Coupled Space- and Velocity-Focusing in Time-of-Flight Mass Spectrometry-a Comprehensive Theoretical Investigation.

A comprehensive theoretical calculation that couples space- and velocity-focusing is developed for optimizing the design of a time-of-flight (TOF) mass spectrometer. Conventional designs for ion sources of TOF mass spectrometers deviate from the optimal condition because the velocity- and space-focusing conditions are considered separately for two ions with simplified equations. The result of a reexamination taking into account all essential ions reveals that the conventional ion source design, especially the length of the ion extraction region, results in poor resolving power. The comprehensive calculation demonstrates that the resolving power increases when the length of the extraction region is shorter than that of the conventional ion source. A numerical analysis indicates that the resolving power dramatically increases when the effective extraction potential compensates for the initial kinetic energy spread of ions. With typically used extraction potentials, the newly optimized ion source improves the resolving power by more than two orders of magnitude compared with the conventional design. This new theoretical interpretation can also be used to predict the optimal extraction potential and extraction delay in conventional ion sources to substantially improve the resolving power. This comprehensive calculation method is effective not only for designing new high-resolution instruments but also for optimizing commercial products.