(a) The refractive index of a plasma (neglecting collisions) is approximately given by (se...

(a) The refractive index of a plasma (neglecting collisions) is approximately given by (see Sec. 7.6)

where

    s –1

is known as the plasma frequency. In the ionosphere the maximum value of N0 is ≈ 10 10 – 10 12 electrons/m3. Calculate the plasma frequency. Notice that at high frequencies n2 ≈ 1; thus high frequency waves (like the one used in TV) are not reflected by the ionosphere. On the other hand, for low frequencies, the refractive index is imaginary (like in a conductor – see Sec. 24.3) and the beam gets reflected. This fact is used in long distance radio communications (see also Fig. 3.27).

(b) Assume that for x ≈ 200 km, N = 10 12 electrons/m3 and that the electron density increases to 2 × 10 12 electrons/m3 at x ≈ 300 km. For x < 300 km, the electron density decreases. Assuming a parabolic variation of N, plot the corresponding refractive index variation.