UNApproximation for the Eigenvalue Spectrum of Time-Dependent, One-Speed and One-Dimensional Neutron Transport Problem with Anisotropic Scattering

Abstract

The eigenvalue spectrum is studied in one-speed time-dependent neutron transport theory in a uniform finite slab. The linear anisotropic scattering kernel together with the combination of forward and backward scattering is used and time-dependent neutron transport equation is reduced to a stationary one. Numerical results of eigenvalues for various combinations of the scattering parameters and the selected values of the time decay constant are performed by using the Chebyshev polynomials approximation method.

Keywords

• Neutron transport equation,anisotropic scattering,eigenvalues,UN approximation

Zamana Bağlı, Tek-Hızlı ve Tek-Boyutlu Anizotropik Saçılmalı Nötron Transport Probleminin Özdeğer Spektrumu için UNYaklaşımı

Abstract

Düzgün sonlu bir dilimde tek-hızlı zamana bağlı nötron transport teorisinde özdeğer spektrumu çalışılmıştır. İleri ve geri saçılmayla birlikte lineer anizotropik saçılma foknsiyonu kullanılmış ve zamana bağlı nötron transport denklemi kararlı denkleme indirgenmiştir. Nümerik özdeğerler, Chebyshev polinomları yaklaşımı yöntemi kullanılarak, zaman bozunum sabitinin seçilmiş bazı değerleri ve saçılma parametrelerinin farklı değerleri için hesaplanmıştır.

Keywords

• Nötron transport denklemi,anizotropik saçılma,özdeğerler,UNyaklaşımı

References

1. Sahni D.C., Sjöstrand N.G., Garis N.S., 1992. Criticality and time eigenvalues for one-speed neutrons in a slab with forward and backward scattering, Journal of Physics D: Applied Physics,25: 1381-1389.
2. Yildiz C., 1999. Influence of anisotropic scattering on the size of time-dependent systems in monoenergetic neutron transport, Journal of Physics D: Applied Physics, 32: 317-325.
3. Öztürk H., 2008.Study of the effect of anisotropic scattering on the critical slab problem in neutron transport theory using Chebyshev polynomials, Kerntechnik, 73: 284-287.
4. Bell G.I., Glasstone S., 1972. Nuclear reactor theory, VNR Company, New York, p. 611.
5. Sahni D.C., Sjöstrand N.G., 1990. Criticality and time eigenvalues for one-speed neutron transport, Progress in Nuclear Energy, 23: 241–289.
6. Carlvik I., 1968. Monoenergetic critical parameters and decay constants for small homogeneous spheres and thin homogeneous slabs, Nuclear Science and Engineering, 31: 295-303.