Ethan T. Vishniac

Reconnection in a Weakly Stochastic Field

We examine the effect of weak, small-scale magnetic field structure on the rate of reconnection in a strongly magnetized plasma. This affects the rate of reconnection by reducing the transverse scale for reconnection flows and by allowing many independent flux reconnection events to occur simultaneously. Allowing only for the first effect and using Goldreich & Sridhars model of strong turbulence in a magnetized plasma with negligible intermittency, we find a lower limit for the reconnection speed ~VA-3/16L3/4, where VA is the Alfven speed, L is the Lundquist number, and is the large-scale magnetic Mach number of the turbulence. We derive an upper limit of ~VA2 by invoking both effects. We argue that generic reconnection in turbulent plasmas will normally occur at close to this upper limit. The fraction of magnetic energy that goes directly into electron heating scales as -2/5L8/5, and the thickness of the current sheet scales as -3/5L-2/5. A significant fraction of the magnetic energy goes into high-frequency Alfven waves. The angle between adjacent field lines on the same side of the reconnection layer is ~-1/5L6/5 on the scale of the current sheet thickness. We claim that the qualitative sense of these conclusions, that reconnection is fast even though current sheets are narrow, is almost independent of the local physics of reconnection and the nature of the turbulent cascade. As the consequence of this the Galactic and solar dynamos are generically fast, i.e., do not depend on the plasma resistivity.

The Anisotropy of Magnetohydrodynamic Alfvénic Turbulence

We perform direct three-dimensional numerical simulations for magnetohydrodynamic (MHD) turbulence in a periodic box of size 2π threaded by strong uniform magnetic fields. We use a pseudospectral code with hyperviscosity and hyperdiffusivity to solve the incompressible MHD equations. We analyze the structure of the eddies as a function of scale. A straightforward calculation of anisotropy in wavevector space shows that the anisotropy is scale independent. We discuss why this is not the true scaling law and how the curvature of large-scale magnetic fields affects the power spectrum and leads to the wrong conclusion. When we correct for this effect, we find that the anisotropy of eddies depends on their size: smaller eddies are more elongated than larger ones along local magnetic field lines. The results are consistent with the scaling law ∥ ~ recently proposed by Goldreich & Sridhar. Here ∥ (and ⊥) are wavenumbers measured relative to the local magnetic field direction. However, we see some systematic deviations that may be a sign of limitations to the model or our inability to fully resolve the inertial range of turbulence in our simulations.We perform direct 3-dimensional numerical simulations for magnetohydrodynamic (MHD) turbulence in a periodic box of size

Simulations of Magnetohydrodynamic Turbulence in a Strongly Magnetized Medium

2\pi

NONLINEAR INSTABILITIES IN SHOCK-BOUNDED SLABS

threaded by strong uniform magnetic fields. We use a pseudo-spectral code with hyperviscosity and hyperdiffusivity to solve the incompressible MHD equations. We analyze the structure of the eddies as a function of scale. A straightforward calculation of anisotropy in wavevector space shows that the anisotropy is scale-{\it independent}. We discuss why this is {\it not} the true scaling law and how the curvature of large-scale magnetic fields affects the power spectrum and leads to the wrong conclusion. When we correct for this effect, we find that the anisotropy of eddies depends on their size: smaller eddies are more elongated than larger ones along {\it local} magnetic field lines. The results are consistent with the scaling law

Simulations of MHD Turbulence in a Strongly Magnetized Medium

\tilde{k}_{\parallel} \sim \tilde{k}_{\perp}^{2/3}

Numerical Tests of Fast Reconnection in Weakly Stochastic Magnetic Fields

proposed by Goldreich and Sridhar (1995, 1997). Here

Reionization and small-scale fluctuations in the microwave background

\tilde{k}_{\|}

Magnetic Field Structure and Stochastic Reconnection in a Partially Ionized Gas

(and

An Incoherent α-Ω Dynamo in Accretion Disks

\tilde{k}_{\perp}

The Generation of Magnetic Fields through Driven Turbulence

) are wavenumbers measured relative to the local magnetic field direction. However, we see some systematic deviations which may be a sign of limitations to the model, or our inability to fully resolve the inertial range of turbulence in our simulations.