Spectral analysis of the heliotron field with the toroidal harmonic function in a study of the structure of built-in divertor

Representation of the vacuum magnetic field by a set of harmonic functions is useful for an analysis of a magnetic configuration. To analyze a helical configuration precisely, a harmonic function describing a pure helicity of the configuration is desired especially in heliotrons, where the good quasi-symmetry is regarded as an advantage for a helical built-in divertor. Owing to the specific mode numbers in both the toroidal and the poloidal directions, the toroidal harmonic function is appropriate for a study of the helical field when a practical method for a numerical calculation is provided. The helical components resonant with the helicity of the coil are dominant. A deviation from the natural winding law was found to be peculiar: only the components resonant with the helicity of the coil are dominant. A deviation from the natural winding law, such as in a traditional winding law, causes an enhancement of off-resonant components. The unique toroidal coordinates and, hence, the unique spectral representation is determined by a spectral series of the maximum area for the convergence of the field expression. The high accuracy of the representation was applied to a numerical investigation of the intricate structure of a helical divertor. A reticular structure of the scrap-off layer in a helical system is visualized with a trace of unclosed separatrix. The field line at the X-point is a nearly pure helix in the toroidal coordinates, and it was confirmed that the deviation is sufficiently small for divertor baffles to be rigidly installed, even when some additional field is expected in an experiment.