Systematic errors in VLF direction-finding of whistler ducts—II

In the previous paper (Strangeways, 1980) it was shown that the systematic error in the azimuthal bearing due to multipath propagation and incident wave polarisation (when this also constitutes an error) was given by only three different forms for all VLF direction-finders currently used to investigate the position of whistler ducts. In this paper the magnitude of this error is investigated for different ionospheric and ground parameters for these three different systematic error types. By incorporating an ionosphere for which the refractive index is given by the full Appleton-Hartree formula, the variation of the systematic error with ionospheric electron density and latitude and direction of propagation is investigated in addition to the variation with wave frequency, ground conductivity and dielectric constant and distance of propagation. The systematic bearing error is also investigated for the three methods when the azimuthal bearing is averaged over a 2 kHz bandwidth. This is found to lead to a significantly smaller bearing error which, for the crossed-loops goniometer, approximates the bearing error calculated when phase-dependent terms in the receiver response are ignored

Trapping of whistler-waves through the side of ducts

It is shown that, when the whistler-mode phase refractive index is plotted along the length of geomagnetic field lines as a function of altitude, there is a minimum at an altitude of between 1400 and 2200 kms depending on magnetospheric model and wave frequency. Ray-tracing calculations are presented which show that the wave normal direction of upgoing whistler-mode waves can become field-aligned at and above the altitude of the refractive index minimum and this can lead to trapping of waves through the side of a suitably positioned duct. The mechanism is made possible by the increase of refractive index along the duct length above the altitude of the refractive index minimum. Ray paths resulting from trapping by this mechanism in both a winter night and a summer day model of the magnetospheric plasma are presented and discussed

Error sources and travel time residuals in plasmaspheric whistler interpretation

In the interpretation of observed whistlers by curve fitting, systematic travel time residuals appeared which were studied by extensive simulations using ray-tracing, numerical integration and curve fitting. The residuals were found to originate from the commonly used approximations in the refractive index and ray path of whistler mode waves, which result in travel time increments or decrements, not accounted for in whistler interpretation. These approximations and the assumed form of the electron density distribution also lead to systematic errors in the diagnostics of plasmaspheric electron density by whistlers. In addition, the effects of other error sources, including random measurement errors, are also reviewed briefly. It is shown that the fine structure of residual curves is connected to propagation conditions. Thus, their study may yield a new research tool for studying whistler trapping, ducting structures and other features of whistler propagation. The application of residual analysis in conjunction with digital matched filtering of whistlers seems to be especially promising for further whistler studies

High latitude observations of whistlers using three spaced goniometer receivers

One-hop whistlers were recorded simultaneously at three high latitude stations in northern Norway during February 1978 using VLF goniometer receivers. Triangulation of the azimuthal bearings of whistlers received during an auroral substorm from 22.00 to 22.37 UT on 12 February located their whistler exit-points about 100 km to the north-east of Tromso, corresponding to an L-value for all the determinations of 6.4 ± 0.2. The frequency-time profiles of the same whistlers were analysed using the curve-fitting procedure of Tarcsai (J. atmos. terr. Phys.37, 1447, 1975) to determine their L-value of ducted propagation. These were found to lie in the L-value range 2.8–4.0, assuming a diffusive equilibrium distribution along the field lines. The L-values determined for the whistlers' exit-points were thus found to be considerably greater than that corresponding to the field line along which they were ducted. This discrepancy explained by the whistlers first following a field-aligned ducted path through the plasmasphere and then, after being reflected by sporadic-E ionisation in the lower ionosphere, following a sub-protonospheric path (Carpenteret al., J. geophys. Res.69, 5009, 1964) to higher latitude. It is shown by curve-fitting to whistler frequency—time profiles obtained by ray-tracing that such a path combination yields whistler spectra consistent with those observed

Multi-station VLF direction-finding measurements in eastern Canada

The directions of propagation, in the earth-ionosphere waveguide, of multi-component two-hop whistlers recorded on 10 July 1972 by four VLF goniometer receivers in eastern Canada have been determined. Using the bearings of these great circle paths, triangulation of several whistler exit-points has been accomplished. The L-values of the whistler exit-points determined by this method are systematically lower than those expected from their nose frequencies, by ~ 0.6. Various explanations are discussed for this effect. The most satisfactory is that the whistler waves leave through the side of the ducts (in which they had propagated for most of their path through the magnetosphere) at an altitude of a few thousand kilometres, and then are refracted to lower L-values before exiting from the lower ionosphere. The results are consistent with both the duct termination altitude predicted by Bernhardt and Park (1977) for the appropriate conditions and also with the observed upper cut-off frequency of the whistlers

Whistler mode signals from VLF transmitters, observed at Faraday, Antarctica

The Doppler shift, one-hop group travel time and arrival direction of whistler mode signals from the NAA (24kHz) and NSS (21.4kHz) VLF transmitters in eastern U.S.A. have been measured in the conjugate region, at Faraday Station, Antarctica (65°S 64°W, L=2.3). Two identical narrow-band receivers of the type described by N. R. THOMSON (J. Geophys. Res., 86,4795,1981) were used. The technique enables cross-L plasma drifts and flux tube filling and emptying rates in the inner magnetosphere to be inferred continuously with a time resolution of 15min. Ducted whistler mode signals, of typical strength ∿1 μVm^ from both transmitters were observed every night during February-March 1986,usually with multi-duct structure evident. Such structure was generally similar for the two transmitters, indicating propagation along a common set of ducts. This permitted the determination of the L-values of the ducts without reference to natural whistler data. Typical one hop group travel times were in the range 300-900ms and Doppler shifts in the range -500mHz to +500mHz. Most ducts could be tracked for several hours, and during the night their associated group travel times often exhibited a steady decrease followed by a steady increase, suggesting a change from inward to outward cross-L drifting under the action of east-west electric fields of magnitude ∿0.3mVm^. This drift reversal occurred at ∿02 LT and was accompanied by a rapid change from positive to negative Doppler shifts

Group delay times of whistler-mode signals from VLF transmitters observed at Faraday, Antarctica

The group delay times (tg) of whistler-mode waves generated by the NAA (f= 24.0 kHz) and NSS (f = 21.4 kHz) U.S. Navy transmitters and recorded at Faraday, Antarctica (L= 2.3), after following a ducted field-aligned path are analysed theoretically for different L-shells of propagation using models of electron density, temperature, and ion composition distribution for typical day and night-time conditions. tg is presented as the sum of (1) a group delay time calculated for the simplest model of wave propagation parallel to the magnetic field in a cold, dense plasma with the effects of ions neglected (tgo) and (2) the corrections due to finite electron density, that is, finite ratio of electron plasma frequency to electron gyro frequency (Δtgc), contribution of ions (Δtgr), and non-zero electron temperature (Δtgh). It is pointed out that the correction Δtgc is the dominant one, while the ratioΔtgh/Δtgc is only about 1 % for L close to 2.3. The total correction Δtgs, = Δtgc + Δtgr + Δtgh at L = 2.3is about 10 ms and is to be taken into account when interpreting the measurements of tg. However, on the assumption of strictly longitudinal propagation, the parameter [tgm(NSS) – tgm(NAA)]tgm(NSS) [index m indicates measured parameters] can be used for estimating L without taking into account the corrections Δtgs, if we do not require an accuracy better than ± 0.02