Magnetic and drift surfaces in stellarators

In this paper we study the structure of a stellarator field in toroidal geometry. A field line tracing code is developed to explore the structure of magnetic fields on the fine scale of the electron gyroradius pe, so as to explain anomalous electron transport. The magnetic field is modelled by a simple analytic representation with finite number of parameters, so that we can integrate the field lines to a high accuracy. In a typical Heliac field we find that (i) most of the magnetic surfaces are well behaved on the fine scale, even when there is no two‐dimensional symmetry and (ii) the width of an island, formed in the vicinity of a magnetic surface with rational rotational transform i = n/m, decays exponentially with m. Among those numerical studies, we have an example where the island width w is less than the electron gyroradius pe for m greater than 17. This demonstrates that higher‐order islands do not affect the electron transport. Our numerical results indicate that the anomalous electron transport observed in experiments may be due to the presence of an ambipolar electrostatic potential Φ. To reconfirm this proposition we compute the guiding center orbits of electrons and estimate the island widths of the drift surfaces that are swept out. We find that with a small electric potential depending on toroidal and poloidal angles, the drift surface island width w is an order of magnitude larger than that without the electric potential and decays exponentially at a slower rate. Since the drift step size is of the order of the maximum of pe and w, the electron transport, which scales like the square of the step size, is enhanced when there is an electric potential.