Ideal instabilities in a magnetic flux tube

Some theoretical aspects of ideal instabilities which arise in an axially symmetric magnetic flux tube are reviewed. The interest in the stability of these structures derives from the fact that their observed lifetime in astrophysical plasmas is often much longer than the relevant hydromagnetic timescale and that they exhibit a dynamical active behavior. Therefore, these structures must be globally stable with respect to fast destructive instabilities and, at the same time, must allow some local, nondisruptive process to take place. The ideal instabilities are classified in terms of their axial and azimuthal wave numbers, and the way the energy principle and normal mode approaches can lead to information on the stability properties of the models is described. The importance of the axial boundary conditions is noted, and it is shown that, when these conditions are taken into account, the nature of the instability strongly depends on the topology of the equilibrium magnetic field. 28 refs