We report kinetic energies (KE) of multiply charged atomic ions (MCAI) from interactions of moderately intense nanosecond lasers at 532 nm with argon containing clusters, including neat and doped clusters with a trace amount of trichlorobenzene. We develop a mathematical method to retrieve speed and thereby kinetic energy information from analyzing the time-of-flight profiles of the MCAI. This method should be generally applicable in detections of energetic charged particles with high velocities, a realm where velocity map imaging is inadequate. From this analysis, we discover that the KE of MCAI from doped clusters demonstrates a quadratic dependence on the charge of the atomic ions, while for neat clusters, the dependence is cubic. This result confirms the nature of the cluster disintegration process to be dominated by Coulomb explosion. This result bears more similarity to reports from extreme vacuum ultraviolet (EUV) fields with similar intensities, than to reports from near infrared (NIR) intense laser fields. However, the charge state distribution from our experiment is the opposite: we observe more higher charge state ions than reported in EUV fields, and our charge state distribution is actually similar to those reported in NIR fields. We also report a significant effect of the external electric field on the charge state distribution of the atomic ions: the presence of an electric field can significantly increase the charge from the atomic ions, as shown by a three-fold reduction in the average kinetic energy per charge. Although molecular dynamics simulations have been implemented for experiments in the EUV and NIR, our results allude to the need of a concerted effort in this regime of moderately intense nanosecond laser fields. The significant decrease in charge state distribution and the significant increase in KE from doped clusters, compared with neat clusters, is a telltale sign that the true interaction time between the laser field and the cluster may be substantially shorter than the duration of the laser, a welcome relief for molecular dynamics simulations.
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