Techniques for Evaluating the Uniform Current Vector Potential at the Isolated Singularity of the Cylindrical Wire Kernel

The cylindrical wire kernel possesses a singularity which must be properly treated in order to evaluate the uniform current vector potential. Traditionally, the singular part of the kernel is extracted resulting in a slowly varying function which is convenient for numerical integration. This paper provides some new accurate and computationally efficient methods for evaluating the remaining singular integral. It is shown that this double integral may be converted to a single integral which no longer possesses a singular integrand and consequently may be efficiently evaluated numerically. This form of the integral is independent of the restrictions involving wire length and radius which are inherent in various approximations. Also presented is a highly convergent exact series representation of the integral which is valid except in the immediate vicinity of the singularity. Finally, a new approximation is derived which is found to be an improvement over the classical thin wire approximation. It is demonstrated that each of these methods provides extremely accurate as well as efficient results for a wide range of wire radii and field point locations.