Electric field lines of relativistically moving point charges

Abstract

Generation of electromagnetic fields by moving charges is a fascinating topic where the tight connection between classical electrodynamics and special relativity becomes particularly apparent. One can gain direct insight into the fascinating structure of such fields by visualizing the electric field lines. However, the calculation of electric field lines for arbitrarily moving charges is far from trivial. Here, we derive an equation for the director that points from the retarded position of a moving charge towards a specific field line position, which allows for a simple construction of these lines. We analytically solve this equation for several special but important cases: for an arbitrary rectilinear motion, for the motion within the wiggler magnetic field of a free electron laser, and for the motion in a synchrotron. arXiv:1809.05868v2 [physics.class-ph]

Extreme Electron Acceleration with Fixed Radiation Energy

“…Kinetic processes responsible for converting the outflow energy of blazars, pulsar wind nebulae, and gamma ray bursters into electron acceleration radiation allow electrons to be accelerated to very high Lorentz factors before radiation damping is appreciable; see, e.g., [ 34 ]. The electric fields lines experience a tight stretching effect due to their non-uniform acceleration relative to uniform acceleration (see Figures 2 and 3 of [ 35 ]). An illustration of the electric field lines is shown in Figure 8 .…”

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“…Field line sections in between these boundaries describe a field affected by the charge acceleration. This example is well known and well investigated [21,22].…”

Space-Time Computation and Visualization of the Electromagnetic Fields and Potentials Generated by Moving Point Charges

“…These often involve fairly complex vector calculus and can leave many students struggling to visualize or appreciate the solution. It is therefore unfortunate that few computational approaches have been developed to model such moving potential problems [4]. Unlike many acclaimed simulation * matthew.filipovich@queensu.ca tools with Maxwell's equations, such as the finite-difference time-domain (FDTD) method, there are no well known approaches to computationally solving problems with moving charges directly in space and time.…”