Ideal velocity focusing in a reflectron time-of-flight mass spectrometer

A single-stage ion mirror in a time-of-flight (TOF) mass spectrometer (MS) can perform first order velocity focusing of ions initially located at a start focal plane while second order velocity focusing can be achieved using a double-stage reflectron. The situation is quite different when an ion source extraction field is taken into account. In this case which is common in any practical matrix-assisted laser desorption/ionization (MALDI) TOF-MS a single-stage reflectron, for example, cannot perform velocity focusing at all. In this paper an exact, analytic solution for an electric field inside a one-dimensional reflectron has been found to achieve universal temporal focusing of ions having an initial velocity distribution. The general solution is valid for arbitrary electric field distributions in the upstream (from the ion source to the reflectron) and downstream (from the reflectron to an ion detector) regions and in a decelerating part of the reflectron of a reflectron TOF mass spectrometer. The results obtained are especially useful for designing MALDI reflectron TOF mass spectrometers in which the initial velocity distribution of MALDI ions is the major limiting factor for achieving high mass resolution. Using analytical expressions obtained for an arbitrary case, convenient working formulas are derived for the case of a reflectron TOF-MS with a dual-stage extraction ion source. The special case of a MALDI reflectron TOF-MS with an ion source having a low acceleration voltage (or large extraction region) is considered. The formulas derived correct the effect of the acceleration regions in a MALDI ion source and after the reflectron before detecting ions.