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The superfluid and superconducting core of a cold rotating neutron star isexpected to be threaded by a tremendous number of neutron quantised vorticesand proton fluxoids. Their interactions are unavoidable and may have importantastrophysical implications. In this paper, the various contributions to theforce acting on a single vortex to which fluxoids are pinned are clarified. Thegeneral expression of the force is derived by applying the variationalmultifluid formalism developed by Carter and collaborators. Pinning to fluxoidsleads to an additional Magnus type force due to proton circulation around thevortex. Pinning in the core of a neutron star may thus have a dramatic impacton the vortex dynamics, and therefore on the magneto-rotational evolution ofthe star.

Force on a neutron quantised vortex pinned to proton fluxoids in the superfluid core of cold neutron stars