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

Abstract

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.

In pursuit of resolution in time‐of‐flight mass spectrometry: A historical perspective

“…A method similar to that described by Managadze et al (), was used to solve equations for the total flight time of an ion in an ion mirror. Later, a similar approach for space focusing in linear and ion mirror TOF was introduced by Doroshenko (). A general solution was presented for one‐ and two‐stage acceleration in both the case of a linear TOF and the case of an ion mirror.…”

“…Yoshida (1986) and Andersen et al (1998) explored so-called quadraticfield ion mirrors in various TOFs and tandem TOFs. The socalled curved-field ion mirror was promoted by Cotter and also Doroshenko (Doroshenko & Cotter, 1999;Doroshenko, 2000). Constant momentum TOF was developed by Santacruz et al (2006).…”

The Secrets of Time-of Flight Mass Spectrometry Revealed

“…The last missing bit is the time spent in the post-acceleration gap, d p of Figure 3, which is again calculated using Equations (16), (17) and 22: Now we have all the parts to build the time-of-flight equation for the whole instrument. The derived formulae are exact for any instrument that uses homogeneous electric fields.…”