= I. H. McLaren
{c}
<I. H. McLaren> coauthored with <W. C. Wiley> the 1955 Bendix study of <time-of-flight mass spectrometry> with improved <mass resolving power>. A notable part of their analysis was <time-lag focusing>: waiting between ion formation and application of an accelerating pulse lets initial <velocities> become position differences that can compensate some arrival-time spread.<Time-of-Flight Mass Spectrometer with Improved Resolution by W. C. Wiley and I. H. McLaren>[Printed p. 1150, byline and affiliation; p. 1154, Time-Lag Energy Focusing and Figure 3]{ref}
A first-order calculation exposes the mechanism. Let $T(v,s)$ be arrival time after immediate extraction for initial axial <velocity> $v$ and position $s$. During a field-free delay $\tau$, an <ion> moves to $s+v\tau$. Apart from the common delay added to all times,
$$
T(v,s+v\tau)\simeq T(0,s)+\left(T_v+\tau T_s\right)v.
$$
The <partial derivatives> are evaluated at $v=0$ and the reference position. First-order sensitivity to $v$ vanishes if
$$
\tau=-\frac{T_v}{T_s}.
$$
A positive delay requires opposite signs of these sensitivities. For example, $T_v=2\times10^{-9}\,\mathrm{s^2\,m^{-1}}$ and $T_s=-10^{-3}\,\mathrm{s\,m^{-1}}$ give $\tau=2\,\mathrm{\mu s}$. These values illustrate the cancellation, rather than reproducing an instrument setting from the paper.
This also reveals the tradeoff: the cancellation needs a nonzero position sensitivity, whereas ideal first-order <space focusing> sets $T_s=0$. The paper's delayed-extraction condition and measured spectra therefore address competing sources of broadening, not a universal elimination of every initial-condition effect.<Time-of-Flight Mass Spectrometer with Improved Resolution by W. C. Wiley and I. H. McLaren>[Printed p. 1154, equations 13–13a and discussion of the compromise between space resolution and time-lag energy focusing]{ref}
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