Surface-charge and -current densities induced by moderately relativistic particle in cylindrical drift-tube

Using the Darwin model and method of Green´s function, we calculate the surface-charge and -current densities induced by a moderately relativistic point-like charged-particle that moves arbitrarily in a grounded, ideally conducting, unbounded circular cylindrical drift-tube. Results of analytical derivation of the quasi-static (evanescent, i.e. propagating with the speed of the point-like charge) electric and magnetic fields, which constitute together the complete space-charge field of moderately relativistic charged-particle, are presented. We explore the applicability of obtained expressions for numerical modelling of totally three-dimensional dynamics of charged-particle beams using the point-to-point interaction (PPI) method in the moderately relativistic - the first post-Newtonian - approximation.