I'm trying to find a formula for the current flowing through a wire that is only undergoing corona discharge into air. The wire is connected to a charged sphere, which provides the voltage. So far, I've just found formulas for certain ionization coefficients and electric fields, but no current formulas. Is there such a formula? I imagine it would involve the voltage on the sphere, the resistance on the wire, and perhaps the thinness of the wire. Also, would it matter if the wire is bent rather than straight? I am assuming that corona discharge will occur because the wire ends at a sharp point, but I have noticed that corona discharge experiments usually have the discharging point near an oppositely charged conductor. Is this necessary, and would the current be adversely affected if the discharging point were instead near a similarly charged conductor?