Plasmas are very good at shielding electric fields.
However, there is a phenomenon, called "double layer." It appears as a quasi 1D spike of an electric field. It is believed to occur when a current flows through the plasma and passes a layer of anomalous resistivity. A more formal solution for the electric field distribution can be constructed with no recourse to the anomalous resistivity. Known since Langmuir times.
A good discussion is in a book by Artsimovich and Sagdeev, but unfortunately in Russian. No English translation is available. I used it in a plasma course for the grad students at UCSD. Will post the lecture notes.
Unfortunately, this is a too-general question. It depends on the electrode configuration creating the electric field and plasma discharge and the working medium (e.g., a gas). If you are working with a rare gas (like Ar) at low pressure ~ 1 torr, a spherical electrode within a larger spherical electrode will give multiple plasma layers (probably with weaker light-emitting plasma separating them). I hope this helps.
The double layer is an object in one-dimensional geometry. Therefore it is necessary to select correctly the dimensions of your device. The distance between plates should be much less then dimensions of plates. For these conditions, I think, it is difficult to provide the uniformity of the injection of particles from an irradiated surface.