Equilibrium magnetic fields and currents in a non-axisymmetric torus

This paper describes an investigation of the three dimensional (3-D) magnetic fields produced by currents flowing in plasmas that are confined in stellarators and in tokamaks with magnetic field ripples. A simple semianalytical procedure is proposed and a linear 3-D equation is derived that makes it possible to investigate the influence of finite pressure effects and plasma currents on the ripples of the longitudinal magnetic field. Analytical estimations are presented that can be useful for the analysis of the transport properties of finite beta plasmas. It is shown that the accuracy of the experimental identification of the magnetohydrodynamic (MHD) equilibria can be improved using external measurements of the 3-D magnetic fields. This method appears to have considerable promise for the investigation of fairly weak effects, as for example, for distinguishing bootstrap current profiles in stellarators. Analytical expressions for the 3-D external magnetic fields produced by plasma currents are derived that can be used for a rough interpretation of the experimental data