A radio wave is sent vertically into an idealised model of the ionosphere: a sharp-edged

PHYSICS · Multi-part · Fermi University Physics · Plasma Physics · Waves in plasmas · Waves in plasmas

Plasma Physics, Ch Plasma oscillations and light in an unmagnetised plasma

Problem

2.0\,\mathrm{MHz}

radio wave is sent vertically into an idealised model of the ionosphere: a sharp-edged, uniform slab of electron density

n_e = 4.0\times10^{11}\,\mathrm{m^{-3}}

filling all space above a boundary, with no field below the boundary except the wave falling on it. ((a)) Find the plasma frequency

f_{pe}

of the slab and confirm that the

2.0\,\mathrm{MHz}

wave is below cutoff there. ((b)) Estimate the

1/e

decay length of the wave's electric field inside the uniform slab. ((c)) Find the critical density

n_c

for a

2.0\,\mathrm{MHz}

wave, and use it to explain why, in the real ionosphere (where density rises gradually with height rather than jumping to

4.0\times10^{11}\,\mathrm{m^{-3}}

at a sharp edge), the wave never actually has to cross the decay length found in part (b).