ABSTRACT
The confined plasma can be treated as a magnetohydrodynamic (MHD) structure. The most promising configuration is thought to be a torus in which the winding magnetic field lines form embedded magnetic surfaces. The principal difficulty to be overcome in creating such structures is to make them stable. Until recently, sufficient conditions for stable confinement had not been stated, even in the approximation of ideal MHD. The spectral method is used in most papers to investigate plasma stability. To do this, one linearizes the MHD equations around the equilibrium state and investigates the frequencies of linear oscillations. The energy principle is a simpler version of this method. This approach yields sufficient conditions for a given configuration to be unstable or for the absence of perturbations that would grow exponentially in time. The sufficient condition for stability is fulfilled if the nonlinear system under investigation has a Lyapunov functional that is positive definite for an equilibrium configuration.
