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Density fluctuations in a moderately dilute g'as of hard spheres are analyzed using a kinetic equation which is the generalization of the linearized Boltzmann equation to arbitrary frequencies and wave numbers.The phase-space memory function derived recently by Mazenko is evaluated for the hard-sphere interaction, and the result is shown to be explicitly frequency independent.In the case of the self-correlation function, the memory function is found to be identical to the collision operator in the appropriate Boltzmann equation, thus implying that in this special case the Boltzmann-equation description is valid at all frequencies and wavelengths.Wave-number-dependent matrix elements of the memory functions are calculated using the Hermite function as a basis, and a number of interesting features are observed. The matrix elements are utilized in a kinetic-model formulation of the initial-value problem of evaluating the spectral densities of thermal fluctuations. Numerically converged results are presented and compared with previous Boltzmann-equation calculations. While the qualitative behavior of the spectral distribution still can be characterized by the ratio of wavelength to collision mean free path, details of the line shape now depend on density and wave number. At reasonable density and wave-number values, a narrowing effect is observed.This effect, which is most pronounced at small and moderate wavelength-to-mean-freepath ratios, is sufficiently significant that further investigation is warranted.

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A Texas Nuclear Cockcroft–Walton neutron generator was refurbished for use as a general fusion-product source. This well-calibrated source is now used routinely for characterizing energetic charged-particle detectors, for the development of nuclear fusion diagnostics, for studying radiation damage, and for calibrating x-ray detectors for laboratory and space plasmas. This paper is an overview of the facility. We describe the main accelerator operating systems, the primary fusion reactions studied, and several diagnostics used to characterize the fusion-product source.