Magnetic island evolution in hot ion plasmas

Effects of finite ion temperature on magnetic island evolution are studied by means of numerical simulations of a reduced set of two-fluid equations which include ion as well as electron diamagnetism in slab geometry. The polarization current is found to be almost an order of magnitude larger in hot than in cold ion plasmas, due to the strong shear of ion velocity around the separatrix of the magnetic islands. As a function of the island width, the propagation speed decreases from the electron drift velocity (for islands thinner than the Larmor radius) to values close to the guiding-center velocity (for islands of order 10 times the Larmor radius). In the latter regime, the polarization current is destabilizing (i.e., it drives magnetic island growth). This is in contrast to cold ion plasmas, where the polarization current is generally found to have a healing effect on freely propagating magnetic island

Pressure-driven instabilities in astrophysical jets

Astrophysical jets are widely believed to be self-collimated by the hoop-stress due to the azimuthal component of their magnetic field. However this implies that the magnetic field is largely dominated by its azimuthal component in the outer jet region. In the fusion context, it is well-known that such configurations are highly unstable in static columns, leading to plasma disruption. It has long been pointed out that a similar outcome may follow for MHD jets, and the reasons preventing disruption are still not elucidated, although some progress has been accomplished in the recent years. In these notes, I review the present status of this open problem for pressure-driven instabilities, one of the two major sources of ideal MHD instability in static columns (the other one being current-driven instabilities). I first discuss in a heuristic way the origin of these instabilities. Magnetic resonances and magnetic shear are introduced, and their role in pressure-driven instabilities discussed in relation to Suydam's criterion. A dispersion relation is derived for pressure-driven modes in the limit of large azimuthal magnetic fields, which gives back the two criteria derived by Kadomtsev for this instability. The growth rates of these instabilities are expected to be short in comparison with the jet propagation time. What is known about the potential stabilizing role of the axial velocity of jets is then reviewed. In particular, a nonlinear stabilization mechanism recently identified in the fusion literature is discussed. Key words: Ideal MHD: stability, pressure-driven modes; Jets: stabilityComment: 20 pages, 3 figures. Lecture given at the JETSET European school "Numerical MHD and Instabilities". To be published by Springer in the "Lectures notes in physics" serie

Stability of short wavelength tearing and twisting modes

The stability and mutual interaction of tearing and twisting modes in a torus is governed by matrices that generalize the well-known {Delta}{prime} stability index. The diagonal elements of these matrices determine the intrinsic stability of modes that reconnect the magnetic field at a single resonant surface. The off-diagonal elements indicate the strength of the coupling between the different modes. The author shows how the elements of these matrices can be evaluated, in the limit of short wavelength, from the free energy driving radially extended ballooning modes. The author applies the results by calculating the tearing and twisting {Delta}{prime} for a model high-beta equilibrium with circular flux surfaces

Ballooning instabilities in tokamaks with sheared toroidal flows

The stability of ballooning modes in the presence of sheared toroidal flows is investigated. The eigenmodes are shown to be related by a Fourier transformation to the non-exponentially growing Floquet solutions found by Cooper. It is further shown that the problem cannot be reduced further than to a two dimensional partial differential equation. Next, the generalized ballooning equation is solved analytically for a circular tokamak equilibrium with sonic flows, but with a small rotation shear compared to the sound speed. With this ordering, the centrifugal forces are comparable to the pressure gradient forces driving the instability, but coupling of the mode with the sound wave is avoided. A new stability criterion is derived which explicitly demonstrates that flow shear is stabilizing at constant centrifugal force gradient. 34 refs