Calculating Electron Density in F2 Layer Using Ionosonde Pulse

[stunner5000pt]

The electron densities, ne, at any height h < 300 km on the lower side of an F2 layer can be described by a scale height relationship:
$$n_{e}(h) = n_{e}(300) \exp\left(\frac{0.75(h-300)}{H_{O}}\right)$$
where HO is the neutral atomic oxygen scale height. If the ionosphere has an isothermal temperature of 1500 K and a 9 MHz ionosonde pulse is reflected from 200 km, calculate the electron density at 300 km. [Magnetic field effects may be ignored and you may assume that we only have an F2 layer]

i can easily calculate the scale height Ho. The problem is... how does the EM pulse relate to the density of electrons in the atmosphere?
am i missing something... some formula that sohuld be used?

should it be
$$f = 9 \times 10^{-3} \sqrt{N_{e}}$$
where Ne is the density of electrons in the atmosphere (F2 region)? That represents a critical frequency. Typically teh F2 region's threshold is 3-30 Mhz isn't it ?

your help is greatly appreciated! Thank you

 

[Tide]

For normal incidence into the F2 layer the wave will obey

$$\frac {\partial^2 E}{\partial z^2} + \frac {\omega^2 - \omega_p^2}{c^2} E = 0$$

where $\omega_p$ is the plasma frequency (proportional to $\sqrt {N_e}$). This tells you the wave turns around at z such that

$$\omega_p^2(z) = \omega^2$$

You were also given that the height at which the wave reflects and you can infer the density at that point. You should be able to handle the rest.

 

[stunner5000pt]

i am not familiar with the that differential equation i don't think we were supposed to use it but...

do i solve for E? WHat is omega? Is it the frequency of the wave which we sent, so that is a constant as well? So do i solve that differntial equation?

i,m not quite sure how the height of the reflection says anything aobut hte elctron density...

 

[Tide]

No, you don't have to solve for E. The equation was just to demonstrate that the light wave reflects off of what is called the "critical surface," i.e. where the (fixed) radio wave frequency $\omega$ is equal to the plasma frequency $\omega_p$.

The plasma frequency is related to the electron density:

$$\omega_p = \frac {4 \pi n_e e^2}{m_e}$$

(in cgs units - look it up for the units you need) so the plasma frequency varies with height since the electron density varies with height.