Computer exercise for lecture
"Ionospheric Physics" (5 op)

(University of Helsinki, winter 2011, Lecturer: Dos. Olaf Amm)

Chapman α-layer for vertically incident solar radiation

- Given:

n₀ = 2 ∙ 10²⁵ m^-3 (density of neutrals to be ionized, at z=0)

H = 10 km (scale heights of neutrals)

= 2 ∙ 10^-21 m² (average ionization cross section for relevant wavelength range)

I_∞ = 2 ∙ 10^-3 W m^-2 (solar spectrum until 100 nm, above the ionosphere)

- Using the equations given in the lecture, calculate:

a) The height z₀ of the maximum electron density of the Chapman α layer

b) The light intensity I(z) and the absorption rate q(z) for the altitude range [ z₀ – 2 H ; z₀ + 2 H ]. Plot a graph of both curves.

c) The recombination coefficient α under the assumption of a stationary situation, and that α-recombination is the only loss process. For this, the electron density at the layer maximum z₀ be 2 ∙ 10¹¹ m^-3 (E-layer, daytime, low latitudes), and the parameter γ (number of produced ion/electron pairs per energy unit) be 2 ∙ 10¹⁷ J^-1.

d) With the value for α as calculated in part c), use the balance equation (55), inserting L for α-recombination, to calculate n_e(t) at z=z₀ for the case that q(z₀) is instantly “switched on” at t=0, and the initial electron density is zero. That is,

n_e(t=0) = 0 ; q(t) = 0 for t<0 ; q(t) = q(z₀) for t≥0, with the value for q(z₀) from b)

How long does it take until n_e(t) increases from zero to half of its stationary value?

Plot a graph of n_e(t) for the time interval from zero to the time as calculated above.

Note: Task d) can be completed either analytically or computationally!