There is a similar behaviour between the toroidal coordinates and the dipole magnetic field produced by a circular loop. In this work we evaluate up to what extent the former can be used as a representation of the latter. While the tori in the toroidal coordinates have circular cross sections, those of the circular loop magnetic field are nearly elliptical ovoids, but they are very similar for large aspect ratios. The centres of the latter displace from the axis faster than the former. By making a comparison between tori of similar aspect ratios, we find quantitative criteria to evaluate the accuracy of the approximation.

Existe cierta semejanza entre las coordenadas toroidales y el campo dipolar magnético producido por una espira circular. En este trabajo se evalúa hasta que punto las primeras pueden ser empleadas como una aproximación del segundo. Mientras que los toros de las coordenadas toroidales tienen secciones transversales circulares, los del campo de una espira circular son ovoides cercanos a elipses. Sin embargo para razones de aspecto grandes, los centros de los segundos se desplazan del eje con mayor rapidez que los primeros. Haciendo una comparación entre toros con razones de aspecto semejantes, se encuentran criterios cuantitativos para evaluar la precisión de la aproximación.

Poloidal divertors are, more than ever before, a crucial topic for the advancement of magnetic fusion technology. Due to the often non linear and stochastic nature of the plasma edge phenomena, canonical mapping has provided a powerful method at modelling their characteristics, albeit many authors rely on heuristically adapted schemes. Thus, it is reported here a specific and physically consistent map model of the tokamak single null magnetic configuration, assuming plasma-field equilibrium, based on the construction of a fundamental Hamiltonian form. Then, the magnetohydrodynamically non ideal perturbations are introduced through the Rayleigh function of the system. As an illustration, the resulting compact canonical map is applied to the analysis of some of the most relevant features of the edge magnetic topology.