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

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. (C) 2001 American Institute of Physics.