Imagine a horizontally stratified ionosphere in the absence of a magnetic field, constituted only of electrons (density

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Imagine a horizontally stratified ionosphere in the absence of a magnetic field, constituted only of electrons (density n, temperature T, charge –e, mass me) and one type of ions (density n, temperature T, charge +e, mass mi), subjected to the gravitational field (g), vertical pressure gradient (∇p), and the internal electric field (E) due to the charge separation associated with ambipolar diffusion. Neglect the gravitational force for the electrons and consider the system in equilibrium. Using the collisionless equations of motion for the electrons and the ions, show that the internal electric field acts downward on the electrons with a force mig/2, and upward on the ions with the same force. Consequently, the net effect is the same as if both ions and electrons had mass mi/2.

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