Ideal MHD instabilities

Macroturbulence in plasma is generated by MHD instabilities. These instabilities can be classfied as ‘ideal’ and ‘resistive’: dissipative processes play no role in ideal MHD and play an essential role in resistive MHD. Ideal MHD instabilities can be further divided according to the source of free energy and to the geometric structure of the plasma. In this Section we summarize the ideal MHD instabilities which depend solely on the geometric structure of the plasma. This topic is of central importance for laboratory devices, such as tokamaks, which need to be designed to maximize the confinement time. It is also of interest in astrophysical applications, e.g. to the stability of magnetic loop structures in the solar atmosphere. Our primary interest in this Chapter is in the generation and dissipation of MHD turbulence; the ideal MHD instabilities discussed in this Section are not particularly effective in generating turbulence because the supply of free energy is limited to that made available from changing the geometric configuration of the plasma. The discussion of these instabilities here involves little more than an introduction to the terminology used to describe the various instabilities and brief summaries of their properties.

A plasma confined by a magnetic field is intrinsically unstable. This follows from the fact that the only stable solution of the Vlasov equation is a uniform Maxwellian distribution, and this is independent of the presence or absence of a magnetic field.