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Ideal Space Focusing in a Time-of-Flight Mass Spectrometer: An Optimization Using an Analytical Approach

An exact, analytical solution for an electric field in a nonlinear acceleration region of an ion source for the cases of linear and reflectron time-of-flight (TOF) mass spectrometers has been found to achieve universal temporal focusing of ions having an initial space distribution. The general solutions are valid for an arbitrary electric field distribution in the drift region (from the ion source to an ion detector) of a linear TOF mass spectrometer, and in the upstream (from the ion source to the reflectron) and downstream (from the reflectron to an ion detector) regions of a reflectron TOF instrument. This may include, for example, electrostatic lenses commonly used after an ion source for angular focusing of ions onto the detector to increase the instrument sensitivity and additional acceleration of ions before their detection. Using analytical expressions obtained for an arbitrary case, convenient working formulae are derived for the widely used single- and dual-stage ion extraction schemes in the cases of linear and reflectron TOF mass spectrometers. The formulae are used in optimizing the TOF mass spectrometer design by decreasing the curvature of the nonlinear acceleration potential in the ion source. The relationship has been shown between the conditions for an ideal space focusing using an optimized curved extraction field and a finite-order space-focusing using a linear extraction field in an ion source. The results obtained are especially useful for designing miniature TOF mass spectrometers or instruments with large volume ion sources.