Plasma tubes becoming collimated as a result of magnetohydrodynamic pumping Phys. Plasmas 17, 062108 (2010) Mirror instability in a plasma with cold gyrating dust particles Phys. Plasmas 17, 033701 (2010) Initial experiments using radial foils on the Cornell Beam Research Accelerator pulsed power generator Phys. Plasmas 17, 012706 (2010) The excitation of magnetorotational instability ͑MRI͒ in rotating laboratory plasmas is investigated. In contrast to astrophysical plasmas, in which gravitation plays an important role, in laboratory plasmas it can be neglected and the plasma rotation is equilibrated by the pressure gradient. The analysis is restricted to the simple model of a magnetic confinement configuration with cylindrical symmetry, in which nonaxisymmetric perturbations are investigated using the local approximation. Starting from the simplest case of an ideal plasma, the corresponding dispersion relations are derived for more complicated models including the physical effects of parallel and perpendicular viscosities. The Friemann-Rotenberg approach used for ideal plasmas is generalized for the viscous model and an analytical expression for the instability boundary is obtained. It is shown that, in addition to the standard effect of radial derivative of the rotation frequency ͑the Velikhov effect͒, which can be destabilizing or stabilizing depending on the sign of this derivative in the ideal plasma, there is a destabilizing effect proportional to the fourth power of the rotation frequency, or, what is the same, to the square of the plasma pressure gradient, and to the square of the azimuthal mode number of the perturbations. It is shown that the instability boundary also depends on the product of the plasma pressure and density gradients, which has a destabilizing effect when it is negative. In the case of parallel viscosity, the MRI looks like an ideal instability independent of viscosity, while, in the case of strong perpendicular viscosity, it is a dissipative instability with the growth rate inversely proportional to the characteristic viscous decay rate. We point out, however, that the modes of the continuous range of the magnetohydrodynamics spectrum are not taken into account in this paper, and they can be more dangerous than those that are considered.
The charged dust effect on stability of a magnetized rotating plasma is analysed using approximation of immobile dust. In the presence of the dust, a term with the electric field appears in the one-fluid equation of plasma motion. This electric field affects the equilibrium plasma rotation and also gives rise to a family of instabilities of the rotating plasma called dust-induced rotational instabilities (DRIs). The DRIs are related to the charge imbalance between the plasma ions and electrons because of the charged dust. In contrast to the wellknown magnetorotational instability driven by the radially decreasing plasma rotation frequency, the DRI can appear for an arbitrary rotation frequency profile. A mathematical technique for the analysis of the magnetorotational phenomena is presented. It is based on the one-fluid magnetohydrodynamic approach developed for a pure plasma and generalized to include the immobile dust effects. The mode equation and local dispersion relation are derived in terms of the canonical parameters.
Concrete types of viscous-resistive ballooning MHD modes in a Tokamak are investigated. It is shown that the averaged ballooning equation of incompressible disturbances, derived in Part I (1989, Plasma Phys. contr. Fusion 31, 1741), has an exact solution. The general dispersion equation of incompressible weakly ballooning modes is deduced, and different limits of this equation are considered. It is shown that viscosity results in stabilization of resistive-interchange instability in a high pressure plasma and decreases the ideal ballooning modes' increment.
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