Construction of Bessel-type beamlike solutions to the Maxwell equations

The aim of this report is to construct the transient solutions to Maxwell´s equations describing the Bessel type beamlike TM waves in free space. We suppose that the current pulse of special transverse and angular distributions belongs to a plane that is at rest or starts its motion with a constant velocity v at the fixed moment of time. The explicit solutions of the initial-value problem are the transient beamlike modes of the cylindric coordinates system. We discuss peculiarities of these solutions, which describe both transient and steady-state waves