ABSTRACT
This chapter deals with an explanation of the approach used to describe magnetohydrodynamic (MHD) perturbations in a cylindrical plasma in the large-aspect-ratio approximation. It provides the standard single-fluid MHD equations and explores their linearization. The chapter introduces the perturbed plasma displacement, the perturbed plasma pressure and magnetic field and the notion of plasma compressibility. Among the numerous studies on the theory of MHD instabilities in the cylindrical approximation. In one can find useful transformations of the potential energy of perturbations of a cylindrical plasma. The chapter describes the resistivity and obtain equations for resistive MHD instabilities. The key problem of the theory of MHD instabilities is to determine the conditions for ideal stability.
