Visualizing Electromagnetic Field using Gnuplot-Part 3 Field from uniformly accelerating charged particle

Somnath Datta

NCERT

This article is a continuation of our efforts to demonstrate how to plot the E field from a time varying source, using Gnuplot. In the present case the source has been taken to be a charged particle in accelerated motion, moving with moderately relativistic (β=0.1, 0.5) to ultra relativistic (β=0.8,0.9,0.95) speeds. Two specific examples of acceleration have been taken, namely, (a) rectilinear motion under a constant force which starts and stops after a fixed interval, (b) circular motion with constant speed. The formulas used for the plots have been taken from a 1972 article by Roger Y. Tsien. However, these formulas have been re-derived in details to make the article reader friendly and pedagogical. We have highlighted the lessons that the reader can derive from these plots: (1) Clarification of concepts related to retarded time, and propagation of the E field from the source at the retarded time tr to the observer at the present time t. (2) Confirmation of the ``Purcell condition'' tanφβ=γ tan φ0, which tanφβ and tan φ0 are the angles that a given field line makes with the direction of motion, after and before a period of acceleration. (3) Insight into the phenomenon of synchrotron radiation, which is also an important component of the pulsed radiations from pulsars and the Crab nebula. The commands used for writing the relevant equations, and plotting them, have been copied from the Console into an Appendix, so that an interested reader can replicate all the plots on his personal computer.