On the sharing of space charge energy between neighboring mass peaks in time-of-flight mass spectrometers

Time-of-flight mass spectrometry at increasing space charge densities revea ls a hitherto overlooked feature: lighter masses gain energy whereas heavie r masses loose energy. These energy shifts are quite substantial, in partic ular for nearly equal masses such as isotopes. In case of Xe ionization usi ng a focused KrF laser beam (0.5 ps, 5 mJ, f = 174 mm), the observed energy difference between Xe-128(+) and Xe-136(+) is much as 115 eV, whereas the space charge energy is only about 20 eV. We model this effect in case of a two-body problem. The two ion concentrations of different specific charges are considered as initially overlapping positively charged cylinders of rig id geometry, Owing to the external repeller field they become spatially sep arated, whence the nonoverlapping regions experience an additional repellin g force. In the limit of infinitely large external fields we can derive sim ple analytical expressions which readily explain our observations.