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Fig. 4

image

Expression Eq. (14) (the plot for Eq. (19) is indistinguishable) as a function of x, plotted for fixed θ = π∕8, π∕16 and π∕64. The horizontal dashed lines are at , 1, and sec 2π∕8. When ωωp or x ≫ 1, asymptotes to sec2θ, while when ωωp or x ≪ 1, becomes unity regardless of the angle θ. Note Eq. (18) only needs to be satisfied at the emission site, and determines the central phase velocity direction, the same θ is then kept by the wave as it propagates. So as the wave rises in altitude, the refractive index that the wave experiences at new sites along its trajectory can be estimated by simply tracing along one of the curves in this figure to the left (ωp thus x drops with increasing altitude, as the plasma becomes more rarefied).

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