The stability of cylindersymmetric plasma configuration with volume currents is investigated by the method of small perturbations. The problem is reduced to only one eigen-value differential equation of second order. For
special current distribution with relativly strong concentration to the axis the eigen-values are computed numerically. For this current distribution specially for long wave lengths instability shows up. The rates of growth for different kinds of pertubations are given as a function of the wave length.
The effect of adding a By magnetic component to a solar wind already carrying a Bz magnetic component is studied using 3‐D MHD computer simulations. It is found that the tail structure and the Bx lobe fields are rotated and become asymmetric. In addition a By component is generated in the neutral sheet. These results are found to correlate with observational data.
Die Stabilität von hydrodynamischen Gleichgewichtskonfigurationen wird mit Hilfe der Methode der kleinen Störungen untersucht. Es wird gezeigt, daß das Stabilitätsverhalten durch eine Differentialgleichung 2. Ordnung in der Zeit bestimmt ist, wenn man die Viskosität, den elektrischen Widerstand und die thermische Leitfähigkeit vernachlässigt. Da die Differentialgleichung selbstadjungiert ist, können einige allgemeine Theoreme abgeleitet werden, welche für alle Gleichgewichtskonfigurationen gelten. Man kann zeigen, daß der zeitliche Anstieg von Störungen unter gewissen Bedingungen beschränkt ist. Weiterhin können einige hinreichende Bedingungen für die Stabilität angegeben werden. Für den Spezialfall, daß innerhalb eines Plasmazylinders das Magnetfeld verschwindet, werden die Differentialgleichungen explizit gelöst und Bedingungen für die Stabilität abgeleitet. Schließlich wird auch gezeigt, daß die Differentialgleichung auch selbstadjungiert ist, wenn der Druck nicht isotrop ist.
It is shown that the stability of hydromagnetic equilibrium as studied by the method of small perturbations is controlled by one differential equation of second order in time, if one neglects viscosity, electrical resistivity and thermal conductivity. Since the differential equation is self-adjoint some general theorems can be derived which hold for all configurations of hydromagnetic equilibrium. It is possible to show that the rates of growing are limited under certain conditions. Also some sufficient conditions of stability can be given. For a plasma cylinder, inside of which the magnetic field vanishes, the differential equations are solved explicitly and conditions for stability are given. Finally it is shown that the differential equation is also self-adjoint if the pressure is not isotropic.
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