Buoyancy Instabilities in Weakly Magnetized Low Collisionality Plasmas

I calculate the linear stability of a stratified low collisionality plasma in the presence of a weak magnetic field. Heat is assumed to flow only along magnetic field lines. In the absence of a heat flux in the background plasma, Balbus (2000) demonstrated that plasmas in which the temperature increases in the direction of gravity are buoyantly unstable to convective-like motions (the ``magnetothermal instability''). I show that in the presence of a background heat flux, an analogous instability is present when the temperature decreases in the direction of gravity. The instability is driven by the background heat flux and the fastest growing mode has a growth time of order the local dynamical time. Thus, independent of the sign of the temperature gradient, weakly magnetized low collisionality plasmas are unstable on a dynamical time to magnetically-mediated buoyancy instabilities. The instability described in this paper is predicted to be present in clusters of galaxies at radii from ~ 0.1-100 kpc, where the observed temperature increases outwards. Possible consequences for the origin of cluster magnetic fields, ``cooling flows,'' and the thermodynamics of the intercluster medium are briefly discussed.Comment: 5 pages; 1 cartoon; ApJ in pres

The Character of Transport Caused by ExB Drift Turbulence

The basic character of diffusive transport in a magnetised plasma depends on what kind of transport is modelled. ExB turbulence under drift ordering has special characteristics: it is nearly incompressible, and it cannot lead to magnetic flux diffusion if it is electrostatic. The ExB velocity is also related to the Poynting energy flux. Under quasineutral dynamics, electric fields are not caused by transport of electric charge but by the requirement that the total current is divergence free. Consequences for well constructed computational transport models are discussed in the context of a general mean field analysis, which also yields several anomalous transfer mechanisms not normally considered by current models.Comment: 31 pages including 2 figures, submitted to Physics of Plasma

Compressible MHD Turbulence in Interstellar Plasmas

Radio-wave scintillation observations reveal a nearly Kolmogorov spectrum of density fluctuations in the ionized interstellar medium. Although this density spectrum is suggestive of turbulence, no theory relevant to its interpretation exists. We calculate the density spectrum in turbulent magnetized plasmas by extending the theory of incompressible MHD turbulence given by Goldreich & Sridhar to include the effects of compressibility and particle transport. Our most important results are as follows. (1) Density fluctuations are due to the slow mode and the entropy mode. Both modes are passively mixed by the cascade of shear Alfven waves. Since the shear Alfven waves have a Kolmogorov spectrum, so do the density fluctuations. (2) Observed density fluctuation amplitudes imply either that the magnetic and gas pressures are comparable, or that the outer scale of the turbulence is very small. (3) A high degree of ionization is required for the cascade to survive damping by neutrals and thereby to extend to small lengthscales. Regions that are insufficiently ionized produce density fluctuations only on lengthscales larger than the neutral damping scale. These regions may account for the excess of power that is found on large scales. (4) Both the entropy mode and the slow mode are damped on lengthscales below that at which protons can diffuse across an eddy during the eddy's turnover time. Consequently, eddies whose extents along the magnetic field are smaller than the proton collisional mean free path do not contribute to the density spectrum. However, in MHD turbulence eddies are highly elongated along the magnetic field. From an observational perspective, the relevant lengthscale is that transverse to the magnetic field. Thus the cut-off lengthscale for density fluctuations is significantly smaller than the proton mean free path.Comment: 19 pages, 2 figures, submitted to Ap

Nonlinear polarisation and dissipative correspondence between low frequency fluid and gyrofluid equations

The correspondence between gyrofluid and low frequency fluid equations is examined. The lowest order conservative effects in ExB advection, parallel dynamics, and curvature match trivially. The principal concerns are polarisation fluxes, and dissipative parallel viscosity and parallel heat fluxes. The emergence of the polarisation heat flux in the fluid model and its contribution to the energy theorem is reviewed. It is shown that gyroviscosity and the polarisation fluxes are matched by the finite gyroradius corrections to advection in the long wavelength limit, provided that the differences between gyrocenter and particle representations is taken into account. The dissipative parallel viscosity is matched by the residual thermal anisotropy in the gyrofluid model in the collision dominated limit. The dissipative parallel heat flux is matched by the gyrofluid parallel heat flux variables in the collision dominated limit. Hence, the gyrofluid equations are a complete superset of the low frequency fluid equations.Comment: RevTeX 4, 28 pages, no figures, final revised version for Physics of Plasmas prior to proof stag

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

Inertial range turbulence in kinetic plasmas

The transfer of turbulent energy through an inertial range from the driving scale to dissipative scales in a kinetic plasma followed by the conversion of this energy into heat is a fundamental plasma physics process. A theoretical foundation for the study of this process is constructed, but the details of the kinetic cascade are not well understood. Several important properties are identified: (a) the conservation of a generalized energy by the cascade; (b) the need for collisions to increase entropy and realize irreversible plasma heating; and (c) the key role played by the entropy cascade--a dual cascade of energy to small scales in both physical and velocity space--to convert ultimately the turbulent energy into heat. A strategy for nonlinear numerical simulations of kinetic turbulence is outlined. Initial numerical results are consistent with the operation of the entropy cascade. Inertial range turbulence arises in a broad range of space and astrophysical plasmas and may play an important role in the thermalization of fusion energy in burning plasmas.Comment: 11 pages, 2 figures, submitted to Physics of Plasmas, DPP Meeting Special Issu

Impurity and Trace Tritium Transport in Tokamak Edge Turbulence

The turbulent transport of impurity or minority species, as for example Tritium, is investigated in drift-Alfv\'en edge turbulence. The full effects of perpendicular and parallel convection are kept for the impurity species. The impurity density develops a granular structure with steep gradients and locally exceeds its initial values due to the compressibility of the flow. An approximate decomposition of the impurity flux into a diffusive part and an effective convective part (characterized by a pinch velocity) is performed and a net inward pinch effect is recovered. The pinch velocity is explained in terms of Turbulent Equipartition and is found to vary poloidally. The results show that impurity transport modeling needs to be two-dimensional, considering besides the radial direction also the strong poloidal variation in the transport coefficients.Comment: 12 Pages, 5 Figure

Late-Time Convection in the Collapse of a 23 Solar Mass Star

The results of a 3-dimensional SNSPH simulation of the core collapse of a 23 solar mass star are presented. This simulation did not launch an explosion until over 600ms after collapse, allowing an ideal opportunity to study the evolution and structure of the convection below the accretion shock to late times. This late-time convection allows us to study several of the recent claims in the literature about the role of convection: is it dominated by an l=1 mode driven by vortical-acoustic (or other) instability, does it produce strong neutron star kicks, and, finally, is it the key to a new explosion mechanism? The convective region buffets the neutron star, imparting a 150-200 km/s kick. Because the l=1 mode does not dominate the convection, the neutron star does not achieve large (>450 km/s) velocities. Finally, the neutron star in this simulation moves, but does not develop strong oscillations, the energy source for a recently proposed supernova engine. We discuss the implications these results have on supernovae, hypernovae (and gamma-ray bursts), and stellar-massed black holes.Comment: 31 pages (including 13 figures), submitted to Ap