focusing process organizes the plasma into large-scale density irregularities or striations. The threshold for creating these striations depends on the striation width Xx. As the electric field intensity of the incident radiation increases, the resulting selffocused striations become narrower. The threshold power flux density for under- dense thermal self-focusing in the ionosphere is given by (9) where Eo is the electric field amplitude of the incident wave, D = kiL/2k0 — (Xx • b) L, k is the wave vector perpendicular to the radio-wave propagation direction, h is the direction of the magnetic field, L is the ionosphere scale height, k0 = hrflc', nm is the maximum plasma density, Xo = c/f; Xmfp is the electron mean free path, and nc is the critical electron density at f„ = f. For a reasonable spatial growth rate (D = 5) and typical ionospheric conditions, the SPS self-focusing threshold is approximately 50 W/m2, well below the proposed microwave power flux density of 230 W/m2. Thus, beam self-focusing is expected to occur for the solar power satellite. The resulting striation width is approximately 500 m, with induced density fluctuations of a few percent. Another study, assuming an initial condition that low-level spatially- coherent density fluctuations are already naturally present in the ionosphere, predicts density variations of up to 80% (10). In both studies, the SPS microwave beam is predicted to generate large-scale ionospheric irregularities. The environmental and system impacts of this process will depend on the degree of beam self-focusing, the size and geometry of the resulting large-scale density striations, and the magnitude of the density fluctuations within the irregularities. Secondary instabilities may develop along the striation density gradients. Ionospheric striations may cause scintillation of radio waves using trans- ionospheric propagation through the perturbed region, including the SPS pilot beam. In addition, HF radio waves will undergo multiple reflections in the striated region, resembling a natural spread-F environment. Recent experimental observations of self-focusing electromagnetic waves in the ionosphere are described in the following section. 2.2.2 Experimental Observations. Thermal self-focusing of high-frequency electromagnetic radiation has been observed in overdense ionospheric modification experiments. The overdense self-focusing instability develops with theoretically predicted threshold fields, scale lengths, and growth rates (11). Associated density irregularities form on time scales of seconds to tens of seconds, and decay on a time scale of minutes. Above the HF wave-reflection height, these striations are extended along the geomagnetic field for at least 100 km. For overdense self-focusing, the theoretical threshold can be expressed as (9) exceeded in the F region by both the Platteville (~ 50 /zW/m2) and Arecibo (~ 120 /zW/m2) HF facilities. The threshold striation scale size in the magnetic meridian can be found from (12) For typical ionospheric parameters and
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