Equilibrium magnetic fields and currents in a nonaxisymmetric torus: external magnetic fields in stellarators

The three dimensional (3-D) and axisymmetric (2-D) magnetic fields produced by currents flowing in plasmas that are confined in stellarators with a nearly planar geometrical axis are investigated. Using the Green's function method to solve the 3-D linear equation derived previously, a simple procedure is presented here to determine the structure of plasma induced external magnetic fields in stellarators. A detailed numerical analysis of the values of the external 3-D magnetic fields and their dependences on the plasma profiles is performed. Analytical formulas are derived that could be useful for estimations. The possibility of using the measurements of these fields for the experimental identification of the magnetohydrodynamic (MHD) equilibria is considered. Also discussed are some interesting aspects of the influence of the magnetic hump on the value of the Pursch-Schluter currents (that appear in recent Heliotron-E experiments) and the influence of different features of the vacuum magnetic field on the dipole component of plasma induced field is classified. The results of calculations related to the modern experiments are presented, and the case that may be typical for future experiments is also considered