The Green`s function method for critical heterogeneous slabs

Conference · Tue Oct 01 04:00:00 EDT 1996

OSTI ID:385562

Kornreich, D E

Recently, the Green`s Function Method (GFM) has been employed to obtain benchmark-quality results for nuclear engineering and radiative transfer calculations. This was possible because of fast and accurate calculations of the Green`s function and the associated Fourier and Laplace transform inversions. Calculations have been provided in one-dimensional slab geometries for both homogeneous and heterogeneous media. A heterogeneous medium is analyzed as a series of homogeneous slabs, and Placzek`s lemma is used to extend each slab to infinity. This allows use of the infinite medium Green`s function (the anisotropic plane source in an infinite homogeneous medium) in the solution. To this point, a drawback of the GFM has been the limitation to media with c < 1, where c is the number of secondary particles produced in a collision. Clearly, no physical steady-state solution exists for an infinite medium that contains an infinite source and is described by c >1; however, mathematical solutions exist which result in oscillating Green`s functions. Such calculations are briefly discussing. The limitation to media with c < 1 has been relaxed so that the Green`s function may also be calculated for media with c {ge} 1. Thus, materials that contain fissionable isotopes may be modeled.

• Research Organization: Los Alamos National Lab., NM (United States)
• Sponsoring Organization: USDOE, Washington, DC (United States)
• DOE Contract Number: W-7405-ENG-36
• OSTI ID: 385562
• Report Number(s): LA-UR--96-1953; CONF-961103--15; ON: DE96014037
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
BENCHMARKS
DISPERSION RELATIONS
GREEN FUNCTION
LAPLACE TRANSFORMATION
NEUTRON TRANSPORT THEORY
SLABS