The singular eigenfunction method: the critical slab problem for linearly anisotropic scattering
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R. G. Türeci
Abstract
The critical slab problem for linearly anisotropic scattering is investigated using the singular eigenfunction method. The third form of the transport equation is considered. The singular eigenfunctions for linearly anisotropic scattering are inserted into the Green's function. This Green's function with the full range orthogonality relations of the singular eigenfunctions together with the appropriate boundary conditions provide the criticality equation. This equation is exact and leads as shown in tables to fast converging numerical results.
Kurzfassung
Das kritische Plattenproblem für linear anisotrope Streuung wird untersucht mit Hilfe der Methode der singulären Eigenfunktion. Dazu wird die dritte Form der Transportgleichung betrachtet. Die singulären Eigenfunktionen für linear anisotrope Streuung werden in die Green's Funktion eingesetzt. Diese Green's Funktion mit dem vollen Satz der Orthogonalitätsbeziehungen der singulären Eigenfunktionen zusammen mit den geeigneten Randbedingungen liefern die Kritikalitätsgleichung. Diese Gleichung ist genau und führt, wie dies in den Tabellen gezeigt wird zu schnell konvergierenden numerischen Ergebnissen.
References
1 Case, K. M.: Ann. Phys.9 (1960) 1.10.1016/0003-4916(60)90060-9Suche in Google Scholar
2 Case, K. M.; Zweifel, P. F.: Linear Transport Theory, Addison-Wesley, 1967.Suche in Google Scholar
3 Mitsis, G. J.: Nucl. Sci. Eng.17 (1963) 55.Suche in Google Scholar
4 Davison, B.: Neutron Transport Theory, London: Oxford University Press, 1958.10.1063/1.3062414Suche in Google Scholar
5 Williams, N. M. R.: Mathematical Methods in Particle Transport Theory, London: Oxford University Press, 1971.Suche in Google Scholar
6 Bell, G. I.; Glasstone, S.: Nuclear Reactor Theory, New York: Von Nostrand Reinhold, 1972.Suche in Google Scholar
7 Siewert, C. E.; Williams, N. M. R.: J. Physics D.54 (1977) 94.Suche in Google Scholar
8 Siewert, C. E.; Benoist, P.: Nucl. Sci. Eng.69 (1979) 156.Suche in Google Scholar
9 Dahl, E. B.; Sjöstrand, N. G.: Nucl. Sci. Eng.69 (1979) 114.Suche in Google Scholar
10 Grandjean, P.; Siewert, C. E.: Nucl. Sci. Eng.69 (1979) 161.Suche in Google Scholar
11 Sjötrand, N. G.: Atomkernenergie31 (1978) 16.Suche in Google Scholar
12 Sjöstrand, N. G.: Ann. Nucl. Energy7 (1980) 435.10.1016/0306-4549(80)90133-4Suche in Google Scholar
13 Protopopescu, V.; Sjöstrand, N. G.: Progress Nucl. Energy7 (1981) 47.10.1016/0149-1970(81)90059-7Suche in Google Scholar
14 Mitsis, G J.: Transport Solution the Monoenergetic Critical Problems, thesis. ANL-6787, Argonne National Laboratory, 1983.Suche in Google Scholar
15 Sahni, D. C.; Sjöstrand, N. G.: Progress Nucl. Energy23 (1990) 241.10.1016/0149-1970(90)90004-OSuche in Google Scholar
16 Garis, N. S.: Nucl. Sci. Eng.107 (1991) 343.Suche in Google Scholar
17 Atalay, M. A.: Progress Nucl. Energy31 (1996) 229.10.1016/0149-1970(95)00094-1Suche in Google Scholar
18 Atalay, M. A.: Progress Nucl. Energy44 (2004) 153.10.1016/S0149-1970(04)90013-3Suche in Google Scholar
19 Yildiz, C.: Ann. Nucl. Energy25 (1998) 529.10.1016/S0306-4549(97)00114-XSuche in Google Scholar
20 Erdoğan, F.; Güleçyüz, M. Ç.; Kaşkaş, A.; Tezcan, C.: Ann. Nucl. Energy6 (1996) 533.10.1016/0306-4549(95)00053-4Suche in Google Scholar
21 Tezcan, C.; Kaşkaş, A.; Güleçyüz, M. Ç.: J. Quant. Spect. Radiat. Transf.62 (1999) 49.10.1016/S0022-4073(98)00040-5Suche in Google Scholar
22 Güleçyüz, M. Ç.; Kaşkaş, A.; Tezcan, C.: J. Quant. Spect. Radiat. Transf.61 (1999) 329.10.1016/S0022-4073(97)00241-0Suche in Google Scholar
23 Güleçyüz, M. Ç.; Kaşkaş, A.; Tezcan, C.: J. Quant. Spect. Radiat. Transf.70 (2001) 55.10.1016/S0022-4073(00)00119-9Suche in Google Scholar
24 Kaşkaş, A.; Güleçyüz, M. Ç.; Tezcan, C.: J. Quant. Spect. Radiat. Transf.66 (2000) 519.10.1016/S0022-4073(99)00180-6Suche in Google Scholar
25 Benoist, P.; Kavenoky, A.: Nucl. Sci. Eng.32 (1968) 225.Suche in Google Scholar
26 Kavenoky, A.: Nucl. Sci. Eng.65 (1978) 209.Suche in Google Scholar
27 Kavenoky, A.: Nucl. Sci. Eng.65 (1978) 514.Suche in Google Scholar
© 2005, Carl Hanser Verlag, München
Artikel in diesem Heft
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- Summaries/Kurzfassungen
- Summaries/Kurzfassungen
- Technical Contributions/Fachbeiträge
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- Phenomenological model for non-equilibrium deuteron emission in nucleon induced reactions
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- Simulation of the hydrogen distribution in the confinement of the Ignalina nuclear power plant
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- On the plane-wave theory in fertile uranium
- Safety and security of radioactive sources – international provisions
- The singular eigenfunction method: the critical slab problem for linearly anisotropic scattering
- Technical Notes/Technische Mitteilungen
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Artikel in diesem Heft
- Contents/Inhalt
- Contents
- Summaries/Kurzfassungen
- Summaries/Kurzfassungen
- Technical Contributions/Fachbeiträge
- Integrated management systems in the nuclear field
- Phenomenological model for non-equilibrium deuteron emission in nucleon induced reactions
- Best estimate analysis of group distribution header blockage events in RBMK-1500 reactors
- Simulation of the hydrogen distribution in the confinement of the Ignalina nuclear power plant
- Neutronic calculations for the new fuel configuration of the ETRR-1 research reactor
- Design stability and safety margins of the ETRR-2 core cooling system regarding seismic loads
- Thermal-hydraulic assessment of topaz irradiation processes at the ETRR-2 research reactor
- The HN method for slab albedo problem for linearly anisotropic scattering
- On the plane-wave theory in fertile uranium
- Safety and security of radioactive sources – international provisions
- The singular eigenfunction method: the critical slab problem for linearly anisotropic scattering
- Technical Notes/Technische Mitteilungen
- Results of in vitro intercomparison tests of the Coordinating Office on Incorporation Monitoring in Germany
