Plasma instabilities are normal modes of a system that grow in space or time. Thus the word “instability” implies a well-defined relationship between wavevector k and frequency ω; this in turn implies that the associated plasma fluctuations are relatively weak so that linear theory is appropriate to describe the physics.

This book uses linear Vlasov theory to describe the propagation, damping and growth of plasma modes. Linear theory cannot describe the ultimate fate of a plasma instability, nor its interactions with other modes. Of course the questions of how an instability reaches maximum amplitude, whether and how it contributes to plasma transport and whether such transport affects the overall flow of mass, momentum and energy at large scales are crucial for establishing the relevance of microphysics to large scale modelling of space plasmas. But these questions must be addressed by nonlinear theory and computer simulation, which are beyond the purview of this book. Our relatively modest goal is to use computer solutions of the unapproximated Vlasov dispersion equation to firmly establish the properties of plasma normal modes; our hope is that this information will provide a useful foundation for the interpretation of computer simulations and spacecraft observations under conditions of relatively weak fluctuation amplitudes.

Micro- vs macro-

The most general classification of growing modes in a plasma divides them into two broad categories: macroinstabilities at relatively long wavelengths and microinstabilities at shorter wavelengths.