only be satisfied when degrees which is beyond the region of validity of the theory. The threshold power is shown as a function of wavelength for three values of in Figure B-2. Here we assume that and . (The plasma becomes more stable as n decreases and T increases. ) We note that for degrees, a design power of will excite only plasma wavelengths greater than 130 m. (This angle, we note, is greater than the 87 degree maximum angle for which ion diffusion perpendicular to the field can be safely ignored. ) For 0 = 85 degrees only wavelengths greater than 320 m can be excited. For 2. 2 GHz and , so there will only be a small amount of spatial amplification for m. (The spatial amplification is exp () for a thickness of slant length. ) Even a power flux of with degrees will only excite wavelengths greater than 70 m. Figure B-3 shows the growth rate Y in sec as a function of the perturbation wavelength for 5 values of . This has been carried to angles as close to perpendicular as degrees for the same electron density and temperature as Figure B-2 with a power flux of . At 89.9 degrees, wavelengths greater than 30 m have positive growth rates while at 85 degrees only wavelengths greater than 300 m are unstable. Similar curves are shown in Figure B-4 for the case where the plasma density in the ionosphere is . It is clear that only wave vectors in a narrow cone about the direction perpendicular to both the magnetic field and the propagation direction have short wavelength instabilities. For directions with between 87 and 89.7 degrees, a simplified theory is possible in which we assume that electrons move parallel to the magnetic field but ions move only perpendicular to the field. This approximation is valid for:
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