Instability of Toroidal Magnetic Field in Jets and Plerions

Jets and pulsar-fed supernova remnants (plerions) tend to develop highlyorganized toroidal magnetic field. Such a field structure could explain thepolarization properties of some jets, and contribute to their lateralconfinement. A toroidal field geometry is also central to models for the CrabNebula - the archetypal plerion - and leads to the deduction that the Crabpulsar's wind must have a weak magnetic field. Yet this `Z-pinch' fieldconfiguration is well known to be locally unstable, even when the magneticfield is weak and/or boundary conditions slow or suppress global modes. Thus,the magnetic field structures imputed to the interiors of jets and plerions areunlikely to persist. To demonstrate this, I present a local analysis of Z-pinch instabilities forrelativistic fluids in the ideal MHD limit. Kink instabilities dominate,destroying the concentric field structure and probably driving the systemtoward a more chaotic state in which the mean field strength is independent ofradius (and in which resistive dissipation of the field may be enhanced). Iestimate the timescales over which the field structure is likely to berearranged and relate these to distances along relativistic jets and radii fromthe central pulsar in a plerion. I conclude that a concentric toroidal field is unlikely to exist well outsidethe Crab pulsar's wind termination shock. There is thus no dynamical reason toconclude that the magnetic energy flux carried by the pulsar wind is muchweaker than the kinetic energy flux. Abandoning this inference would resolve along-standing puzzle in pulsar wind theory.Comment: 28 pages, plain TeX. Accepted for publication in Ap