Current distribution of a VLF electric dipole antenna in the plasmasphere

Abstract

[1] In a recent paper (Inan et al., 2003) a method of remediating enhanced energetic electron fluxes in the radiation belt was proposed in which injection of VLF whistler mode waves from spacecraft within the radiation belts would dramatically increase the pitch angle scattering of the relativistic electrons and cause these particles to be rapidly lost from the belts, thereby mitigating the flux enhancement. The VLF wave transmitting system discussed by Inan et al. (2003) involves electric dipole antennas. One of the most important characteristics of such an antenna is the current distribution along the length of the dipole, since it is this current which ultimately determines the amount of VLF power which can be radiated from the antenna into the plasma. In past work it has been assumed without proof that the dipole current has a triangular distribution. In the present work we determine the dipole antenna current distribution from first principles, constructing an integral equation of the Hallén type relating the current distribution to the wave vector potential. In this development it is assumed that the length of the thin cylindrical dipole antenna is small compared to the wavelength of whistler mode waves which propagate parallel to the Earth's magnetic field B o . In the case of the dipole antenna oriented parallel to B o , it is found that the assumption of a triangular current distribution is reasonable for antenna lengths up to hundreds of meters. For the case of the antenna perpendicular to B o , it is found that the current decays exponentially along the antenna from the feed points to the antenna ends. In this case we find the conditions under which a triangular current distribution is still a reasonable approximation. We also give the conditions under which the quasi-static model of Balmain (1964) reasonably describes the electric fields associated with the dipole antenna.

Fluid simulation of the collisionless plasma sheath surrounding an electric dipole antenna in the inner magnetosphere

“…Thus one might expect, based on our findings, that the tuning circuit used to maximize the power delivered to the antenna would be the same for each dipole element, albeit complicated. It is also clear from our warm plasma findings that for frequencies above f LHR , the complex impedance of the antenna is dominated by the sheath characteristics as opposed to the almost perfectly tuned antenna that the cold plasma model predicts [ Bell et al , 2006].…”

Dependence of quasi‐linear diffusion coefficients on wave parameters

“…Theories of VLF power radiation into a magnetized plasma currently lack consensus and verification, despite substantial analysis [ Wang and Bell , 1972; Bell et al , 2006; Song et al , 2007; Krafft and Zaboronkova , 2010], numerical simulation [ Tu et al , 2008; Chevalier et al , 2010], and experimental studies [ James , 2003; Paznukhov et al , 2010; Pribyl et al , 2010]. One notable theoretical expectation is that VLF waves are radiated most effectively at wavelengths comparable to the antenna length.…”

Generation of whistler waves by a rotating magnetic field source

“…This slow decay rate distinguishes the generation of the whistler waves by magnetic dipole and the RMF source antennas from the generation of whistler waves by an electric dipole antenna, which has been studied by many authors theoretically, experimentally, and numerically. [12][13][14][15][16][17][18] In Ref. 14 it is clearly demonstrated that in the case of linear small magnitude whistler waves driven by the electric dipole antenna the magnitude of the wave decays very fast along the ambient magnetic field even in the collisionless plasma due to the fact that the energy radiated is nearly evenly distributed inside the resonance cone.…”