fHF are the power density and frequency at another frequency in the spectrum (7). It follows from Eq. 2 that heating the ionosphere using radio waves at a lower frequency than that of the SPS requires a smaller power density to achieve the same heating rate as the SPS. Provided the heating is accomplished by radio waves that pass through the ionosphere (the underdense case), high-powered HF waves can be used to simulate SPS heating. In addition to heating the ionosphere through ohmic processes, the SPS microwave beam can generate instabilities driven by the heating due to the power beam. Ripples of ohmic heating which can give rise to successive perturbations in the temperature and electron density can result. The electron density perturbation leads to changes in the index of refraction, which, in turn, divert the microwave beam into the troughs of the density perturbations. The process is self-reinforcing and unstable, hence the name thermal self-focusing instability (8). At present the threshold for the onset of thermal self-focusing is thought to be proportional to the cube of wave frequency (3). Thus, an expression for the rate at which power is imparted into the self-focusing instability can be written in a form analogous to Eq. 2: Equations 2 and 3 indicate that the amount of power density associated with the operation of the SPS that goes into heating the ionospheric plasma and that could generate the thermal self-focusing instability can be simulated using much lower frequencies and power densities provided that the lower frequencies pass through the ionosphere. This provides the justification for ground-based simulation of the SPS ionospheric heating. The ground-based ionospheric heating facility located at Platteville, Colorado, and the soon to be completed heater facility located at Arecibo, Puerto Rico, funded by the United States National Science Foundation, are capable of producing continuous SPS-equivalent ohmic heating in the lower ionosphere. At higher heights, the delivered power flux density is significantly less than the frequency-scaled SPS microwave beam, following a (I//2) scaling law because the power density falls off as 1 /r2, where r is the height in the ionosphere. The power density at full HF power that scales to the SPS scenario for the onset of self-focusing (1 /f3) is greater than the SPS
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