Molecular-Beam Time-of-Flight Spectroscopy

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Abstract
A method for determining the speed distribution and density of a molecular beam from time‐domain measurements of propagated beam perturbations is examined. Algebraic relations between the moments of the measured time‐of‐flight signal, of the speed‐distribution function, of the modulator gate function, and of the dynamic function of the detector and its electronics are derived. By extracting a sufficient number of moments, one can characterize any speed‐distribution function to any desired accuracy. For use in applications, moments and recursion relations of a general class of speed‐distribution functions and moments of some typical gate functions are developed. Sufficient conditions for approximating a rectangular gate function by an impulsive gate function are presented. An application to time‐of‐flight measurements in an arc‐heated supersonic molecular beam illustrates the use of the general method and emphasizes the need to consider the characteristic time of the gate function and the dynamic response functions of the detector and its electronics when interpreting time‐of‐flight signals.

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