Impact of Depth of Penetration on Mutual Inductance and Electrical Resistance of Individual Toroidal Coils Using Analytical and Finite Element Methods Applicable to Tokamak Reactors

A toroidal field coil is composed of several individual toroidal coils (ITCs) which are connected in a series and distributed in a toroidal and symmetrical form. Cross section of ITCs is rectangular or negligible. This paper presents analytical equations of mutual inductance of two ITCs applicable to tokamak reactors using the filament method. These equations are based on those formulated by Neumann. The numerical analysis of the integrations resulting from these equations is solved using the extended three-point Gaussian algorithm. The finite element method (FEM) is employed to verify the mutual inductance equations of ITCs. The results obtained using FEM, when dimensional parameters of ITCs are changed, confirm the analytical and empirical results showing an error of less than 0.2043% in the worst case. This indicates the reliability of the presented equations. This paper also employs FEM to obtain depth of penetration of electromagnetic waves in high-conductivity conductors (HCCs). The results show that the ratio of real depth of penetration, obtained by FEM, to ideal depth of penetration in HCCs is independent of frequency. This ratio shows that the magnitude of traveling plane waves in HCC decreases with
$e^{-1.7916}$
rather than
$e^{-1}$
.