Effect of Size of a Circular Tokamak Plasma on Self-Magnetic Field: A Numerical Approach

The topology of magnetic field due to a filamentary current carrying conductor is not very difficult to follow and rich literature gives a number of clues to estimate the field at desired locations. The real situations do not always deal with the current sources that can be regarded as filamentary. One of such examples is the toroidal current in tokamak like toroidal machines and the subject points, at which the magnetic field needs to be estimated due to this current, remains, may be, at a close vicinity of the torus. For these situations, the magnetic field topology can always not be approximated by the filamentary current model, in which the entire current is assumed to flow through the geometric center of the column and the magnetic field depends on the distance from this center. Moreover, the current density in toroidal machines may have specific radial profiles and hence the corresponding impact of the profile on the external magnetic field topology needs to be explored, provided the accuracy in the estimated magnetic field is a major concern. Our previous work has reported that the cross-sectional area of the toroidal current column has a significant impact on the external magnetic field topology at the vicinity of the machine and magnetic field is very sensitive to the choice of location, at which the measurement of magnetic field, i.e., B, is subjected, though the physical interpretation for such an impact was not addressed. The present work starts by studying the impact on the nature of external magnetic field due to both the change in cross-sectional area as well as the change in the current density profiles. Consequently, the fundamental nature of dependency of magnetic field on the geometrical aspect of the source conductor is explored. Finally, all these interesting behavior are summarized in terms of mathematical interpolating expressions, which essentially conclude about the existence of a magnetic center, playing a crucial role in determining the nature of external magnetic topology. Hence, the applicability of this analysis for any toroidal machine, including tokamaks, is established.