Fields from a relativistic magnetic explosion

TL;DR

This paper models the relativistic expansion of magnetic fields from explosive events, analyzing the resulting electromagnetic fields and jet formation with analytical solutions, highlighting the importance of timescales and magnetic field strength.

Contribution

It provides analytical and semi-analytical models of relativistically expanding magnetic fields from explosive events, including jet formation and energy estimates.

Findings

Short magnetic winding times produce strong radiant fields.

A jet with $10^{51}$ erg energy can form under certain pressure conditions.

The magnetic field and electric field evolution depend on initial conditions and confinement.

Abstract

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.