Towards molecular reconstruction in Coulomb explosion imaging
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The interaction of a fast laser with molecules at the femtosecond time scale, leads to the latter losing most of its valence electrons and become positively charged. The molecule which was initially in an equilibrium state, undergoes internal repulsion which leads to fragmentation of the molecule into constituent ions and other neutral fragments. The unidirectional electric field in lens accelerates the charged ions towards a position-sensitive detector, and their arrivals are based on their charge per mass ratio. The ion with the highest ratio of charge per mass arrives first at the detector; its time-of-flight and position of impact on the detector by the ion is recorded. The same information is recorded for subsequent ions that arrive at the detector. This research attempts to reconstruct the molecular structure prior to a Coulomb explosion of the ionized molecule using only the information available at the detector. There are broadly two components to the approach examined here: the forward and the backward (inverse) problems. In the forward problem, we develop a model using the classical equations of motion to describe the time evolution of the constituent ions immediately after the fragmentation of the parent molecule. The goal being to accurately reproduce a given impact pattern on the target screen, consistent with the ions time of arrival. The inverse problem uses the positions and time-of-flights of the constituent ions to systematically predict the original molecular structure. The inverse problem is characterized by a shortage of information from the detector due to the fact that not all the atoms of the molecule become ionized during any particular laser-molecule interaction and the electric field is inhomogeneous. Therefore, one way to reconstruct the initial positions of the photo-fragments is to simulate the inhomogeneous field and reverse the paths of detected ions.