Question

The plasma density in the lower ionsphere has been measured during satellite Re-entry to be about 10^18 m^-3 at 50 Km altitude, 10^17 at 70 Km, and 10^14 at 8Km. What are the plasma frequencies their?

Kindly solve this step by step?

Answer 1

1) Write the equation to find the plasma frequency:

$$f=\frac{\omega}{2\pi}=\frac{e}{2\pi}\sqrt{\frac{n}{m^*\epsilon_0}}.$$

2) Determine what we need for this equation:

e - charge of electron (we know it);

π - a constant (we know it);

n - concentration of electrons expressed in m^-3 (we know it);

m^* - the effective mass of electrons. Since we are not given any details on this, put that the effective mass of electrons is equal to its rest mass m_e expressed in kilograms;

ε₀ - permittivity of free space (a constant, we know it) expressed in SI units.

3) Since all values are constants, all we need is to substitute the concentrations for each value of heights in the equation.

4) Make calculations. This will give you the following results:

50 km: 8.98 GHz

70 km: 2.84 GHz

8 km: 89.8 MHz.