Structure and Stability of Keplerian MHD Jets

MHD jet equilibria that depend on source properties are obtained using a simplified model for stationary, axisymmetric and rotating magnetized outflows. The present rotation laws are more complex than previously considered and include a Keplerian disc. The ensuing jets have a dense, current-carrying central core surrounded by an outer collar with a return current. The intermediate part of the jet is almost current-free and is magnetically dominated. Most of the momentum is located around the axis in the dense core and this region is likely to dominate the dynamics of the jet. We address the linear stability and the non-linear development of instabilities for our models using both analytical and 2.5-D numerical simulation's. The instabilities seen in the simulations develop with a wavelength and growth time that are well matched by the stability analysis. The modes explored in this work may provide a natural explanation for knots observed in astrophysical jets.Comment: 35 pages, accepted by the Ap

Axisymmetric equilibria of a gravitating plasma with incompressible flows

It is found that the ideal magnetohydrodynamic equilibrium of an axisymmetric gravitating magnetically confined plasma with incompressible flows is governed by a second-order elliptic differential equation for the poloidal magnetic flux function containing five flux functions coupled with a Poisson equation for the gravitation potential, and an algebraic relation for the pressure. This set of equations is amenable to analytic solutions. As an application, the magnetic-dipole static axisymmetric equilibria with vanishing poloidal plasma currents derived recently by Krasheninnikov, Catto, and Hazeltine [Phys. Rev. Lett. {\bf 82}, 2689 (1999)] are extended to plasmas with finite poloidal currents, subject to gravitating forces from a massive body (a star or black hole) and inertial forces due to incompressible sheared flows. Explicit solutions are obtained in two regimes: (a) in the low-energy regime $\beta_0\approx \gamma_0\approx \delta_0 \approx\epsilon_0\ll 1$, where $\beta_0$, $\gamma_0$, $\delta_0$, and $\epsilon_0$ are related to the thermal, poloidal-current, flow and gravitating energies normalized to the poloidal-magnetic-field energy, respectively, and (b) in the high-energy regime $\beta_0\approx \gamma_0\approx \delta_0 \approx\epsilon_0\gg 1$. It turns out that in the high-energy regime all four forces, pressure-gradient, toroidal-magnetic-field, inertial, and gravitating contribute equally to the formation of magnetic surfaces very extended and localized about the symmetry plane such that the resulting equilibria resemble the accretion disks in astrophysics.Comment: 12 pages, latex, to be published in Geophys. Astrophys. Fluid Dynamic