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For a few years, the study of magnetoplasmadynamic instabilities has received increased attention because they may explain the so-called `onset' phenomena which limit the efficiency and, thus, the use of coaxial plasma accelerators in space propulsion and other applications. A systematic investigation of instabilities in magnetoplasmadynamic flows was initiated at the Institut für Raumfahrtsysteme in 1987. Among other instabilities, a particular one with the characteristics of the space charge instability was found. This instability had until then been known to occur only in finite gas discharge geometries. It will be shown in this paper that, in the presence of gradients of the flow variables, space charge instabilities can also appear in unbounded plasmas. The conditions for their development and growth are determined and discussed.

The investigation of magnetoplasmadynamic (MPD) instabilities in connection with the performance of MPD thrusters has received increased attention for several years. A systematic investigation of macroscopic drift and gradient driven instabilities at the Institut für Raumfahrtsysteme (IRS), carried out since 1987, showed that the occurrence of acoustic wave and space charge instabilities was possible. The calculation of the linear development of instabilities using a three-fluid theory of the plasma flow will be presented. Furthermore, in order to identify the instabilities found in the three-fluid formalism, two-fluid and one-fluid models are investigated and links established. When possible, analytical approximations for the unstable roots of the linear dispersion relation are derived, giving the explicit dependence of the oscillation frequencies and growth rates on the wavevector and the various plasma parameters.

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