An analysis is made on the performance characteristics of a liquid-metal MHD induction converter with liquid-gas two-phase mixture as working fluid. The equivalent electrical conductivity and the velocity vary along the generator channel in this kind of induction converter.
Two important parameters which represent the variations of the equivalent electri-cal conductivity and the velocity respectively are defined. With these parameters the induction equation is analytically solved with the perturbation technique.
Quantities representing generator performance, such as power densities and gener-ator efficiency, are obtained from the perturbed magnetic field and the parameters mentioned above.
Suitable combination of values for these parameters will tend to let the effects brought by the variations of electrical conductivity and of velocity cancel each other, and the relation between these parameters is analytically derived that assures the non-perturbation of the magnetic field and of the gross output power density. In this condi-tion of non-perturbation, the generator efficiency approaches that for the unperturbed case when the velocity variation and the inlet slip ratio are small.

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Statistic formulation of the neutron counts registered in a gate triggered by the family-first-pulse-which corresponds to the accumulated data in the usual Rossi-α ex-periment-is extended to the second moment. The second factorial moment <c(c-1)> of neutron counts which are correlated with the trigger pulse is expressed as a function of the gate width and of the waiting time from the family-birth to the triggering ; and it is shown that the function cannot be divided to contain the two variables separately.
Neutron counts uncorrelated with the trigger pulse are analyzed into two components, and the second factorial cumulant <c(c-1)>-<c>² of that originating from the families born before the trigger is shown to manifest the same dependence on gate width as that of correlated counts, with an amplitude ratio identical with the first moments.
The uncorrelated counts of the second kind originating from the families newly born after the trigger present a somewhat different relation to the gate width, and hence constitute what are for practical purpose the only truly uncorrelated counts.
The second factorial cumulant of the all-inclusive (correlated as well as the two kinds of uncorrelated) counts in stationary neutron field is formulated. Considerations are also presented on the effect of differences in the detector efficiency on the expected number of correlated count pairs in one gate.

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Examining properties common to various analytical solutions obtained by many authors, a new method is proposed for solving the time-energy distribution of neutrons in an infinite homogeneous medium. The essence of this method is to express the solution in terms of an effective parameter ∑(t, u) which may always be approximated by a simple rational fraction of time. Coefficients in this rational fraction are deter-mined by using the time moments.
The present method gives a variety of practically correct closed-form solutions relevant to the set of moments used. Applications of the present method to several cases show that a practically correct solution can be obtained with use made of only the first several time moments.

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A new four-factor formula is proposed for deriving a " finite multiplication factor " k*-he ratio between neutron production and absorption rates in a finite medium-from experimentally determined lattice parameters in a slightly-enriched Pu-U lattice.
The "two-group multiplication factor" k*_∞2-related to τ+L² and equal to (1 +τB²_C) (1+L²B²_C) at criticality-is derived from k*.
The experimental lattice parameters are corrected to account for neutron leakage, from which the " infinite multiplication factor " k_∞ is derived.
There are found differences between k*, k*_∞2 and k_∞ amounting to about 1-2% in the Advanced Thermal Reactor (ATR)-type heavy-water lattice, despite the fact that all these three quantities are often indiscriminately called " infinite multiplication factor."
The proposed four-factor formula for deriving k* was applied to the Deuterium Criti-cal Assembly (DCA) of 1.2%-enriched UO₂ lattices of 28-pin clusters in square arrays spaced at 22.5 cm. The values of k* calculated with a lattice design code METHUSELAH II were in fairly good agreement with those determined by experiment. The calculation tended to somewhat overestimate k*, particularly in lattices of highly voided coolant. A similar tendency was observed in the case of 1.5%-enriched UO₂ lattices of 22.5 cm pitch in the ATR Sumitomo-Two-Region Critical Facility.

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A numerical method is proposed for analyzing the transient state of a three-com-ponent cascade. The method is applied to an examination of the behavior of minor isotopes of uranium in an enrichment plant.
It is shown that the transient behavior of ²³⁴U in cascade differs significantly from that of ²³⁵U. It is indicated that in order to apply MIST (" Minor Isotope Data as a Safeguards Technique " proposed by Blumkin et al.) effectively, it would be necessary to examine the behavior of the isotopic ratio (²³⁵U/²³⁴U ) at various transient states as well as at steady state.
The concentration of ²³⁶U does not necessarily distribute monotonically from the top toward the bottom of the cascade for the production of highly enriched uranium. It is shown how the characteristic distribution of ²³⁶U establishes itself gradually with lapse of time.

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