We evaluate the conductivity tensor for molecular gas at densities ranging from 10^4 to 10^15 cm^-3 for a variety of grain models. The Hall contribution to the conductivity has generally been neglected in treatments of the dynamics of molecular gas. We find that it is not important if only 0.1 micron grains are considered, but for a Mathis-Rumpl-Nordsieck grain-size distribution (with or without PAHs) it becomes important for densities between 10^7 and 10^11 cm^-3. If PAHs are included, this range is reduced to 10^9 -- 10^10 cm^-3. The consequences for the magnetic field evolution and dynamics of dense molecular gas are profound. To illustrate this, we consider the propagation of Alfven waves under these conditions. A linear analysis yields a dispersion relation valid for frequencies below the neutral collision frequencies of the charged species. The dispersion relation shows that there is a pair of circularly polarised modes with distinct propagation speeds and damping rates. We note that the gravitational collapse of dense cloud cores may be substantially modified by the Hall term.Comment: MNRAS accepted; 9 pp incl 8 figs, LaTeX, uses epsf.sty mn.st

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Weak magnetohydrodynamic turbulence in the presence of a uniform magnetic field is dominated by three-wave interactions that mediate the collisions of shear-Alfvén wave packets propagating in opposite directions parallel to the magnetic field. The scaling of three-wave couplings is calculated by asymptotic analysis and a direct numerical evaluation of the nonlinear interaction based on the reduced magnetohydrodynamic equations. A new relation is derived between the spectral index of three-wave coupling and the spectral indices of two random-amplitude wave packets. This relation has significant implications for the anisotropic energy spectrum.

Reconnection in nature is generically not quasi-steady. Most often, it is impulsive or bursty, characterized not only by a fast growth rate but a rapid change in the time-derivative of the growth rate. New results, obtained by asymptotic analyses and high-resolution numerical simulations ͓using Adaptive Mesh Refinement͔ of the Hall magnetohydrodynamics ͑MHD͒ or two-fluid equations, are presented. Within the framework of Hall MHD, a two-dimensional collisionless reconnection model is considered in which electron inertia provides the mechanism for breaking field lines, and the electron pressure gradient plays a crucial role in controlling magnetic island dynamics. Current singularities tend to form in finite time and drive fast and impulsive reconnection. In the presence of resistivity, the tendency for current singularity formation slows down, but the reconnection rate continues to accelerate to produce large magnetic islands that eventually become of the order of the system size, quenching near-explosive growth. By a combination of analysis and simulations, the scaling of the reconnection rate in the nonlinear regime is studied, and its dependence on the electron and the ion skin depth, plasma beta, and system size is determined.

The damping of plasma oscillations in a weakly collisional plasma is revisited using a Fokker-Planck collision operator. It is shown that the Case-Van Kampen continuous spectrum is eliminated in the limit of zero collision frequency and replaced by a discrete spectrum. The Landau-damped solutions are recovered in this limit, but as true eigenmodes of the weakly collisional system. For small but nonzero collision frequency, the spectra and eigenmodes are qualitatively different from their counterparts in the collisionless theory. These results are consistent with recent experimental findings.

Electron acceleration by dispersive scale Alfvén waves at Jupiter is investigated using a Gyrofluid‐Kinetic‐Electron model. Specifically, the simulations consider the propagation of an Alfvén wave perturbation from the center of the Io plasma torus to high‐latitude regions that are consistent with recent Juno satellite observations (e.g., Allegrini et al., 2017, https://doi.org/10.1002/2017GL073180; Mauk, et al., 2017a, https://doi.org/10.1038/nature23648; Mauk, et al., 2017b, https://doi.org/10.1002/2016GL072286; Szalay et al., 2018, https://doi.org/10.1029/2018JE005752). As in those observations, the energized electron spectra is broadband in nature and the majority of the energization is under the interaction of inertial Alfvén waves at high latitudes. The extent of the energization associated with these waves is proportional to both the magnitude of the wave perturbation and the ratio of the torus to high‐latitude density.

The interstellar medium and solar wind is permeated by a magnetic field that renders magnetohydrodynamic turbulence anisotropic. In the classic work of Iroshnikov [Astron. Zh. 40, 742 (1963)] and Kraichnan [Phys. Fluids 8, 1385 (1965)], it is assumed that the turbulence is isotropic, and an inertial range energy spectrum that scales as k−3/2 is deduced based on the nonlinear interaction of Alfvén wave packets. Much insight can be gained by analysis and high-resolution numerical simulations of such interactions. In the weak-turbulence limit in which three-wave interactions dominate, analytical and high-resolution numerical results based on random scattering of shear-Alfvén waves propagating parallel to a large-scale magnetic field demonstrate an anisotropic energy spectrum that scales as k⊥−2. Even in the absence of a background magnetic field, when the energy spectrum is globally isotropic, anisotropy is found to develop with respect to the local magnetic field. The two-dimensional case is studied by means of simulations and phenomenological arguments. Despite the presence of local anisotropy, we obtain the Iroshnikov–Kraichnan spectrum, rather than the Kolmogorov spectrum. The same techniques are used to study turbulence in electron magnetohydrodynamics where whistler waves mediate the energy cascade, and comparisons are made with turbulence in magnetohydrodynamics.

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