= Solenoidal time-of-flight energy window
{title2=$K\in[K_0,K_0+q^2B^2a^2/(8m)]$}
A nonrelativistic particle accepted only at a fixed flight time through an ideal uniform-field tube has fixed parallel <speed> $v_\parallel=l/t_0$. On-axis entry and wall clearance bound the independent perpendicular <speed> by $|q|Ba/(2m)$, provided a full gyration occurs before exit. Adding parallel and perpendicular <kinetic energies> gives the displayed ideal <energy> window, where $K_0=mv_\parallel^2/2$. The upper endpoint is a grazing limit; strict wall exclusion makes it a <supremum>.
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