Accuracy of one-dimensional collision integral in the rigid-sphere approximation

Abstract

Solution of many problems of gas kinetics, transport phenomena, and spectroscopy can be significantly simplified using the linearized Boltzmann equation within so called one-dimensional approximation, in which the collision kernel is averaged over the transverse velocities. The error introduced by this approximation is usually considered to be small, however, no quantitative analysis of its value has been done so far. We study the accuracy of the one-dimensional approximation in a particular problem of calculating spectral line shapes in gases. The inaccuracy is shown to be small in the wings of line, in the cases of light buffer molecules or low collision frequency. For arbitrary parameters the error is calculated numerically within the rigid-sphere model. These results outline the area of applicability of computationally economic one-dimensional approach.