Practical model and calculation of AC resistance of long solenoids

In order to study the impedance of long solenoids, a tube model has traditionally been used. The model resistance is expressed in terms of the Bessel functions. We show how to relate the model resistance to the resistance of the actual solenoid, so that the model can be better used in practice. Since the computation accuracy when using the Bessel functions may decrease quickly with increasing the magnitude of their argument, the model results can be calculated only for thin solenoids at low frequencies. This problem has traditionally been solved by using the asymptotic expressions of Bessel functions. We show the appreciable error owing to this and propose a simple approach to make a very accurate correction. Practical formulas for the ac inductance of solenoids are also given.