Axial magnetic flux amplification in Hall-magnetohydrodynamic simulations of externally magnetized z-pinches

It is shown that externally magnetized gas-puff z-pinches under compression can exhibit robust axial flux amplification under suitable axial boundary conditions. This effect relies upon the Hall term in the generalized Ohm's law to generate azimuthal currents in the presence of a driving axial electric field. Under dynamic compression, the total current tends to flow in a mostly force-free boundary layer, separating the predominately azimuthal field outside the layer and the predominately axial field inside the layer. The effect only appears to occur if the axial boundaries allow for outflow or absorption of electromagnetic energy. The effect is mitigated by imposing either periodic or conducting axial boundary conditions. A semi-analytic equilibrium analysis agrees with steady-state solutions of the time-dependent electron-magnetohydrodynamic equations and provides an estimate of the scaling of the boundary layer as well as suggesting a scenario for the formation of the boundary layer. When operative, the effect can significantly impede plasma compression due to the increase in axial flux that diffuses into the pre-compressed plasma or through the presence of conductors that inhibit movement of the generated axial flux. Several facilities have noted unusual implosion behavior in z-pinch experiments with applied axial fields that does not appear to be explainable within the standard magnetohydrodynamic model. It is suggested that these experiments can be explained by the axial flux amplification and concentration effect.