Accurately accounting for effects on times-of-flight caused by finite field-transition times during the ejection of ions from a storage trap: A study for TOF and MRTOF mass spectrometry

In applied forms of time-of-flight mass spectrometry utilizing ion storage devices prior to an analysis device, a non instantaneous electric ejection pulse applied in the region of ion storage is used to accelerate ions into the time-of-flight analyzer. The calculated mass value of the ions from the time-of-flight is dependent on the duration of the field transition up to full strength. For novel applications dedicated to precision measurements, such as multi-reflection time-of-flight mass spectrometry of short-lived isotopes, the goal is to continuously decrease the measurement uncertainty while providing a mass accuracy on the same order. Even though dynamic-field models for time-of-flight mass spectrometry have been considered in the past for technological advances, it is important to study the accuracy of the measured mass in this context. Using a simplified linear model for the field transition, we provide a basic investigation of the scenario, and discuss the deviation from the classical "mass-over-charge" dependency of the ions' time-of-flight, which becomes violated. The emerging mass discrepancy depends on the distance between the mass of the ion used for calibration and that of the ion of interest and, in extreme cases, can increase to about one percent for systems with short times-of-flight. However, for typical conditions in single-reference multi-reflection time-of-flight mass spectrometry, mass deviations caused by this effect typically remain below the 1 ppm level. If a mass calibration using two or more ion species is possible during the measurement, the effect becomes negligible for appropriate choices of reference masses.