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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.

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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.

This paper presents the results of a 3-D simulation of (e earth's ingntophere. The results show the existence of multiple x-potnts in the til. Strong plasm flow 's seen to exist in both earthward and tailward directions during formation of neutral lines. The exact magnetic field and plasma behavior is found to be very position depen dewnt'.

A fully ionized plasma is assumed. To this plasma cylindrically-symmetric magnetic fields are applied, thus causing a pinch collapse. The plasma is treated in hydromagnetic approximation, including electric and thermal conductivity. Separate temperatures are assigned to the electrons and ions.Two schemes are developed for solving numerically the resulting system of six partial differential equations: the explicit scheme for rather fast pinches, where a numerical stability requirement causes the timestep to be bounded by the characteristics given by the ALFVEN speed, and an implicit scheme, which consists essentially in converting the momentum equation into a second order difference equation with coefficients determined by iteration; here there is no such restriction on the timestep. These schemes were made to work on the U.K.A.E.A. IBM 704 and IBM 709.A run is described in which the initial state was one with uniform density, temperature and B z field. The boundary temperatures were assumed to remain constant, while the magnetic fields at the boundary were determined by the circuits for the j z and currents. The results of the computations are in good agreement with experimental results obtained at the Technische Hochschule Mün-chen by one of the authors (KÖPPENDÖRFER) .The whole program is a joint effort between A.E.R.E. Harwell and the Max-Planck-Institut, intended to discover by comparison with experiments how good the hydromagnetic approximations are. If the agreement is satisfactory (eventually using a generalised program which includes neutral gas) it should be possible to design experiments so that specified field configurations are set up. This paper treats the simplest possible model for the dynamical problem of the pinch collapse, namely a fully ionized plasma. It is the first of a series of papers dealing with calculations on the pinch. The series will describe a joint attempt by A.E.R.E. Harwell and the Max-Planck-Institut für Physik und Astrophysik, to set up quite general programs for big computers to calculate the pinch effect in hydromagnetic approximation. Within this restriction the equations should be as close as possible to the physics of the actual experiments. The comparison between experiments and these computations should give evidence on how good the hydromagnetic approximation is. It is planned to generalize this program in some respects, e. g. by including neutral gas, anisotropic pressure, toroidal geometry. Eventually one would hope to be able to design circuits to achieve field distributions specified beforehand, e. g. for reasons of stability.The paper consists mainly of three parts. In the first part the set of equations is derived and the boundary conditions are discussed. In the second part the numerical methods are described. The third part gives the comparison between experiments and computations. I. The hydromagnetic equations (two fluid model)A fully ionized plasma is assumed to fill an infinitely long cylinder. Only z and Q magnetic field components are allowed. All quantiti...

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