The Four-Vector Potential for Arbitrary Sources in Cylindrical Drift Tube

Using the method of Green functions we found the four-vector potential and electromagnetic field components for a charge moving along an arbitrary path in a perfectly conducting cylindrical waveguide. Solutions are expressed analytically through the Green functions of the d´Alembert operator with Dirichlet and Neumann boundary conditions. Boundary conditions for a four-vector potential in cylindrical coordinates are obtained via analysis of those for corresponding fields on the perfectly conducting surface and the Lorentz gauge condition. We also propose a method, which enables one to reduce the problem for the vector potential to a system of scalar d´Alambert equations in cylindrical coordinate system.