= On-axis entry into a solenoidal tube
{title2=$r_{\max}=2mv_\perp/(|q|B)$}
A particle entering a uniform axial <magnetic field> on the tube axis follows a transverse circle through that entry point. Its <guiding centre> is one <Larmor radius> from the axis, so the maximum radial displacement from the axis is twice the <Larmor radius>. For tube <radius> $a$, clearance requires $v_\perp\le |q|Ba/(2m)$ when the transit samples a complete gyration. If the transit is shorter, the actual sampled arc determines clearance instead. The axis is revisited after each full cyclotron <period>, not after each half-period.
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