Plasma sheath structures around a radio frequency antenna

Abstract

A one‐dimensional particle‐in‐cell (PIC) simulation code is developed to investigate plasma sheath structures around a high‐voltage transmitting antenna in the inner magnetosphere. We consider an electrically short dipole antenna assumed to be bare and perfectly conducting. The oscillation frequency of the antenna current is chosen to be well below the electron plasma frequency but higher than the ion plasma frequency. The magnetic field effects are neglected in the present simulations. Simulations are conducted for the cases without and with ion dynamics. In both cases, there is an initial period, about one‐fourth of an oscillation cycle, of antenna charging because of attraction of electrons to the antenna and the formation of an ion plasma sheath around the antenna. With the ion dynamics neglected, the antenna is charged completely negatively so that no more electrons in the plasma can reach the antenna after the formation of the sheath. When the ion dynamics are included, the electrons impulsively impinge upon the antenna while the ions reach the antenna in a continuous manner. In such a case, the antenna charge density and electric field have a brief excursion of slightly positive values during which there is an electron sheath. The electron and ion currents collected by the antenna are weak and balance each other over each oscillation cycle. The sheath–plasma boundary is a transition layer with fine structures in electron density, charge density, and electric field distributions. The sheath radius oscillates at the antenna current frequency. The calculated antenna reactance is improved from the theoretical value by 10%, demonstrating the advantage of including the plasma sheath effects self‐consistently using the PIC simulations. The sheath tends to shield the electric field from penetrating into the plasma. There is, however, leakage of an electric field component with significant amplitude into the plasma, implying the applicability of the high‐voltage antennas in whistler wave transmission in the inner magnetosphere.

Impedance characteristics of an active antenna at whistler mode frequencies

“…The frequency range covered by the V71 experiment was 18–80 kHz with 300 Hz steps and a dwell time on each frequency of ∼0.125 s. For each frequency, the radiation lasted for more than 2000 cycles. If the antenna charging took few wave cycles as shown by Tu et al [2008], the radiation can be considered steady state transmission. The RMS voltage was calculated by averaging RF samples for each frequency once every 3 min.…”

“…The sheath radius goes to zero at the maximum of the AC voltage and becomes largest when the voltage is at its minimum. Tu et al [2008] presented a full‐particle simulation of these processes. They confirmed the basic ideas of the model and further showed that the antenna charging process takes only less than a wave cycle.…”

“…While these works have brought a conceptual understanding of the antenna‐plasma interaction, some models often lacked self‐consistency, since in most cases electrostatic conditions were assumed and the radiation resistance was not considered in the system. A new self‐consistent model has recently been proposed by Song et al [2007] and numerically investigated by Tu et al [2008]. In the former work, an analytical solution for a time‐dependent one‐dimensional situation was presented while assuming immobile ions.…”

Radiation pattern of a ULF space-based antenna for controlled removal of energetic trapped protons

“…His approximation, however, neglects the divergence of the plasma current due to the transverse electric field, which correctly captures the radiation resistance but is not capable of reproducing the imaginary part of the impedance. There are also studies about the formation of a thick oscillatory sheath around an electric dipole antenna [6], [7], [9], [14], and about the effect of this perturbed plasma region on the radiation impedance and the current distribution along the antenna [4], [5]. For non-capacitive loop antennas, however, there are only far-field analyses of single loop configurations, like the quasi-static approximations by Wang and Bell [19], [20], [21] which provided analytical expressions for the radiation impedance of a small filamentary ULF/VLF loop antenna immersed in a cold magnetized plasma.…”

Whistler waves with angular momentum in space and laboratory plasmas and their counterparts in free space

“…Any current-carrying or magnetized object in motion creates a Cherenkov-like wing of whistler or Alfvén waves, depending on the source size compared to the wavelength [30,31]. In order to excite large amplitude whistlers with electric dipoles the sheath nonlinearity creates unknown effects [32,33]. Likewise magnetic loops can distort the near-zone magnetic field which creates unknown radiation patterns.…”