Imprint of Lienard–Wiechert field on a one-dimensional manifold

Abstract A method is developed that determines parametric expressions of the electromagnetic field of a charged particle moving in vacuum on one-dimensional manifolds. This method does not require solving the retardation equation (the spatial distribution of the field is found on the basis of exact Lienard-Wiechert equations). The method is applied to a charged particle moving along a helical trajectory. One-dimensional manifolds are represented by straight lines in the plane orthogonal to the helix axis. Field packages with maximal amplitudes are identified and their motion with time is considered. It is shown that these packages are marked by the regions of the electric field line concentrations. It is shown that the field of a particle moving along the helix contains a plane with zero component along the axis of the helix. This plane is orthogonal to the helix axis and passes through the position of the particle at the time of observation.