525 – 31 (1983).

    Article  Google Scholar 

  46. L. Bondar et al, Determination of Plutonium in Mixed Oxide Fabrication Plant Wastes by Passive Neutron Assay, 6‐th Ann. Symp. Safeguards and Nuclear Mat. Mgt., ESARDA, Venice, May 1984.

    Google Scholar 

  47. For an example of a passive neutron technique which discusses the effect of spatial distribution of the assayed material in the sample, see

    Google Scholar 

  48. A. Notea, Y. Segal, A. Bar‐Ilan, A. Knoll and N. Shenhav, Interpretational Models of Passive Gamma and Neutron Assay Systems, in Monitoring of Pu‐Contaminated Waste, EUR 6629 EN Sept. 1979, pp 363 – 81.

    Google Scholar 

  49. A. Knoll, A. Notea, Y. Segal, Probabilistic Interpretation of Nuclear Waste by Passive Gamma Technique, Nucl. Tech., 56: 351 – 60 (1982).

    Google Scholar 

  50. M. S. Zucker and E. V. Weinstock, Passive Measurements of Waste in 55 Gallon Drums and Conventional Scrap in 2 Liter Bot‐ties, Inst. Nucl Mat. Mgt., 11‐th annual eonf., May 1970, Gatlin-burg, Tenn., pp. 281–315.

    Google Scholar 

  51. R. A. Harlan et. al., Neutron Interrogation of Low‐Specific‐ Activity Wastes with a Reactor, Inst. Nucl. Mat. Mgt., 12‐th annual conf., June 1971, Palm Beach, Fla., pp. 373–98.

    Book  Google Scholar 

  52. M. M. Thorpe, et. al., Active Assay of Fissionable Materials, Inst. Nucl. Mat. Mgt., 12‐th annual conf., June 1971, Palm Beach, Fla., pp. 631–47.

    Book  Google Scholar 

  53. R. A. Harlan et al, Operational Assay for Fissile Material in Crated Nuclear Energy Wastes, 6‐th Ann. Symp. Safeguards and Nuclear Mat. Mgt., ESARDA, Venice, May 1984.

    Google Scholar 

  54. P. Dell’Oro et. al., Field Experience on Non‐Destructive Assay of Low‐Enrichment Uranium by Means of Photoneutron Interrogation, ibid.

    Google Scholar 

  55. For an example see the reference in note [17].

    Google Scholar 

  56. For an interesting design which exploits rotation of the sample and collimation of the detector see

    Google Scholar 

  57. H. O. Menlove et. al., Neutron Interrogation Techniques for Fissionable Material Assay, Inst. Nucl. Mat. Mgt. 11‐th Annual Conf., May 1970, Gatlinburg, Tenn., pp.316‐47.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Nuclear Engineering, Technion-Israel Institute of Technology, Haifa, Israel

    Yakov Ben-Haim

Authors
  1. Yakov Ben-Haim
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 1985 D. Reidel Publishing Company, Dordrecht, Holland

About this chapter

Cite this chapter

Ben-Haim, Y. (1985). Deterministic Design I: Conceptual Formulation. In: The Assay of Spatially Random Material. Mathematics and Its Applications, vol 20. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-5422-9_2

Download citation

  • DOI: https://doi.org/10.1007/978-94-009-5422-9_2

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-8893-0

  • Online ISBN: 978-94-009-5422-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation