Abstract
The self-inductance for an infinitely long helical conductor and the mutual inductancebetween two coaxial helical conductors are investigated over the whole range from solenoidswith an infinitesimal pitch length to straight conductors with an infinite pitch length. Theprincipal terms, apart from the logarithmically divergent term due to the infinite length ofthe self- and mutual inductances, are rigorously obtained, evaluating the double integrals ofNeumann’s formula, using analytical expressions for the vector potential of asingle helical thin conductor. The relations between the conventional approximateand the rigorously obtained expressions for the self- and mutual inductances ofsolenoids are also compared. This analytical method is applied for calculations ofthe self-inductance of a twisted bifilar lead and for the current distribution of atwisted superconducting 6 around 1 strand cable with insulated strands, using thecancellation of the logarithmically divergent term. As a result, it is shown that theanalytical method for the inductance calculation for infinitely long helical conductorsis useful, by obtaining results consistent with the magnetic energy calculation.
Published Version
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