A comment on Whistler mode waves with electric field in magnetospheric plasma of an outer planet

Abstract

Propagation of electromagnetic waves in plasma of magnetosphere of Jupiter, Saturn, Uranus or Neptune has been a subject of great interest. Various theoretical investigations have been carried out, where temperatures parallel and perpendicular to ambient magnetic field of magnetosphere are taken unequal (temperature anisotropy). The electric field (AC/DC) is often taken perpendicular to the magnetic field, in some investigations, the electric field is taken parallel to the magnetic field, and in few cases only magnetic field (no electric field) is considered. Case of inhomogeneous electric field perpendicular to magnetic field is also investigated. Plasma in the magnetosphere is either relativistic or non-relativistic, and various distribution laws are used. It is found that the claim made for relativistic treatment of plasma is not valid. Even for non-relativistic plasma, those all investigations are found erroneous, because of the use of wrong dispersion relation. It is also found that the same situation of investigation is published repeatedly. We have also found that by using (so claimed) expressions for propagation of wave parallel to the magnetic field for non-relativistic plasma, in very simple manner, corresponding expressions for oblique propagation of wave and for relativistic plasma are obtained, which is not realistic procedure. We have derived correct dispersion relation for propagation of waves parallel to magnetic field in non-relativistic plasma, when AC electric field perpendicular to magnetic field and for that relation, further instigation is carried out.