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Register a new userInstability of toroidal magnetic field in jets and plerions
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Authors
Mitchell C. Begelman
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Jets and pulsar-fed supernova remnants (plerions) tend to develop highly organized toroidal magnetic field. Such a field structure could explain the polarization properties of some jets, and contribute to their lateral confinement. A toroidal field geometry is also central to models for the Crab Nebula - the archetypal plerion - and leads to the deduction that the Crab pulsars wind must have a weak magnetic field. Yet this `Z-pinch field configuration is well known to be locally unstable, even when the magnetic field is weak and/or boundary conditions slow or suppress global modes. Thus, the magnetic field structures imputed to the interiors of jets and plerions are unlikely to persist. To demonstrate this, I present a local analysis of Z-pinch instabilities for relativistic fluids in the ideal MHD limit. Kink instabilities dominate, destroying the concentric field structure and probably driving the system toward a more chaotic state in which the mean field strength is independent of radius (and in which resistive dissipation of the field may be enhanced). I estimate the timescales over which the field structure is likely to be rearranged and relate these to distances along relativistic jets and radii from the central pulsar in a plerion. I conclude that a concentric toroidal field is unlikely to exist well outside the Crab pulsars wind termination shock. There is thus no dynamical reason to conclude that the magnetic energy flux carried by the pulsar wind is much weaker than the kinetic energy flux. Abandoning this inference would resolve a long-standing puzzle in pulsar wind theory.
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Several observations of astrophysical jets show evidence of a structure in the direction perpendicular to the jet axis, leading to the development of spine & sheath models of jets. Most studies focus on a two-component jet consisting of a highly relativistic inner jet and a slower - but still relativistic - outer jet surrounded by an unmagnetized environment. These jets are believed to be susceptible to a relativistic Rayleigh-Taylor-type instability, depending on the effective inertia ratio of the two components. We extend previous studies by taking into account the presence of a non-zero toroidal magnetic field. Different values of magnetization are examined, to detect possible differences in the evolution and stability of the jet. We find that the toroidal field, above a certain level of magnetization $sigma$, roughly equal to 0.01, can stabilize the jet against the previously mentioned instabilities and that there is a clear trend in the behaviour of the average Lorentz factor and the effective radius of the jet when we continuously increase the magnetization. The simulations are performed using the relativistic MHD module from the open source, parallel, grid adaptive, MPI-AMRVAC code.
The properties of relativistic jets, their interaction with the ambient environment, and particle acceleration due to kinetic instabilities are studied self-consistently with Particle-in-Cell simulations. An important key issue is how a toroidal magnetic field affects the evolution of an e$^{pm}$ and an e$^{-}$ - p$^{+}$ jet, how kinetic instabilities such as the Weibel instability (WI), the mushroom instability (MI) and the kinetic Kelvin-Helmholtz instability (kKHI) are excited, and how such instabilities contribute to particle acceleration. We show that WI, MI and kKHI excited at the linear stage, generate a quasi-steady $x$-component of electric field which accelerates and decelerates electrons. In this work, we use a new jet injection scheme where an electric current is self-consistently generated at the jet orifice by the jet particles. We inject both e$^{pm}$ and e$^{-}$ - p$^{+}$ jets with a toroidal magnetic field (with a top-hat jet density profile) and for a sufficiently long time in order to examine the non-linear effects of the jet evolution. Despite the weakness of the initial magnetic field, we observe significant differences in the structure of the strong electromagnetic fields that are driven by the kinetic instabilities. We find that different jet compositions present different strongly excited instability modes. The magnetic field in the non-linear stage generated by different instabilities becomes dissipated and reorganized into a new topology. The 3-dimensional magnetic field topology indicates possible reconnection sites and the accelerated particles are significantly accelerated in the non-linear stage by the dissipation of the magnetic field and/or reconnection. This study will shed further light on the nature of astrophysical relativistic magnetized jet phenomena.
A 3D simulation of a non-relativistic, magnetically driven jet propagating in a stratified atmosphere is presented, covering about three decades in distance and two decades in sideways expansion. The simulation captures the jet acceleration through the critical surfaces and the development of (kink-)instabilities driven by the free energy in the toroidal magnetic field component. The instabilities destroy the ordered helical structure of the magnetic field, dissipating the toroidal field energy on a length scale of about 2-15 times the Alfven distance. We compare the results with a 2.5D (axisymmetric) simulation, which does not become unstable. The acceleration of the flow is found to be quite similar in both cases, but the mechanisms of acceleration differ. In the 2.5D case approximately 20% of the Poynting flux remains in the flow, in the 3D case this fraction is largely dissipated internally. Half of the dissipated energy is available for light emission; the resulting radiation would produce structures resembling those seen in protostellar jets.
Toroidal magnetic fields subject to the Tayler instability can transport angular momentum. We show that the Maxwell and Reynolds stress of the nonaxisymmetric field pattern depend linearly on the shear in the cylindrical gap geometry. Resulting angular momentum transport also scales linear with shear. It is directed outwards for astrophysical relevant flows and directed inwards for superrotating flows with dOmega/dR>0. We define an eddy viscosity based on the linear relation between shear and angular momentum transport and show that its maximum for given Prandtl and Hartmann number depends linear on the magnetic Reynolds number Rm. For Rm=1000 the eddy viscosity is of the size of 30 in units of the microscopic value.
We have investigated magnetic field generation in velocity shears via the kinetic Kelvin-Helmholtz instability (kKHI) using a relativistic plasma jet core and stationary plasma sheath. Our three-dimensional particle-in-cell simulations consider plasma jet cores with Lorentz factors of 1.5, 5, and 15 for both electron-proton and electron-positron plasmas. For electron-proton plasmas we find generation of strong large-scale DC currents and magnetic fields which extend over the entire shear-surface and reach thicknesses of a few tens of electron skin depths. For electron-positron plasmas we find generation of alternating currents and magnetic fields. Jet and sheath plasmas are accelerated across the shear surface in the strong magnetic fields generated by the kKHI. The mixing of jet and sheath plasmas generates transverse structure similar to that produced by the Weibel instability.
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