The magnetic pressure in cylindrical wires and rectangular rods, and the inverse pinch effect

The magnetic pressure in a cylindrical wire has been calculated for constant current, steady-state sinusoidal current, and the pulse current of an overdamped discharge. As previously shown by Haines (1959) for conductors carrying time-varying currents, an inverse current density distribution is produced corresponding to an `inverse skin effect'. Maninger (1959) and Haines predicted that the inverse skin effect also creates an inverse pinch effect, thereby producing an outer shell of magnetic tension in the wire. A quantitative analysis for a pulse current-carrying conductor shows that the inverse pinch effect becomes dominant over the normal pinch effect in later time instants of the current pulsing. The distribution of the magnetic pressure in a rectangular rod carrying a constant current has been calculated for different ratios of thickness and width. The validity of this solution for thin foils is discussed for the case of applied alternating currents.