The Six Electromagnetic Field Components at Low Frequency in an Axisymmetric Infinitely

In this study B. Zotter’s formalism is applied to a circular infinitely long beam pipe made of a conductor of infinite thickness where an offset point-charge travels at any given speed. Simple formulae are found for the impedances and electromagnetic fields both at intermediate frequencies (recovering Chao’s results) and in the low frequency regime where the usual classic thick wall impedance formula does not apply anymore due to the large skin depth compared to the pipe radius