摘要:

AbstractThe purpose of this paper is to present the mechanics of the derivation of Avery’s coupled reactor kinetics equations, which have been given by his physical consideration. Firstly, the diffusion equation and its adjoint equation are expressed in the matrix form. Then the partial flux and the partial adjoint flux are defined explicitly. The neutron flux, introduced by Henry, is represented as an amplitudeT(t) times a shape functionψ(r, t). The adiabatic approximation is adopted in the neutron-flux shape function. Using the commutation law (given in the Appendix) between the diffusion operator and its adjoint operator, Avery’s equations are derived from the time-dependent diffusion equations for the partial adjoint flux. The assumptions introduced are; (a) the delayed-neutron fission spectrum is the same as the prompt-neutron fission spectrum, (b) the neutron-flux shape function is approximated by the adiabatic method, (c) the time constant of the amplitudeT(t) is much smaller than the minimum time constant of the shape functionψ(r, t) at that instant. As the result of these assumptions, the delay time associated with the transfer of neutron does not appear explicitly in Avery’s equations.

ISSN:0029-5639    

DOI:10.13182/NSE69-A21154

出版商:Taylor&Francis    

年代:1969

数据来源: Taylor

摘要:

AbstractA two energy group model is proposed in this paper for studying the criticality of a slab of finite thickness in the framework of neutron transport theory. The system of the two stationary Boltzmann equations which, in the case of isotropic scattering, govern the flux distributions of the two neutron groups, is first solved by a Fourier transform technique. Explicit series expressions are then derived for the angular as well as for the total flux distributions in the interior and at the boundary of the critical slab. These series expressions are shown by numerical calculations to be rapidly convergent to the required solutions of the problem under examination. Results for the critical parameter and for the total and angular flux distributions are at last reported.

ISSN:0029-5639    

DOI:10.13182/NSE69-A21155

出版商:Taylor&Francis    

年代:1969

数据来源: Taylor

摘要:

AbstractThe crosscorrelation method of determining the impulse response of a dynamic system, which has been widely used in experiments, is applied numerically to a complicated mathematical model of a spatially dependent reactor system, and is concluded to be a practical alternative to analog computer analysis.The method is applied using two families of periodic discrete level signals as the input perturbation. It is demonstrated that a relatively new class of signals, having three possible levels, which has had very limited use to date, leads to a more accurate determination of the impulse response in the presence of strong system nonlinearities than do the better known and more widely used binary signals.

ISSN:0029-5639    

DOI:10.13182/NSE69-A21156

出版商:Taylor&Francis    

年代:1969

数据来源: Taylor

摘要:

AbstractThe problem of optimally controlling xenon spatial oscillations is formulated as a problem in the calculus of variations for distributed parameter systems. The resulting partial differential equations (space- and time-dependent) are then approximated by a nodal representation to obtain a set of ordinary differential equations (time-dependent) with mixed (initial and final) boundary conditions. An iterative solution scheme, which utilizes a quasilinearization of the equations and a transformation matrix relating initial to final values of certain variables, is employed to obtain numerical results. Feasibility of the method is established by several sample calculations. A physical interpretation is given the Lagrange multiplier functions which initially are introduced for mathematical considerations.

ISSN:0029-5639    

DOI:10.13182/NSE69-A21157

出版商:Taylor&Francis    

年代:1969

数据来源: Taylor

摘要:

AbstractThe purpose of this paper is twofold. The first is to provide a fast and accurate method of approximating theJ(θ,β) function for a single resonance. The second objective is to provide a rapid method of averaging unresolved levels by use of this approximateJfunction and a recently developed quadrature scheme of the Gaussian type. These approximations are well suited for use in day-to-day reactor design and evaluation and are substantially faster and more accurate than other approximations currently available in the literature. The approximateJfunction has been tested on that portion of theθ,βplane for whichβ≥5.0×10−5andθ≥5.0×10−4. This portion of the plane encompasses almost every conceivable practical situation. On this domain, typical relative errors incurred inJ(θ,β) are 0.25% or less and the maximum relative error for any (θ,β) pair is 2.2% which is encountered at an extreme value ofβ= 5.0×10−5.The technique forJ-function averaging produces relative errors<0.10% for cases of practical interest.

ISSN:0029-5639    

DOI:10.13182/NSE69-A21158

出版商:Taylor&Francis    

年代:1969

数据来源: Taylor

摘要:

AbstractThe utility of reflection and transmission function (or collectively, response function) concepts in reactor physics is investigated. A review of previous work is given, indicating the relation between the differential (invariant imbedding) and functional (adding) equations for the response functions. In addition, a numerical halving technique is developed from the adding relations. By combining the invariant imbedding and functional equations, an efficient calculational technique for albedo, shielding, and criticality problems in slab geometry is obtained. The feasibility of performing response function experiments to obtain cross section and criticality information is also examined. The envisioned experimental setup is described and calculations are carried out to verify the numerical procedures.

ISSN:0029-5639    

DOI:10.13182/NSE69-A21159

出版商:Taylor&Francis    

年代:1969

数据来源: Taylor

摘要:

AbstractCalculations have been carried out to determine the time dependence of the residual-photon dose rate inside an accelerator tunnel due to a 3-GeV proton beam located on the axis of an iron cylinder. The photon dose rate produced by the activation of the concrete tunnel wall is calculated and combined with the results from a previous calculation for the dose rate contributed by the iron to obtain the total photon dose rate inside the tunnel. The effectiveness of lowering the total photon dose rate by reducing the24Na production in the concrete is evaluated. The development of the nucleon-meson cascade, the residual nuclei production, and the photon transport are calculated using Monte Carlo methods.

ISSN:0029-5639    

DOI:10.13182/NSE69-A21160

出版商:Taylor&Francis    

年代:1969

数据来源: Taylor

ISSN:0029-5639    

DOI:10.13182/NSE69-A21161

出版商:Taylor&Francis    

年代:1969

数据来源: Taylor

ISSN:0029-5639    

DOI:10.13182/NSE69-A21162

出版商:Taylor&Francis    

年代:1969

数据来源: Taylor

ISSN:0029-5639    

DOI:10.13182/NSE69-A21163

出版商:Taylor&Francis    

年代:1969

数据来源: Taylor