Analytical field results for low aspect ratio stellarator configurations

One of the ways of exploring the existence of nonergodic vacuum magnetic configurations in nonaxisymmetric toroidal confinement systems has been through the use of the magnetic scalar potential φM. In the absence of a macroscopic current density in a region of space, the magnetic field can be described as H=-∇φM, B=μ0(H+M) where M is the magnetization density. Considering the case of the volume enclosed in a torus with surface current densities flowing on its boundary, we can reproduce the magnetic field inside the domain in the following way: i) given the current j flowing on the surface we can replace it by an equivalent magnetization density M outside the torus so that ∇ΛM=j; ii) we then evaluate ∇·M outside the torus; iii) we finally solve the Laplace-Poisson scalar problem ∇2φM=∇·M. (author) 5 refs., 4 figs