Connection between thermodynamical and dynamical stability in the collisionless plasma

Abstract

The connection is discussed between the extremum properties of the free energy and information functionals previously defined for characterizing collisionless (in general nonthermal) plasma equilibria and the stability of these equilibria described by means of the dynamical equations. For a given equilibrium many information functionals can be defined, each one being associated with a special class of excitation modes. These modes are selected by a special choice of the information variables, that is the variables depending linearly on one current component or on the charge density, through which the information density depends on space. A different choice of the coefficients of the linear dependence selects the excitation modes which are related to interchanges involving different kinds of energy, as for instance (in the low β case) the part of the magnetic energy related either to the magnetization current or the guiding center drift current, or also the gravitational energy, the azimuthal kinetic energy, and so on. The condition for a minimum of the proper information is necessary and sufficient for the instability of the associated modes in an infinite plasma. This is proved for a certain class of low frequency non-MHD modes (near a marginal frequency ω = 0) by showing that the condition for a minimum of the information is the same as the condition for the existence of associated zero-frequency modes which are marginally unstable as a result of a general stability analysis based on a lagrangian formulation. In the case of low β MHD interchanges or of the gravitational instability it is shown that the minimum of the information, constructed by taking the drift current as information variable, implies a negative plasma energy variation during an interchange. So through the proper definition of the information variables and of the related interchange energy and information functional, a point of view is reached in which physically different instabilities can be seen in the frame of the same general formalism. It is hoped that, by means of a proper choice of the information variables, which can be suggested by physical considerations, other modes can be taken into account and that one can look for new possible unstable modes by examining the extremum properties of the related information functional.