Neutron wave propagation problems, espetially the Milne and the albedo problems, are investi-gated by making use of the Wiener-Hopf technique for treating the Boltzmann equation with an isotropic one-term degenerate kernel in a semi-infinite prism.
A pole of the solution of the integral-transformed Boltzmann equation corresponds to an eigenvalue - or physically, to a complex wave number varying on the two-dimensional complex plane with transverse buckling and wave oscillation frequency.
In the Milne problem, the solution ceases to exist when the imaginary part of the complex wave number exceeds Σ_min. In the albedo problem, however, the solution always exists irrespectively of the oscillation frequency ω, and the discrete eigenvalue presents a continuous spectrum as soon as ω exceeds a critical frequency ω_c. Detailed forms of solutions are derived for the case of constant velocity, and complex eigenvalues are evaluated numerically.

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A UCLA reactor fuel element was subjected to forced vibration tests to determine if vibra-tion-induced changes in the moderator-coolant channel width could cause reactor power fluctuations during an earthquake. The response of the fuel element was monitored by foil-strain gages while the element was vibrated in water. At the natural frequency of the fuel element (11.1) cps, an average coolant channel width increase of 0.0009 in. was observed. We estimate that fuel vibrations with this amplitude could cause a maximum power change of 2.8 % in the UCLA reactor.
Several interesting conclusions can be drawn from this work. First, based on our "worst case" analysis it appears that earthquake-induced power oscillations do not pose a reactor safety problem. Careful design (especially to increase rigidity) of fuel elements for power reactors could make the problem of vibration-induced power transients negligible. Second, using the techniques described in the report, it is possible to perform out-of-core experiments on reactor fuel elements that accurately predict the in-core dynamic response. The technique may be useful in determining the dynamic response of fuel elements under conditions where direct measurements are difficult; i.e., pressurized water reactors or liquid metal-cooled reactors.

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The Hitachi Training Reactor (HTR) provided with pulse operation capability was utilized for an experimental study on the excursion characteristics of light water reactors. Measurements were performed on reactor power, reactor period, released energy, fuel temperature, fuel cladding strain, pressure in water channel and water activities. The reliability of the instruments and devices employed was confirmed to be satisfactory through pulse operation tests repeated 300 times, with inserted reactivities up to 1.50 $, with reactor periods down to 15 msec, and hot spot fuel temperatures up to 1, 300°C. A description is also given of the instrumentation for the measure-ments and reactor operation.

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This paper describes a very simple formulation of the reactor kinetic equation for arbitrary reactivity variations which can be solved analytically. The method of matched asymptotic expan-sions, which is a generalization of methods used in boundary-layer analysis, is employed to estimate the neutron density and the reactor period for ramp and periodic inputs. The small amounts of error arising in individual cases are analyzed quantitatively by comparison with results obtained from difference approximation (Runge-Kutta-Merson method). The validity of the zero-prompt-lifetime approximation and the stability condition for periodic inputs are also discussed. It is confirmed that the results obtained by the present method are numerically in complete agreement with those by other methods, provided the magnitudes of bias reactivity |ρ₀|, reactivity amplitude |ρ₁| and ramp reactivity |γ_t| are all very small compared with β, that the angular frequency ω<<β/l*, and that, in particular, l*<<10^-3.

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The effect of porosity on the thermal conductivity of sintered ThO₂ of densities ranging from 90 to 95 % of theoretical density was investigated at 20°C. The thermal conductivity was determined by means of laser pulse. Discrepancies were observed between the experimental results and the relation derived by Loeb. This discrepancy was explained by applying a modified Maxwell formula derived by Brailsford et al.
The samples were also examined metallographically. It is concluded that the existence of fluid continuous regions contribute significantly to the thermal resistance of such materials as ThO₂.

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