NOTES AND REFERENCES
- Whitley , S. 1984 . “Review of the Gas Centrifuge until 1962. Part I: Principles of Separation Physics. Part II: Principles of High-Speed Rotation,” . Reviews of Modern Physics , 56 ( 1 ) : 41 – 97 . Whitley notes that the problem of solving the hydrodynamic equations was circumvented during the Manhattan Project by preferring the externally driven machine. See
- Rätz , E. 1983 . Analytische Lösungen für die Trennleistung von Gaszentrifugen zur Urananreicherung , Ph.D. Thesis Technical University of Berlin . Remarkably, the editor compares the main findings of the thesis with 17 other solutions available at that time and highlights equivalences as well as differences in the approaches and results. A shorter and less complete version of this analysis has been published in English: E. Rätz, An Analytical Solution for the Separative Power of Gas Centrifuges, Fifth Workshop on Gases in Strong Rotation, University of Virginia (Charlottesville, 5–9 June, 1983). Other centrifuge solutions, both analytical and numerical, have been published in the open literature. These would produce similar results. One important feature of the the Rätz formalism, besides its simplicity, is the capability of determining performance characteristics for machines operated under off-optimum conditions
- Cohen , K. 1951 . The Theory of Isotope Separation as Applied to the Large-Scale Production of U235 , New York : McGraw-Hill . ch. 6 and, in particular, pp. 106–109. The derivation of the centrifuge equation is also reproduced in: D. G. Avery and E. Davies, Uranium Enrichment by Gas Centrifuge (London, Mills & Boon Limited, 1973), Appendix II
- Cohen, ibid. p. 120
- Rätz, Analytische Lösungen, ch. 8, p. 8.8
- The countercurrent L is defined by the amount of material flowing in one shell of the profile (upflow or downflow) along the centrifuge rotor. The cut θ is the fraction of the feed that leaves the centrifuge as product. The rectifier ZP is the length of the rotor between the feed point and the product end, in which the material is being enriched. Accordingly, the length of the stripper is (Z − ZP )
- Rätz, Analytische Lösungen, ch. 8, p. 8.17
- Rätz, Analytische Lösungen, ch. 2, pp. 2.4–2.5
- Cohen . The Theory of Isotope Separation 110
- Avery and Davies . Uranium Enrichment For a derivation, see for example Appendix I, or Rätz, Analytische Lösungen, sections 3.2 and 8.1
- Rätz . Analytische Lösungen 8.10
- Kehoe , R. B. 2002 . The Enriching Troika. A History of Urenco to the Year 2000 , 56 Marlow, Buckinghamshire , UK : Urenco Ltd . The acronym is sometimes expanded as commercial nuclear obreptitious rotor.
- Hibbs , M. 2005 . “Current Capacity at Natanz Plant about 2,500 SWU/yr, Data Suggest,” . Nuclear Fuel , 30 ( 3 ) : 17
- Hibbs , M. 2005 . “Report Suggests Pakistan Bought Components for Two Steel Centrifuges,” . Nuclear Fuel , 30 ( 14 ) : 3
- Interview with G. R. Aqazadeh, president of the Iranian Atomic Energy Organization, 12 April 2006, Network 2, in Persian. The measuring unit of the rotor length has been misprinted in the transcript (incorrectly reads “1.80 centimeters”). The rotor diameter has been calculated from the quoted revolutions per minute (64,000 rpm) and the peripheral velocity
- Kehoe . The Enriching Troika 56
- Hibbs , M. 1990 . “Iraq Has Early Urenco Centrifuge Design, but Mass Production Years Away, Expert Says,” . Nuclear Fuel , 15 ( 26 ) : 1 M. Hibbs, “Customs Intelligence Data Suggest DPRK Aimed at G-2 Type Centrifuge,” Nuclear Fuel 28(11) (2003): 3
- Hibbs , M. 2007 . “Pakistan Developed More Powerful Centrifuges,” . Nuclear Fuel , 32 ( 3 ) : 1 M. Hibbs, “P-4 Centrifuge Raised Intelligence Concerns about Post-1975 Data Theft,” Nucleonics Week 48(7) (2007): 1
- Hibbs , M. 2005 . “Classified Dutch report suggested Khan saw key 4-M centrifuge data,” . Nuclear Fuel , 30 ( 2 ) : 3
- Hibbs , M. 2005 . “How Much Access?” . Nuclear Fuel , 30 ( 1 ) : 1
- Hibbs , M. “Pakistan Development More Powerful Centrifuges,” op. cit.
- Hibbs , M. “P-4 Centrifuge Raised Intelligence Concerns about Post-1975 Data Theft,” the Urenco designations SLM and TC-10 are given in Kehoe . The Enriching Troika , 113
- Upson , Pat . “Centrifuge Technology: The Future for Enrichment,” World Nuclear Association, Annual Symposium (London, 5–7 September 2001). The same or similar graphs have been used in other Urenco publications and briefings
- Green , R. September 2003 . “Back to the Future,” . In Nuclear Engineering International September , 36 – 39 . www.neimagazine.comFor example, in public documents filed by Louisiana Energy Services in 1991, quoted in
- Several prototypes were studied during that period. Prominent designs are the so-called Set III, which had a capacity of 200 SWU/yr and was deployed in the pilot gas centrifuge enrichment plant in Portsmouth, the Set IV, and the Set V or Advanced Gas Centrifuge (AGC). The targeted separative performance for the AGC was about 600 SWU/yr; see R. Green, “Back to the Future,” op. CH
- The USEC facility is designed for 3.8 million SWU/yr with 11,500 machines deployed, which is consistent with the lower estimate of 330 SWU per year and machine. Yet, “[i]n 2006, the USEC project team at Oak Ridge tested a centrifuge machine that demonstrated performance of about 350 SWU per machine, per year (exceeding our target level of performance of about 320 SWU per machine, per year). This performance level has been reaffirmed in subsequent testing.” Fact Sheet. American Centrifuge Uranium Enrichment Plant, USEC Inc., (2008), www.usec.com, www.americancentrifuge.com (accessed September 1, 2008)
- Typical dimensions listed for the American Centrifuge are a height of 40 feet (∼12 m) and a diameter of about two feet (∼60 cm); quoted, for example, in: D. Charles, “U.S. Centrifuge Work Revived in Updated Form,” The Washington Post, 23 April, 2007, p. A06
- Alternatively, one could also assume and model that the output rates are directly determined by the feed rate, which would maintain a fixed UF6 inventory in the machine at all times
- One torr is defined as 1/760 of an atmosphere and corresponds to 133.32 Pa. In a centrifuge, wall pressures beyond 100 torr are considered impractical because the UF6 gas runs the risk of desubliming on the rotor wall
- Olander , D. R. 1979 . “Separative Performance Transients in a Gas Centrifuge,” . Nuclear Technology , 44 : 307 – 314 .
- In the charge sheet for the South African trial of Daniel Geiger and Gerhard Wisser, several cascade designs are specified. One of these cascades enriches natural uranium to 3.5% and consists of 1968, or 12 × 164, machines. It is pointed out that “[T]he plant was the product of the original German drawings and descriptions as adapted by Pakistani test results, experience and reference calculations.” (“Summary of Substantial Facts,” Charge Sheet, The State versus Daniel Geiges and Gerhard Wisser, High Court of South Africa, Transvaal Provincial Division, 2006, Paragraph 6.19)
- See note 15
- It is not clear, however, if the quoted feed and product rates refer to uranium hexafluoride or to net uranium. To be consistent with the expected separative performance of the P-1, values for net uranium are more plausible, however, because they indicate a higher machine performance, which would still be comparably low (about 1.32 SWU/yr per machine). Several reference P1-designs, optimized for different feed rates, are explored in this article. In any case, the statements on the number of stages (15 total, 10 in enriching section) and machines (164 total, 24 in feed stage) are considered the primary constraints for defining the shape of the reference cascade further below
- For a discussion of ideal cascades, see, for example, Cohen, The Theory of Isotop Separation, ch. 1, or Avery and Davies, Uranium Enrichment, section 5.2
- Olander , D. R. 1976 . “Two-up, One-down Ideal Cascades for Isotope Separation,” . Nuclear Technology , 29 : 108 – 112 . Other ideal, but non-symmetric, cascades are possible and have been considered for use in enrichment cascades. See, for example
- Other names for cascade interconnection are cascades-in-series and parallel overlap
- For instance, the United States has specified some details of its HEU production complex, in which operation of the gaseous diffusion plants in Paducah, Oak Ridge and Portsmouth was integrated in a similar way. See figure 2.2 (p. 27) in Highly Enriched Uranium: Striking a Balance; A Historical Report on the United States Highly Enriched Uranium Production, Acquisition, and Utilization Activities from 1945 through September 30, 1996, Rev. 1., Draft, U.S. Department of Energy, January 2001 (publicly released in 2006), www.ipfmlibrary.org/doe01.pdf (accessed September 1, 2008)
- Note, however, that the number of machines in the HC-01 cascade is equally divisible by 164 (8 × 164 = 1312)
- Even the SWU requirements per kilogram of HEU produced are lower for batch recycling. This does not mean, of course, that batch recycling is the more efficient process. For a complete assessment of the efficiency, the value of the preenriched feedstock has to be taken into account. As pointed out, however, the value of this stock can be excluded because it is already available and does not affect the time line for this scenario
- Here, it is assumed that the HC-type cascades continue to strip the feed down to 0.72%, even though HC-02 and HC-03 could be redesigned to strip down to only 3.5% in order to recycle their tails into the HC-01 cascade. This alternative strategy would make the production process somewhat more efficient