摘要:

Lie series are power series solutions of differential equations, whose expansion coefficients can be derived from algebraic recursion relations. The method of deriving these relations is illustrated by solving three problems: 1) multigroup diffusion theory; 2) multigroupPNtheory in cylindrical geometry; and 3) spaceindependent xenon dynamics. It is shown that the Lie series formalism leads to considerable simplification in the analytical treatment of complex problems.

ISSN:0029-5639    

DOI:10.13182/NSE67-A17465

出版商:Taylor&Francis    

年代:1967

数据来源: Taylor

摘要:

The notions of canonical and involutory transformations from the calculus of variations are applied to neutron transport problems. It is shown that the variational formulations of Vladimirov, Selengut, Pomraning and Clark, and Davis are related through transformations of this type. It is pointed out that the pair of functionals indentified through the involutory transformation are reciprocal in the sense that the minimum of one is the maximum of the other. Implications of this fact for the development of approximation methods are discussed.

ISSN:0029-5639    

DOI:10.13182/NSE67-A17466

出版商:Taylor&Francis    

年代:1967

数据来源: Taylor

摘要:

The invariant imbedding theory for the monoenergetic neutron transport equation in slab geometry is determined in terms of reflection, transmission, and escape functions. The application of this theory to escape probabilities, blackness coefficients, and critical size determinations is shown along with representative numerical evaluations. The high accuracy of the calculations and the fact that the angular dependence is always obtainable make the invariant imbedding method a reasonable approach to many problems.

ISSN:0029-5639    

DOI:10.13182/NSE67-A17467

出版商:Taylor&Francis    

年代:1967

数据来源: Taylor

摘要:

An exact solution to the monoenergetic Boltzmann equation is obtained for the case of a plane isotropic burst of neutrons introduced at the interface separating two adjacent, dissimilar, semi-infinite media. The method of solution used is to remove the time dependence by a Laplace transformation, solve the transformed equation by the normal mode expansion method, and then invert to recover the time dependence. The general result is expressed mainly as a sum of definite, multiple integrals. Certain simplifications were possible at the interface and these are explicitly noted.

ISSN:0029-5639    

DOI:10.13182/NSE67-A17468

出版商:Taylor&Francis    

年代:1967

数据来源: Taylor

摘要:

Using an exact transport solution, numerical calculations of interface flux and current are made for a plane burst of neutrons introduced at the boundary separating two semi-infinite media. Asymptotic flux expressions for large time at the interface are also presented, and these have the exponential dependence given by diffusion theory. Following the neutron burst, the interface current is found to change directions once, at most. The magnitude of the interface current is shown to depend initially on the difference in scattering cross sections of the half-spaces and asymptotically on the difference in absorption cross sections. In the special case of identical half-spaces, diffusion theory yields a more accurate representation of the flux than doesP1theory, although for long times both approximate solutions rapidly approach the exact result.

ISSN:0029-5639    

DOI:10.13182/NSE67-A17469

出版商:Taylor&Francis    

年代:1967

数据来源: Taylor

摘要:

An analytical approach to the solution of the neutron slowing down problem with anisotropic scattering is presented. The basic ideas are the representation of the transport equation by a set of infinitely many first-order linear partial differential equations, the application of the“central limit theorem,”and integral transform techniques. The distribution of then-times scattered neutrons is given as a superposition of space- and angle-dependent functions with coefficients depending on the energy. In the isotropic case, these coefficients are directly related to the Placzek slowing down distributions.

ISSN:0029-5639    

DOI:10.13182/NSE67-A17470

出版商:Taylor&Francis    

年代:1967

数据来源: Taylor

摘要:

A new method of calculation is presented for directional probabilities of interaction in pin clusters and rod lattices. The theory, in principle rigorous from a geometrical point of view, has been programmed for the IBM-7090 as the computer code PROCOPE. Calculation results for Dancoff correction factors and collision probabilities are compared with values obtained with other methods. The validity of the technique is also checked by evaluating the fine structure of the thermal flux distributions in various gas-cooled clusters upon which measurements have been made at Saclay. As a practical illustration, a series of curves describes the behavior of the various independent fuel-to-fuel collision probabilities in 19−(or 7−) pin gas-cooled clusters. Finally, approximate formulas are given for the pin-to-pin collision probability at both the white and the black limits.

ISSN:0029-5639    

DOI:10.13182/NSE67-A17471

出版商:Taylor&Francis    

年代:1967

数据来源: Taylor

摘要:

Nonlinear stability criteria for reactors (Welton, Popov, etc.) can only be used when the reactor is linearly stable at all equilibrium power levels. This paper contains four methods of analysis of nonlinear stability that can be used when the reactors are unstable above a certain equilibrium power. The topological method and the second Liapunov method are often of no practical interest, while the Aizermann and Rosen methods are applicable irrespective of the complexity of the system. The different methods are compared in the case of a reactor with a prompt-positive temperature coefficient and a slow-negative temperature coefficient.

ISSN:0029-5639    

DOI:10.13182/NSE67-A17472

出版商:Taylor&Francis    

年代:1967

数据来源: Taylor

摘要:

On the basis of Kolmogorov's general theory of chain processes, a formula for a conditional count probability as measured by a certain type of time analyzer is derived and compared with the classical Rossi-αformula. The discrepancy between the Rossi-αformula and the experimental results reported by several authors is explained. It is shown that this discrepancy is due to the frequently misunderstood function of the time analyzer used. The mathematical technique employed in the paper is well suited for calculating the conditional count probabilities, which might possibly be measured by other types of time analyzers.

ISSN:0029-5639    

DOI:10.13182/NSE67-A17473

出版商:Taylor&Francis    

年代:1967

数据来源: Taylor

摘要:

Formulas for interval distributions of neutron counts, which open possibilities for new methods of reactor noise measurements, are derived. The proposed experimental techniques promise to be less time consuming than the zero probability method of Mogilner and Zolotukhin. The useful information contained in a sequence of counts lies in its deviation from Poisson statistics. The magnitude of this deviation depends either on the counter efficiency or on the intensity of the external neutron source. From this point of view, the techniques of noise measurements can be divided into two groups: the“efficiency sensitive”methods (Feynman) and the“power sensitive”methods (Rossi-α). The proposed count-to-count interval distribution measurement seems to combine the advantages of both groups.

ISSN:0029-5639    

DOI:10.13182/NSE67-A17474

出版商:Taylor&Francis    

年代:1967

数据来源: Taylor