A harmonic expansion for the magnetic field of the helical solenoid
The authors study a boundary value problem for finding the scalar magnetic potentials inside and outside of a helically symmetric solenoid. The conventional Fourier-Bessel series for the interior and exterior potentials are introduced. Ignoring the question of convergence for the moment, the partial sums of series are used to approximate the potentials numerically. A Green's function integral representation for the series coefficients is derived and the asymptotic behaviour of these coefficients is calculated by the technique of saddle point integration in the complex plane. Two transcendental equations whose solutions are the radii of convergence of the series for the interior and exterior potentials are derived.
Green's function integral representation
scientific article; zbMATH DE number 4064428