VLF wave growth and emission triggering in the magnetosphere are known to depend on the coherence of the input signal. In these experiments the input signal may take the form of a constant frequency pulse (1 s duration) or a linearly chirped pulse (also 1 s duration) with a frequency ramp (1000 Hz/s) of either positive or negative slope. When a frequency ramp of 1000 Hz/s is approximated by a contiguous sequence of short, constant frequency steps, the growth behavior is unchanged for step durations less than 25 ms. For a step duration of 25 ms, the behavior more nearly resembles that of a pure ramp, but some evidence of individual step growth can be seen. For step durations of 50 ms and 100 ms, growth is relatively small and is confined to each individual step, with little coupling between steps. Rising ramps generally show more growth than falling ramps of similar step size and average slope, confirming earlier observations. An equivalent “sawtooth” frequency variation with an average slope of zero and a step size of 25 ms behaves much like a constant frequency pulse. An interpretation of the response to step size can be found in the theory of second‐order resonance, where the spatial rates of change of the electron gyrofrequency and the Doppler‐shifted wave frequency are equal. This theory also accounts for the previously observed “dot‐dash” anomaly, where a long constant frequency pulse shows much more growth and emission triggering than a short pulse.
The rapid (<50 ms) temporal growth of ducted whistlers is simulated using controlled injection of VLF pulses from the Siple Station, Antarctica transmitter. The results show that, when the frequency‐time function of the injected pulse has a positive slope and negative curvature, producing a kind of “chirp” such that it approximates the f(t) shape of a lightning‐generated whistler at frequencies above the ‘nose’ frequency, growth up to a saturation level (20–30 dB) commonly occurs within <50 ms as opposed to 200–300 ms that is required for monochromatic input signals. The phenomenon is explained in terms of second‐order‐resonance theory [Helliwell, 1967; Carlson et al., 1985; Chang et al., 1983] where the frequency variation of the pulse matches the changing cold plasma parameters, facilitating enhanced resonance interactions over extended portions of the field line. Magnetospheric whistler‐mode signals that originate in ground sources (e.g. lightning, VLF transmitters) often stimulate or trigger nonlinear responses in the form of amplified signals, narrowband variable frequency emissions and complex sidebands [Helliwell, 1988]. One such effect commonly associated with nose whistlers is the growth of the whistler in the upper part (above the ‘nose’) of its frequency range and the associated emission triggering that tends to occur at the whistler's upper cutoff frequency (usually at 0.5 fH, where fH is the equatorial electron gyrofrequency). An example of the dynamic spectrum of such an event is shown in Figure 1a where the growth of the whistler is represented by the darkening and broadening of the upper segment of the trace. The whistler triggered emission is, in essence, a narrowband oscillation of slowly‐varying center frequency. What makes this phenomenon remarkable is the relatively short time (∼50 ms) of growth (∼20dB) of the whistler compared with the time (200–400 ms) required for a monochromatic signal under comparable conditions to exhibit the same growth [Helliwell, 1988]. Since the triggered emissions associated with whistlers and constant frequency signals (such as those from VLF transmitters) are comparable in their intensities (as observed on the ground or on satellites) and spectral characteristics, one might expect the mechanisms of their generation to be the same. On the other hand, since the typical peak intensities of whistlers excited by lightning impulses are likely to exceed the signal level injected from ground‐based transmitters that have been used in such experiments, one might simply attribute the observed difference in behavior to unknown nonlinear effects (none is suggested here) related to the high intensity of the input signals. In this paper, we describe a new experiment where the upper part (i.e. frequencies above the nose frequency [Helliwell, 1965]) of a one‐hop nose whistler is simulated using the Siple Station experimental VLF transmitter [Helliwell, 1988] to reproduce two‐hop nose whistlers that may exhibit the rapid growth described above (e.g. Figure 1a).
Whistler mode waves of various polarizations were transmitted by the Siple Station, Antarctica, VLF transmitter and received near the geomagnetic conjugate point at Lake Mistissini, Quebec. Crossed 21‐km horizontal dipole antennas on top of the 2‐km‐thick ice sheet were used to transmit 2‐ to 4‐kHz waves alternately with right‐hand circular, left‐hand circular, and linear polarizations. Excitation of a multiplicity of magnetospheric propagation paths and the received signal strength were observed to depend on the transmitter antenna polarization. Where whistler mode growth and emission triggering occurred, saturated peak values of received signals were independent of antenna polarization and initial injected power levels, in agreement with previous findings. Propagation paths of ducted Siple signals observed at Lake Mistissini were identified with propagation paths deduced from natural whistlers, from which the L shell values and equatorial number densities for the paths were calculated. A combination of L shell data and models of antenna coupling into the whistler mode may aid in the location of ducts. Dynamics Explorer 1 satellite recordings of unducted Siple signals showed trends similar to the ground data on ducted signals. The observations are discussed in the context of a simplified model of the coupling from the Siple antenna into the ionosphere, which provides reasonable agreement with observations.
A combination of simulated VLF noise, 200 Hz wide, superimposed on a variable amplitude constant frequency test signal (≈ 3 kHz) is transmitted from Siple Station, Antarctica, and received at Lake Mistissini, Quebec. As the test signal is slowly ramped up in power a “threshold” level is reached at which growth and triggering of emissions begin (coherent wave instability). Results show that sufficiently strong simulated noise surpresses the coherent wave instability, which corresponds to increasing the threshold level. This experiment is repeated at progressively lower levels of the simulated noise, until the threshold level for growth and triggering on the test signal no longer changes. At this point the simulated noise power is estimated to equal typical background noise levels due to magnetospheric hiss in the interaction region (near the equatorial plane in a duct at L ≈ 4). These results suggest that unducted magnetospheric hiss is responsible for the threshold effect.
Observations of unusual VLF signals in the 0–4 kHz range are presented which appear to be band‐limited segments of sferics and whistlers. These observations can be explained in terms of quasi‐transverse electromagnetic mode propagation over long distances in the Earth‐ionosphere waveguide.
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