Fields from a relativistic magnetic explosion

Following Prendergast we study the relativistically expanding electromagnetic fields generated by an axisymmetric explosion of magnetic energy in a small volume. The magnetic field expands uniformly either within a cone or in all directions and it is therefore accompanied by an electric field. In the highly conducting plasma the charges move to annul the electric field in the frame of the moving plasma. The solutions presented are analytical and semi-analytical. We find that the time-scale for the winding up of the initial magnetic field is crucial, as short time-scales lead to strong radiant fields. Assuming a magnetic field of $10^{13}Gauss$ emerging from a magnetosphere of $10^{9}cm$ we end with a jet when confined by a pressure environment that falls more slowly than $r^{-4}$. The jet carries energy of $10^{51}erg$, which is mostly due to differential rotation at the base.