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

In response to continued improvements in the production of "cold" atoms, mo lecular beams, and in electronic timing resolution, the issue of space focu sing in linear time-of-flight (TOF) mass spectrometers is reevaluated. Star ting with the Wiley-McLaren [W. C. Wiley and I. H. McLaren, Rev. Sci. Instr um. 26, 1150 (1955)] condition for first-order space focusing in the conven tional two-field system, we extend the approach to higher orders in more co mplicated situations. A general, solvable, set of equations for satisfying n-order space focusing in an m-field regime is derived. We demonstrate quan titatively that if higher orders of space focus are employed, then provided the initial velocity distribution of the ions is sufficiently narrow, a si gnificant improvement in the mass resolution can be achieved. The conclusio ns drawn have important implications for the design of the next generation of TOF instruments. (C) 2001 American Institute of Physics.