New Regime of MHD Turbulence: Cascade Below Viscous Cutoff

In astrophysical situations, e.g. in the interstellar medium (ISM), neutrals can provide viscous damping on scales much larger than the magnetic diffusion scale. Through numerical simulations, we have found that the magnetic field can have a rich structure below the dissipation cutoff scale. This implies that magnetic fields in the ISM can have structures on scales much smaller than parsec scales. Our results show that the magnetic energy contained in a wavenumber band is independent of the wavenumber and magnetic structures are intermittent and extremely anisotropic. We discuss the relation between our results and the formation of the tiny-scale atomic structure (TSAS).Comment: ApJ Letters, accepted (Feb. 10, 2002; ApJ, 566, L...); 10 pages, 3 figure

The Anisotropy of MHD Alfv\'{e}nic Turbulence

We perform direct 3-dimensional numerical simulations for magnetohydrodynamic (MHD) turbulence in a periodic box of size $2\pi$ 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 $\tilde{k}_{\parallel} \sim \tilde{k}_{\perp}^{2/3}$ proposed by Goldreich and Sridhar (1995, 1997). Here $\tilde{k}_{\|}$ (and $\tilde{k}_{\perp}$) 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.Comment: 13 pages (11 NEW figures), ApJ, in press (Aug 10, 2000?

Magnetic Field Structure and Stochastic Reconnection in a Partially Ionized Gas

We consider stochastic reconnection in a magnetized, partially ionized medium. Stochastic reconnection is a generic effect, due to field line wandering, in which the speed of reconnection is determined by the ability of ejected plasma to diffuse away from the current sheet along magnetic field lines, rather than by the details of current sheet structure. We consider the limit of weak stochasticity, so that the mean magnetic field energy density is greater than either the turbulent kinetic energy density or the energy density associated with the fluctuating component of the field. We consider field line stochasticity generated through a turbulent cascade, which leads us to consider the effect of neutral drag on the turbulent cascade of energy. In a collisionless plasma, neutral particle viscosity and ion-neutral drag will damp mid-scale turbulent motions, but the power spectrum of the magnetic perturbations extends below the viscous cutoff scale. We give a simple physical picture of the magnetic field structure below this cutoff, consistent with numerical experiments. We provide arguments for the reemergence of the turbulent cascade well below the viscous cut-off scale and derive estimates for field line diffusion on all scales. We note that this explains the persistence of a single power law form for the turbulent power spectrum of the interstellar medium, from scales of tens of parsecs down to thousands of kilometers. We find that under typical conditions in the ISM stochastic reconnection speeds are reduced by the presence of neutrals, but by no more than an order of magnitude.Comment: Astrophysical Journal in pres

The Generation of Magnetic Fields Through Driven Turbulence

We have tested the ability of driven turbulence to generate magnetic field structure from a weak uniform field using three dimensional numerical simulations of incompressible turbulence. We used a pseudo-spectral code with a numerical resolution of up to $144^3$ collocation points. We find that the magnetic fields are amplified through field line stretching at a rate proportional to the difference between the velocity and the magnetic field strength times a constant. Equipartition between the kinetic and magnetic energy densities occurs at a scale somewhat smaller than the kinetic energy peak. Above the equipartition scale the velocity structure is, as expected, nearly isotropic. The magnetic field structure at these scales is uncertain, but the field correlation function is very weak. At the equipartition scale the magnetic fields show only a moderate degree of anisotropy, so that the typical radius of curvature of field lines is comparable to the typical perpendicular scale for field reversal. In other words, there are few field reversals within eddies at the equipartition scale, and no fine-grained series of reversals at smaller scales. At scales below the equipartition scale, both velocity and magnetic structures are anisotropic; the eddies are stretched along the local magnetic field lines, and the magnetic energy dominates the kinetic energy on the same scale by a factor which increases at higher wavenumbers. We do not show a scale-free inertial range, but the power spectra are a function of resolution and/or the imposed viscosity and resistivity. Our results are consistent with the emergence of a scale-free inertial range at higher Reynolds numbers.Comment: 14 pages (8 NEW figures), ApJ, in press (July 20, 2000?

Magnetic Helicity Conservation and Astrophysical Dynamos

We construct a magnetic helicity conserving dynamo theory which incorporates a calculated magnetic helicity current. In this model the fluid helicity plays a small role in large scale magnetic field generation. Instead, the dynamo process is dominated by a new quantity, derived from asymmetries in the second derivative of the velocity correlation function, closely related to the `twist and fold' dynamo model. The turbulent damping term is, as expected, almost unchanged. Numerical simulations with a spatially constant fluid helicity and vanishing resistivity are not expected to generate large scale fields in equipartition with the turbulent energy density. The prospects for driving a fast dynamo under these circumstances are uncertain, but if it is possible, then the field must be largely force-free. On the other hand, there is an efficient analog to the $\alpha-\Omega$ dynamo. Systems whose turbulence is driven by some anisotropic local instability in a shearing flow, like real stars and accretion disks, and some computer simulations, may successfully drive the generation of strong large scale magnetic fields, provided that $\partial_r\Omega>0$. We show that this criterion is usually satisfied. Such dynamos will include a persistent, spatially coherent vertical magnetic helicity current with the same sign as $-\partial_r\Omega$, that is, positive for an accretion disk and negative for the Sun. We comment on the role of random magnetic helicity currents in storing turbulent energy in a disordered magnetic field, which will generate an equipartition, disordered field in a turbulent medium, and also a declining long wavelength tail to the power spectrum. As a result, calculations of the galactic `seed' field are largely irrelevant.Comment: 28 pages, accepted by The Astrophysical Journa