 Space focusing

Space focusing in time-of-flight mass spectrometry reduces differences in arrival time caused by the initial positions of otherwise equivalent ions. An ion starting farther from the exit of an accelerating region spends longer there but can acquire greater kinetic energy, allowing it to catch up during the drift. Electrode geometry and electric fields are chosen so that these effects compensate at the detector.^[ref]

A simple idealized derivation makes the compensation explicit. Consider positive ions of mass $m$ and electric charge $q$, initially at rest, with distance $a$ remaining in a uniform accelerating electric field $E$. Let $L$ be the field-free distance beyond its exit. Their total flight time isThe first term is acceleration time; the second is drift time. Setting the derivative $dt/da$ to zero at a reference position $a_0$ givesFor example, $a_0=1\mathrm{cm}$ gives a first-order space focus at $L=2\mathrm{cm}$ in this simplified single-field model. Nearby position errors then affect arrival time only at higher order in the Taylor expansion. Practical two-field sources allow the focus to be placed at more useful drift distances. Initial velocity spread is a separate contribution to peak width, motivating time-lag focusing.