A ground receiver looks straight up through Earth's F layer at a broadband solar…

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Problem

A ground receiver looks straight up through Earth's F layer at a broadband solar burst spanning

2

20\,\mathrm{MHz}

. The F layer's peak electron density is

n_e = 1.05\times10^{12}\,\mathrm{m^{-3}}

. ((a)) Find the plasma frequency of the layer and state which part of the burst's frequency range is reflected back down rather than reaching a satellite above the layer. Explain, using the energy-flux argument for an evanescent wave, why the reflected components deposit no heat in the layer even though the layer is not a perfect conductor. ((b)) The components that do get through then cross a second, tenuous ionised cloud higher up, of column density

N = \int n_e\,\mathrm{d}\ell = 3.0\times10^{16}\,\mathrm{electrons\,m^{-2}}

, before reaching the satellite. Using the group-velocity expansion for a wave above the plasma cutoff, find the extra delay, relative to light travel time, between the arrival of the

12\,\mathrm{MHz}

and

20\,\mathrm{MHz}

components at the satellite, and say which of the two arrives first. Take

1\,\mathrm{pc\,cm^{-3}} = 3.086\times10^{22}\,\mathrm{m^{-2}}

and

4.149\,\mathrm{ms}\,\mathrm{pc^{-1}\,cm^{3}\,GHz^2}

as the dispersion-delay constant.

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