= Solution
In a sufficiently tight <binary star>, the <main sequence> companion can fill its <Roche lobe>. <Roche-lobe overflow> then transfers gas through the <inner Lagrange point> towards the <neutron star>. The gas carries <angular momentum>, so it generally forms an <accretion disk> rather than falling radially onto the surface. Internal stresses carry <angular momentum> outwards and permit <accretion> inwards. Capture of a stellar wind is another possible supply mechanism if the companion does not fill its <Roche lobe>.
Near the <neutron star>, the rapidly increasing <magnetic dipole field>, with $B\propto r^{-3}$, becomes dynamically important when its <magnetic pressure> $B^2/(2\mu_0)$ is comparable to the inflow stresses. The <accretion disk> is truncated around a magnetospheric radius. Ionized material attaches to <magnetic field lines> and streams along them in <magnetically channelled accretion>, forming an <accretion column> above one or both magnetic poles. The <Lorentz force> impedes motion across the <magnetic field>, but does not forbid motion parallel to it. Gas can therefore reach the polar surface, with its gravitational <potential energy> released in a hot <shock wave> and radiation.
This description presumes the <neutron star> rotates slowly enough for material to reach it: sufficiently rapid rotation can centrifugally expel the inflow instead. A strong <magnetic field> by itself does not guarantee surface <accretion>.
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