Wave propagation in a parabolic ionospheric slab. The ionosphere can approximately b...

Wave propagation in a parabolic ionospheric slab. The ionosphere can approximately be represented by a parabolic profile N(h), of the concentration of free electrons (N) as a function of the altitude (h) above the earth’s surface, within a plasma slab

of thickness 2d as follows:

where hm is the altitude at the middle of the slab and Nm is the maximum electron concentration – at this altitude, which is illustrated in Fig.7.8. A uniform plane time-harmonic electromagnetic wave of frequency f is incident vertically (normally) from the earth’s surface onto the lower boundary of the ionosphere, as shown in Fig.7.8, or from space onto the upper boundary. From Eqs.(7.21), maximum plasma frequency of the ionosphere is If f > (f_p)_max, the propagating condition for a plasma (f > f_p ) is satisfied at every layer of the ionosphere (100 km ≤ h ≤ 500 km), and the wave will pass through the entire slab in Fig.7.8. If f < (f_p)_max, on the other hand, there is an altitude in the ionosphere at which f = f_p, and the wave will bounce back off that layer. Combining Eqs.(7.21) and (7.22), the bounce-off altitude (h_b) is thus determined as

where the solution with the minus sign in the expression for h_b corresponds to the incidence from the earth’s surface onto the lower boundary of the slab, while the solution with the plus sign is for the incidence from space onto the upper boundary. Assuming that h_m = 250 km, d = 100 km, and N_m = 1012 m−3, write a MATLAB code that, based on Eqs.(7.23), calculates and plots the

altitude h_b for each of the frequencies separated by steps of Δf = 0.5 MHz within a frequency range 8 MHz ≤ f ≤ 12 MHz. In a case of the wave passing through the ionosphere, indicate so on the graph. (ME7 23.m on IR) H

Reference: Equation(7.21),(7.22)