Some Results of a Mode‐Conversion Program for VLF

Abstract

A mode-conversion program has been developed which allows for the vertical inhomogeneity of the ionosphere as well as its anisotropy. As an illustration of the potential use of the program for diagnostic studies at VLF, the sunrise amplitude study of Walker [1965] is numerically modelled with allowance for four modes. Exponential profiles of varying reference height and scale height are used to simulate the terminator. Of the models studied, best agreement is obtained with a terminator thickness of 1000 kin. Despite the multimode nature of the models, Crarnbie's [1964] model is found to be valid for the path studied. This is because of weak conversion from the third and fourth nighttime modes to the first daytime mode. INTRODUCTION Crombie [1964] utilized mode-conversion concepts to explain phase steps and amplitude fading at dawn and dusk. His explanation is based on two modes being present in the nighttime portion of the path and only one mode in the daytime portion of the guide. In addition to fitting most experimental data, Crombie's explanation had consequences which were capable of verification by further experimental evidence. Walker [1965] reported results of an experiment designed especially for testing the consequences of Crombie's explanation. Involved in the experiments were a mobile monitor station on board ship and a permanent ground monitor station both of which recorded phase and amplitude of 18.0-kHz signals from Balboa (NBA). Walker's results fully supported Crombie's explanation. Bicket et al. [1970] in a series of in-flight nighttime VLF measurements along radials from Hawaii have convincingly demonstrated that more than two modes are significant during nighttime at 23.4 kHz. Using a nighttime profile (• = 0.5 km -• h -86 km in the notation of Wait and Spies [1964]) similar to that proposed by Bickel et al . [1970] and propagation conditions closely approximating those of Walker's experiment, a mode sum was generated for 18.6 kHz (this frequency rather than 18.0 kHz is used throughout this paper because of the availability of eigenangles from a previous study), and at least four modes were found to be significant.The waveguide program used to generate the mode constants was that reported by Pappert et al. [1967].Recently a mode-conversion program has been developed which allows fully for the vertical inhomogeneity of the ionosphere as well as its anisotropy. As an example of .the application of the program, the sunrise amplitude study of Walker, specifically the occurrence of simultaneous minima during sunrise, is numerically modelled with allowance for four modes. Several terminator models are used in the study. Despite the multimode feature of the nighttime portion of the path we find, using a daytime profile in which • = 0.3 km -x and h -70 km and a terminator thickness of 1000 km,

ELF waves generated by modulated HF heating of the auroral electrojet and observed at a ground distance of ∼4400 km

“…The numerical analysis performed in this section relies on two separate physical models: one model to calculate ELF wave propagation in the Earth‐ionosphere waveguide and one model to calculate the altitude of the Hall current maximum during the HF heating process. In order to approximate the ELF energy coupling to the Earth‐ionosphere waveguide we employ the long‐wave propagation capability (LWPC) code [ Pappert and Snyder , 1972; Pappert and Morfitt , 1975; Ferguson and Snyder , 1987], a multiple‐mode model that uses realistic parameters for the ground conductivity, the Earth's magnetic field, and the altitude profile of nighttime ionospheric conductivity. LWPC is a two‐dimensional (2‐D) code which accounts for coupling between waveguide modes and necessarily assumes ionospheric homogeneity in the dimension transverse to the direction of propagation [ Pappert and Snyder , 1972; Ferguson and Snyder , 1987].…”

“…In order to approximate the ELF energy coupling to the Earth‐ionosphere waveguide we employ the long‐wave propagation capability (LWPC) code [ Pappert and Snyder , 1972; Pappert and Morfitt , 1975; Ferguson and Snyder , 1987], a multiple‐mode model that uses realistic parameters for the ground conductivity, the Earth's magnetic field, and the altitude profile of nighttime ionospheric conductivity. LWPC is a two‐dimensional (2‐D) code which accounts for coupling between waveguide modes and necessarily assumes ionospheric homogeneity in the dimension transverse to the direction of propagation [ Pappert and Snyder , 1972; Ferguson and Snyder , 1987]. Given an altitude and orientation of the radiating dipole, along with the electron density variation with altitude along the path of propagation, LWPC is used to calculate the radial and azimuthal magnetic field components at the receiver.…”

Ionospheric D region electron density profiles derived from the measured interference pattern of VLF waveguide modes

“…Wave propagation in the Earth‐ionosphere waveguide can be quantitatively modeled using the Long Wave Propagation Capability (LWPC) code developed by the Naval Oceans System Center [ Ferguson and Snyder , 1990; Ferguson , 1998]. Based on the two‐dimensional waveguide mode formulation of Budden [1962], which accounts for the curvature of the Earth, the D region electron density profile, and the Earth's magnetic field, the computer code was developed and experimentally verified by R. A. Pappert and his colleagues at the Naval Ocean Systems Center [ Pappert and Snyder , 1972; Pappert and Morfitt , 1975; Pappert and Ferguson , 1986]. LWPC is presently used as the standard model of VLF propagation, both by the U.S. Navy, and by the ionospheric research community [e.g., Cummer et al , 1997].…”

Lightning‐induced electron precipitation events observed at L ∼ 2.4 as phase and amplitude perturbations on subionospheric VLF signals

“…For realistic models of the lower ionosphere and ground conductivity, the mode analysis is complicated by the fact that each waveguide mode has a different attenuation rate along the propagation path [Wait and Spies, 1964], in addition to the differences that exist in the excitation efficiency at the source (usually a vertical antenna) for each mode. As discontinuities (such as sea-ground, sea-ice interfaces or localized ionospheric perturbations) are encountered along the signal path, mode conversion effects must also be taken into account [Pappert and Snyder, 1972]. In general the analysis of a given problem requires the use of a computer-based modeling approach [Tolstoy et al, 1982[Tolstoy et al, , 1986, using average models of the lower ionopshere [Ferguson, 1980].…”