Theoretical study of space focusing in linear time-of-flight mass spectrometers

Abstract

In response to continued improvements in the production of “cold” atoms, molecular beams, and in electronic timing resolution, the issue of space focusing in linear time-of-flight (TOF) mass spectrometers is reevaluated. Starting with the Wiley–McLaren [W. C. Wiley and I. H. McLaren, Rev. Sci. Instrum. 26, 1150 (1955)] condition for first-order space focusing in the conventional two-field system, we extend the approach to higher orders in more complicated situations. A general, solvable, set of equations for satisfying n-order space focusing in an m-field regime is derived. We demonstrate quantitatively that if higher orders of space focus are employed, then provided the initial velocity distribution of the ions is sufficiently narrow, a significant improvement in the mass resolution can be achieved. The conclusions drawn have important implications for the design of the next generation of TOF instruments.