The Hall instability of unsteady inhomogeneous axially symmetric magnetized plasmas

The Hall instability in cylindrically symmetric resistive magnetized plasmas in vacuum is investigated. The unperturbed self-similar equilibrium solutions for imploding Z-pinches with time-dependent total current I _∼ ∼ t^S, S> 1/3, are subjected by short-wave sausage perturbations. The instability criterion is derived in slow-time, frozen-radius approximation. In cylindrically symmetric configurations the instability is driven by the magnetic field curvature. The near-axis and near-edge branches of the neutral curve in the plane of the inverse Hall parameter and phase velocity with the frozen radial coordinate as a parameter are separated by the critical point, where the modified gradient from the unperturbed number density changes sign. The critical radius may be treated as a new characteristic size of the Z-pinch that emerges due to the instability: the pinch is envisaged restructured by the short-scale high-frequency Hall instability, in which a central stable core is surrounded by an outer shell. Such a modified equilibrium may explain the observed enhanced stability against magnetohydrodynamic modes.