Toroidal magnetic field generation during compact toroid formation in a field-reversed theta pinch and a conical theta pinch

The influence that the Hall and ∇Pe terms, in a generalized Ohm’s law, have on the formation of a compact toroid in a field-reversed theta pinch and a conical theta pinch has been examined. The inclusion of these terms leads to the spontaneous generation of toroidal magnetic fields and toroidal velocities. The toroidal fields in the end regions reach peak values of almost 50% of the external poloidal field during the early stages of formation. When the coil geometry is the same at each end of the theta pinch, equal and opposite toroidal fields are generated by the Hall effect, so that no net toroidal flux is generated. When the geometry is not the same at each end, the Hall effect can lead to a net toroidal flux. Calculations for both a conical theta pinch experiment and a field-reversed configuration translation experiment demonstrate the generation of net toroidal flux, as observed experimentally.