Deriving initial kinetic energy and longitudinal spatial distributions of charged particles from time-of-flight profiles

We present strategies for using time-of-flight (TOF) profiles to derive the kinetic energy distribution (KED) and the longitudinal spatial distribution (along the flight axis) of charged particles by varying the bias voltages on the acceleration electrodes. We take advantage of the spatial-focusing condition of the Wiley–McLaren design and, by applying a low field but a relatively high average potential in the acceleration region, can separate forward- and backward-flying ions in their TOF. Using an inversion method, the KED can be derived from the TOF of either forward- or backward-flying ions, and the overall TOF profiles can be reproduced. By grounding one of the electrodes in the acceleration region, the energy gained by a charged particle from the acceleration field becomes a sensitive function of its position along the flight axis. The time spread of the particles can then be used to directly derive the position of ionization along the flight axis when the initial kinetic energy of the charged particles is much lower than the acceleration energy. On the other hand, when both the initial kinetic energy and the longitudinal spatial distributions are significant, an optimization process involving an adjustable Gaussian spatial spread function and a few functions for the speed distribution can be performed. The TOF profile generated from the spatial spread function is convoluted with the TOF profile obtained from the speed distribution, allowing the longitudinal spatial spread and the kinetic energy distributions to be determined simultaneously. Both the theoretical framework and the experimental results are presented.