Fast Reconnection of Weak Magnetic Fields

Fast magnetic reconnection refers to annihilation or topological rearrangement of magnetic fields on a timescale that is independent (or nearly independent) of the plasma resistivity. The resistivity of astrophysical plasmas is so low that reconnection is of little practical interest unless it is fast. Yet, the theory of fast magnetic reconnection is on uncertain ground, as models must avoid the tendency of magnetic fields to pile up at the reconnection layer, slowing down the flow. In this paper it is shown that these problems can be avoided to some extent if the flow is three dimensional. On the other hand, it is shown that in the limited but important case of incompressible stagnation point flows, every flow will amplify most magnetic fields. Although examples of fast magnetic reconnection abound, a weak, disordered magnetic field embedded in stagnation point flow will in general be amplified, and should eventually modify the flow. These results support recent arguments against the operation of turbulent resistivity in highly conducting fluids

Virial theorem analysis of the structure and stability of magnetized clouds

The tensor virial theorem is used to analyze the structure and stability of self-gravitating, magnetized spheroids surrounded by a low-density medium with pressure and magnetic field. Analytical expressions are developed for the effect of a weak field and calculate critical states when the effect of the field is arbitrarily strong, comparing the results with full magnetohydrostatic calculations. This analysis suggests that a magnetic field may prevent gravitational collapse but may also be destabilizing, depending on its degree of concentration within the cloud

The Weak Field Limit of the Magnetorotational Instability

We investigate the behavior of the magneto-rotational instability in the limit of extremely weak magnetic field, i.e., as the ratio of ion cyclotron frequency to orbital frequency (X) becomes small. Considered only in terms of cold two-fluid theory, instability persists to arbitrarily small values of X, and the maximum growth rate is of order the orbital frequency except for the range m_e/m_i < |X| < 1, where it can be rather smaller. In this range, field aligned with rotation (X > 0) produces slower growth than anti-aligned field (X < 0). The maximum growth rate is generally achieved at smaller and smaller wavelengths as |X| diminishes. When |X| < m_e/m_i, new unstable "electromagnetic-rotational" modes appear that do not depend on the equilibrium magnetic field. Because the most rapidly-growing modes have extremely short wavelengths when |X| is small, they are often subject to viscous or resistive damping, which can result in suppressing all but the longest wavelengths, for which growth is much slower. We find that this sort of damping is likely to curtail severely the frequently-invoked mechanism for cosmological magnetic field growth in which a magnetic field seeded by the Biermann battery is then amplified by the magneto-rotational instability. On the other hand, the small |X| case may introduce interesting effects in weakly-ionized disks in which dust grains carry most of the electric charge.Comment: 30 pages, including 4 figures; revised version resubmitted to Ap