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

For an analysis of the magnetic field configuration it is useful to represent the vacuum magnetic field by a set of harmonic functions. To exactly analyse a helical configuration, a harmonic function describing a pure helical mode of the configuration is desirable, especially in heliotrons, where good quasi-symmetry is regarded as an advantage for a built-in helical divertor. Owing to the specific mode numbers in the toroidal and the poloidal directions, toroidal harmonic functions are appropriate for a study of the helical field when a practical method for their numerical calculation is provided. In the paper, helical components are analysed by a numerical calculation with high accuracy. From a spectral analysis of the magnetic field generated by a continuous helical coil, the ''natural winding'' law was found to be an excellent choice for the case where the components resonant with the helicity of the coil are dominant. A deviation from the natural winding law causes an enhancement of off-resonant components. The choice of unique toroidal co-ordinates and, hence, of a unique spectral representation follows naturally from the condition that the spectral series in which the magnetic field is expressed has the largest area for convergence.The high accuracy of the representation was used in a numerical investigation of the intricate structure of a helical divertor. A reticular structure of the scrape-off layer in a helical system was made visible by tracing an unclosed separatrix. The field line at the X-point is a nearly pure helix in the toroidal co-ordinates, and it was confirmed that the deviation due to perturbing fields is sufficiently small to allow a rigid divertor baffle to be installed. (author). 21 refs, 11 figs