Differential rotation occurs in conducting flows in accretion disks and planetary cores. In such systems, the magnetorotational instability can arise from coupling Lorentz and centrifugal forces to cause large radial angular momentum fluxes. We present the first experimental observation of the magnetorotational instability. Our system consists of liquid sodium between differentially rotating spheres, with an imposed coaxial magnetic field. We characterize the observed patterns, dynamics, and torque increases, and establish that this instability can occur from a hydrodynamic turbulent background.

A three-dimensional study of the turbulence and sheared flow generated by the drift-resistive ballooning modes in tokamak edge plasmas has been completed. The fluid simulations show that 10%–15% percent density fluctuations can develop in the nonlinear state when the self-consistently generated shear flow is suppressed. These modes are also found to give rise to poloidally asymmetric particle transport. Characteristic scale lengths of these fluctuations are isotropic in the plane transverse to B and smaller than the connection length along the field line. Sheared poloidal flow is self-consistently driven by both the Reynolds stress and the Stringer mechanisms. In the presence of self-consistent shear flow, the transverse spectrum is no longer isotropic transverse to B. The vortices become elongated in the poloidal direction. Also, there is a substantial reduction in both the level of fluctuations of the density and potential and the associated particle transport. These features are in qualitative agreement with L–H transitions observed in tokamaks.

An analytical and numerical study of the stability of tearing modes is carried out using the Braginskii fluid equations. An electron temperature gradient coupled with finite (nonzero) parallel thermal conductivity causes large parallel currents to flow in the vicinity of the singular layer (where k⋅B=0). The pressure-driven currents are stabilizing and in the limit βL2s/L2n>1, where β is the ratio of the thermal to magnetic pressure and Ls and Ln are the magnetic shear and density scale lengths, the linear tearing mode no longer exists. In this high-β limit, the magnetic perturbation of the tearing mode is completely shielded from the singular layer so that no reconnection of the magnetic field can take place. The relationship between the tearing mode and previously investigated temperature-gradient-driven modes and the implications of the results for resistive modes in present and future tokamak discharges is discussed.

A simplified MHD model is proposed that explains characteristic features of dipolarization fronts observed by the five‐probe THEMIS mission, and in particular the recurrent or multiple fronts, as structures arising from the nonlinear evolution of the interchange instability of the initial reconnection ejecta in the terrestrial magnetotail. Modeling the effects of the magnetic field curvature and plasma braking by an effective gravity and imposing an initial seed perturbation consistent with the observed dawn‐dusk scale of fronts is shown to reproduce the observed variations of the north‐south magnetic field, bulk flow plasma velocity, number density and pressure.

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