[en] A global conservation equation is derived for the one-velocity Psub(N) approximation for the critical slab with isotropic scattering. Its relationship to various sets of boundary conditions in the P₃ approximation (e.g. Marshak or Pomraning-Federighi) is examined, and its implications for the infinite slab (Milne problem) are discussed. (author)

[en] Standard P_N theory is well developed as an approximation to the neutron transport equation. However, this theory contains no physics in the sense that it simply represents the angular flux as a sum of polynomials in angle. Thus, standard P_N theory (with N finite) cannot qualitatively predict correct asymptotic transport behavior except in the limit of pure scattering. In this paper, the authors modify standard P_N theory by incorporating certain transport physics, namely, the Case discrete modes, into a modified P_N expansion of the angular flux. The theory resulting from using this modified P_N-like expansion predicts the exact transport asymptotic growth/decay length, since it contains the discrete Case eigenvalue. Such modified P₃-like equations and associated boundary conditions are derived in planar geometry according to a recently introduced variational calculus. Analyses and numerical calculations reveal that this modified P₃-like theory possesses the following features: (a) It reduces to standard P₃ theory in the limit of pure scattering; (b) it conserves neutrons but exhibits a scalar flux discontinuity at a material interface; (c) it is shown numerically to be exceedingly accurate, much more accurate than standard P₃ theory, in predicting various transport theory behavior for homogeneous problems; and (c) for heterogeneous problems, it is necessary that each material region in the system be sufficiently large for this theory to predict better results than standard P₃ theory

[en] The usual Marshak and Pomraning-Federighi (importance-weighted) free-surface boundary conditions for a critical slab are modified. For the infinite slab, neutron conservation and the exact extrapolation distance are imposed. A minimization criterion is used to complete the required set of equations. These boundary conditions are compared with the usual ones on the P₃ and P₅ approximations with respect to critical size and conservation for finite slabs. (author)

No abstract available

[en] In the present paper, a method is reviewed by which the energy-dependent diffusion theory can be extended to the P₂ and P₃ approximations (higher order, generalized Onsanger equations). The diffusion and other transport coefficientS are found in the same approximation. Applications are presented for representative cases. (author)

No abstract available

[en] One-velocity angular flux of a neutron field generated by a polarly anisotropic point source in an infinite homogeneous region is calculated in P3 approximation, using the spherical harmonics operator formalism adapted to two-dimensional spherical geometry. The problem is reduced to simple algebraic equations. For weak absorption and linearly anisotropic scattering, the solution is given in closed form. (orig.)

[en] Inside the reactor core mechanical vibrations of fuel assemblies can produce high fluctuations around a steady-state configuration, known as neutron noise. This effect can cause the triggering of power reduction measures. Classically, diffusion theory has been used to simulate this behavior. However, this equation has some limitations if the materials of the reactor have strong variations. In this work, we use the diffusive time-dependent simplified spherical harmonics equations that improve the previous results without the necessity of using high computational requirements. In particular, two types of analyses with these equations (SP₃) are made: a frequency-domain and a time-domain. A numerical neutron noise benchmark tests the methodology and compare both formulations. First, numerical results show a good agreement between the amplitudes and phases of the SP3 equations computed with the frequency-domain and time-domain. Therefore, as the frequency-domain computation only requires to solve a linear system, it is a recommendable option for neutron noise computations. Second, one can conclude that for this type of nuclear systems, where the assemblies are not homogenized, the SP₃ approximation results improve considerably the accuracy of the diffusion theory

[en] Full text: This paper deals with the flux distribution in case of void in the reactor cell with natural uranium fuel rods (r_u = 1.29 cm), reactor channel (r₁ = 3.5 cm) and graphite moderator (r_m = 8.9 cm). The void is replaced by equivalent material having only neutron absorption cross section. A homogeneous neutron source is placed in this region. The source is defined to have the number of neutron from the source is equal to the number of absorbed neutrons per unit volume. The atoms of this equivalent medium do not change the direction or energy of neutrons. One-group P₃ approximation of spherical harmonics method was used. Equivalent region was divided into 5 subregions with equal absorption of 0.1 cm^-1. A few iterations were done in each subregion to minimize the error in achieving the equality of the number of created and absorbed neutrons per unit volume

[en] The parameters for a three-pole approximation, both for the plasma dispersion function and its derivative are calculated. It is argued that the existing two pole approximation is not adequate to approximate the dispersion of electron plasma waves. (author)