Real criticality eigenvalues of the one-speed-linear transport operator

Journal Article · Wed Nov 01 04:00:00 EST 1995 · Transport Theory and Statistical Physics

DOI:https://doi.org/10.1080/00411459508206025· OSTI ID:274290

Sahni, D C ^[1]; Dahl, E B; Sjoestrand, N G ^[2]

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1. Bhabha Atomic Research Centre, Bombay (India)
2. Chalmers Univ. of Technology, Goeteborg (Sweden)

The criticality eigenvalue problem has been studied for the one-speed neutron transport equation. Convex bodies of arbitrary shape and with vacuum boundary conditions have been considered. The cross sections may be space dependent, and the scattering is assumed to be anisotropic. Several new conditions have been derived which ensure that a point spectrum of eigenvalues exists and that all th eigenvalues are real. The most general such condition is that the even order coefficients in the development of the scattering function have a different sign than the odd order ones. As a consequence, for linearly anisotropic scattering the eignevalues are all real if the average cosine of the scattering angle is negative. Numerical results computed for homogeneous bodies in the form of spheres and infinite slabs and cylinders confirm the theoretical considerations. 14 refs., 1 fig., 3 tabs.

• Sponsoring Organization: USDOE
• OSTI ID: 274290
• Journal Information: Transport Theory and Statistical Physics, Journal Name: Transport Theory and Statistical Physics Journal Issue: 9 Vol. 24; ISSN TTSPB4; ISSN 0041-1450
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
EIGENVALUES
NEUTRON TRANSPORT THEORY
PERTURBATION THEORY
REACTOR PHYSICS