Explosive instabilities in magnetized plasmas: a geometrical approach

Summary form only given, as follows. Explosive instabilities belong among the most interesting, yet very poorly understood phenomena in plasma physics. In some instances even the simple question of the stability of a plasma configuration and the possibility of explosive behavior presents a very difficult problem. We present a method of investigation of these instabilities for given plasma configuration that does not require the solution of non-linear dynamic equations. Our method is based on a variational approach applied to the Lagrangian of the model, combined with a geometrical treatment of plasma perturbations. The geometrical approach seems to be very promising and much simplified mathematical tool for the description of the plasma. We consider the case of ideal magnetohydrodynamics which is a simple, yet reasonably good approximation to some plasmas. This method can, however, be used in any problem where the Lagrangian can be derived. We show the simplicity and effectiveness of our method by considering several simple plasma configurations (plasma in a box, dipolar field, slightly stretched topology).