Magnetohydrodynamics in type-II superconductors: Application to force-free configurations

Abstract

The magnetohydrodynamics (MHD) equations in a type-II superconductor are reexamined in view of studying the unstable kink modes in nearly-force-free configurations by taking into account the pinning effects. It appears that at the early stage these modes cannot develop against the pinning forces unless the vortices experience an externally driven Bean-London motion. When the modes have perturbed the driving forces by an amount of the order of the pinning force, they escape the latter and undertake a faster growth determined by the viscosity. However, if the magnetic energy reservoir driving the MHD instabilities is not sufficient to reach that second regime, the considered instabilities may be considered harmless. This finally leads to an estimation of the maximum electrical current that may be carried by a superconducting wire immersed in a parallel magnetic field. This critical current, which may be much larger than the Kruskal-Shafranov limit triggering the kink instabilities in magnetized plasmas, is found to be compatible with experimental data available in the literature.

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