The albedo problem for pure-triplet scattering
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R. G. Türeci
Abstract
The singular eigenfunction approach using CN equations can be extended for high order anisotropic scattering (triplet scattering) to the Albedo problem. Case's eigenfunctions and the orthogonality relations of this scattering can be derived mathematically. Thereby, the infinite medium Green function can be written for an homogeneous medium in terms of singular eigenfunctions. Also using the HN method, the constant source albedo problem can be investigated for this type of scattering.
Kurzfassung
Die Methode singulärer Eigenfunktionen unter Verwendung von CN Gleichungen kann für anisotrope Streuung höherer Ordnung (Triplet-Streuung) auf das Albedoproblem angewendet werden. Die Case-Eigenfunktionen und die entsprechenden Orthogonalitätsrelationen können mathematisch abgeleitet werden. Dabei kann die Greenfunktion für unendliche Medien beschrieben werden für ein homogenes Medium in Form singulärer Eigenfunktionen der Methode elementarer Lösungen. Auch mit Hilfe der HN Methode kann das Albedoproblem einer konstanten Quelle für diese Art der Streuung untersucht werden.
References
1 Mika, J.: Neutron Transport with Anisotropic Scattering. Nuclear Science and Engineering11 (1961) 415Suche in Google Scholar
2 Case, K. M.; Zweifel, P. E.: Linear Transport Theory. Addition-Wesley Publishing Co., Massachusetts, USA, 1967Suche in Google Scholar
3 McCormick, N. J.; Kušcer, I.: Singular Eigenfunction Expansions in Neutron Transport Theory. Advances in Nuclear Science and Technology7 (1973) 181Suche in Google Scholar
4 Tezcan, C.; Güleçyüz, M. Ç.; Erdogan, E.: A new approach of solving the third form of the transport equation in plane geometry: Half-space albedo-problem. JQSRT55 (1996) 251Suche in Google Scholar
5 Tezcan, C.; Kaskas, A.; Güleçyüz, M. Ç.: The singular eigenfunctions method: The Milne problem for isotropic and extremely anisotropic scattering. JQSRT62 (1999) 49Suche in Google Scholar
6 Kaskas, A.; Güleçyüz, M. C.; Tezcan, C.: The slab albedo problem using singular eigenfunctions and the third form of the transport equation. Ann Nucl Energy23 (1996) 1371Suche in Google Scholar
7 Kaskas, A.; Tezcan, C.; Güleçyüz, M. Ç.: The solution of the third form transport equation using singular eigenfunctions: The slab and the sphere criticality problems. JQSRT66 (2000) 519Suche in Google Scholar
8 Güleçyüz, M. C.; Kaskas, A.; Tezcan, C.: Slab albedo problem for anisotropic scattering using singualr eigenfunction solution of the C-N equations. JQSRT61 (1999) 329Suche in Google Scholar
9 Güleçyüz, M. Ç.; Kaskas, A.; Tezcan, C.: The singular eigenfunction analysis of the third form transport equation using half-range orthogonality relations: The Half-Space Problems. JQSRT70 (2001) 55Suche in Google Scholar
10 Tiireci, R. G.; Güleçyüz, M. C.; Kaskas, A.; Tezcan, C.: The singular eigenfunction method: the critical slab problem for linearly anisotropic scattering. KERNTECHNIK70 (2005) 322Suche in Google Scholar
11 Kavenoky, A.: The CN Method of Solving the Transport Equation: Application to Plane Geometry. Nuclear Science and Engineering65 (1978) 209Suche in Google Scholar
12 Kavenoky, A.: Nuclear Science and Engineering. 65 (1978) 51410.13182/NSE78-A27182Suche in Google Scholar
13 Kaskas, A.; Tezcan, C.: The FN method for anisotorpic scattering in neutron transport theory: Half Space problems. JQSRT55 (1996) 41Suche in Google Scholar
14 Grandjean, P.; Siewert, C. E.: The Fn method in neutron transport theory Part II: applications and numerical results. Nuclear Science and Engineering. 69 (1979) 161Suche in Google Scholar
15 Tezcan, C.; Güleçyüz, M. Ç.; Tiireci, R. G.; Kaskas, A.: The HNmethod for half-space albedo and constant source problem for isotropic and anisotropic scattering kernels. JQSRT103 (2007) 611Suche in Google Scholar
16 Tezcan, C.; Kaskas, A.; Güleçyüz, M. Ç.: The Hn method for solving linear transport equation: theory and applications. JQSRT78 (2003) 243Suche in Google Scholar
17 Tureci, R. G.; Tureci, D.: Time dependent albedo problem for quadratic anisotropic scattering. KERNTECHNIK72 (1–2) (2007) 59–65Suche in Google Scholar
© 2007, Carl Hanser Verlag, München
Artikel in diesem Heft
- Contents/Inhalt
- Contents
- Summaries/Kurzfassungen
- Summaries
- Technical Contributions/Fachbeiträge
- Effect of fuel particles' size and position variations on multiplication factor in pebble-bed nuclear reactors
- Axial flux harmonics affecting the parallel channel instabilities in boiling water reactors
- Uncontrolled withdrawal of a control rod without SCRAM
- Modelling of Carbon-14, Iodine-129 and Cesium-137 releases from near surface radioactive waste disposal and their impact on environment and humans
- Investigation of nuclear model predictions for proton induced reaction cross-sections up to 150 MeV
- The extension of the 2-D finite element/boundary element hybrid method to general multigroup neutron diffusion theory
- Extension of the HN method for solving radiation transfer problems in plane geometry for general anisotropic scattering
- The albedo problem for pure-triplet scattering
- Studies on the transmission and processing of pulse-shaped signals from nuclear radiation detectors using methods of systems theory
- The preignition problem in nuclear explosive devices (NEDs) for a sigmoidal Rossi-α and a high neutron background
- Comparison of economy and emissions of nuclear power plants and combined gas and wind electricity generators
Artikel in diesem Heft
- Contents/Inhalt
- Contents
- Summaries/Kurzfassungen
- Summaries
- Technical Contributions/Fachbeiträge
- Effect of fuel particles' size and position variations on multiplication factor in pebble-bed nuclear reactors
- Axial flux harmonics affecting the parallel channel instabilities in boiling water reactors
- Uncontrolled withdrawal of a control rod without SCRAM
- Modelling of Carbon-14, Iodine-129 and Cesium-137 releases from near surface radioactive waste disposal and their impact on environment and humans
- Investigation of nuclear model predictions for proton induced reaction cross-sections up to 150 MeV
- The extension of the 2-D finite element/boundary element hybrid method to general multigroup neutron diffusion theory
- Extension of the HN method for solving radiation transfer problems in plane geometry for general anisotropic scattering
- The albedo problem for pure-triplet scattering
- Studies on the transmission and processing of pulse-shaped signals from nuclear radiation detectors using methods of systems theory
- The preignition problem in nuclear explosive devices (NEDs) for a sigmoidal Rossi-α and a high neutron background
- Comparison of economy and emissions of nuclear power plants and combined gas and wind electricity generators
