Problem 3.217

The gap between two plane plates of a capacitor equal to $d$ is filled with a gas. One of the plates emits $v_{0}$ electrons per second which, moving in an electric field, ionize gas molecules; this way each electron produces $\alpha$ new electrons (and ions) along a unit length of its path. Find the electronic current at the opposite plate, neglecting the ionization of gas molecules by formed ions.