Electric field in ionization area of a corona discharge?
Corona discharge is due to a gas transferring phases from a gas to a plasma. From wikipedia:


  The positive charge in ions is achieved by stripping away electrons from atomic nuclei. The number of electrons removed is related to either the increase in temperature or the local density of other ionized matter. This also can be accompanied by the dissociation of molecular bonds,[10] though this fundamental process is distinctly different from chemical processes of ion interactions in liquids or the behavior of ions existing in metals. A significant number of highly charged particles together make plasma electrically conductive so that it responds strongly to electromagnetic fields.


So just some background to get you started (plasma physics is an entire field and it will be difficult to explain in just one answer) 

There exists a Debye Sheath around the outer conductor, because the electrons are repelled by the charge from the outer conductor.

The wire in the middle is like a Langmuir Probe and the plasma has an IV relationship similar to a diode.

You will need to know the density of plasma and the molecular weights of the plasma ion species (the problem will get harder the more ion species there are),  and the potential of the inner and outer conductor. You will also need to assume that that magnetic field is zero. And you will need to read sections 1, 2, and 3 of this if you don't know about plasma physics.