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Imagin_e
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Homework Statement
Hi!
I need to solve a continuity equation for electron density as a function of time in the E-region of Earth's atmosphere. I shall neglect vertical transport and that the ion production rate completely shuts off dusk.
Homework Equations
See below
The Attempt at a Solution
Here is my attempt:
(1+λ)dNe/dt=p(t)-(1+λ)(αd-aλi)Ne2-Ne dλ/dt
Ne is the electron density, dy, λ=ratio of negative ions to electrons , p(t) is the electron production rate, αd is the recombination coeff. for ions and ai is the recombination coeff. negative ions with positive ions.
The effective recombination coefficient is: αeff=(1+λ)(αd+aλi).
If we assume that the is no negative ions, we get:
dNe/dt=p(t)-adNe2 (1)
and aeff simply becomes ad
Here comes the issue, I need to have a solution for equation (1) with respect to the density and time. . How should I integrate this? The density from the beginning is ≈ 1*109 m3 , which I calculated