Improvement in calculation of the self- and mutual inductance of thin-wall solenoids and disk coils

The self-inductance expressions given by Yu and nan (1987) for air-core circular coils with rectangular cross sections, thin solenoids, and disk coils can be solved only by the numerical integration methods. We propose as an alternative a combined analytic and numeric approach. The approach brings some improvement in the calculations of self-inductance of thin-wall solenoids and disk coils that can be encountered in superconducting magnetic energy storage (SMES) problems. We also give a method for the calculation of mutual inductance of disk coils and of thin-wall solenoids. The results are obtained in an analytical form over the complete elliptic integrals of the first and second kind and Heuman's Lambda function. It is important to mention that the kernels of these integrals are always continuous functions on intervals of integration, so singularities are avoided. The results enable one to calculate the self-inductance and the mutual inductance of any thin air-core coil precisely and fast. For practical applications, the results are so simple to use that we recommend them to avoid the problems of solving the singular cases.