A Paradox of Whistling Atmospherics

TL;DR

This paper discusses a paradox in electromagnetic wave propagation in moving plasmas where the group velocity remains unchanged across different frames, challenging expectations and impacting geoelectromagnetic wave analysis.

Contribution

It identifies and explains a paradox in wave group velocity in moving plasmas, highlighting its implications for understanding radio wave and plasma phenomena.

Findings

Group velocity remains the same in comoving and lab frames.

The paradox arises when frequency depends quadratically on wave number.

An explanation for the paradox is proposed.

Abstract

Analyzing paradoxes is interesting and instructive. Sometimes the analysis leads to non-trivial results. This methodological note sets out a paradox arising in the theory of propagation of electromagnetic waves in moving plasmas. The paradox is interesting in itself, and, generally speaking, it should be taken into account when analyzing geoelectromagnetic waves. The paradox is as follows: contrary to expectations, the group velocity of the waves is the same in the comoving and laboratory frames of reference. The condition for the appearance of the paradox is the quadratic dependence of the frequency on the wave number. A paradoxical property manifests itself in the theory of the propagation of radio waves (in particular, whistling atmospherics), Langmuir waves and Alfv\'en waves. From a cognitive point of view, it is interesting that the paradox can be traced in relation to de Broglie waves. An explanation of the paradox is proposed. Keywords: group velocity, moving plasma, Doppler Effect, dispersion, longitudinal waves, transverse waves.