Just a point on V times I measuring the power. This is the total power, and it works for DC plasma. Most non-thermal plasma are generated by pulsed or RF power. So the power density has to take in the reactive power. It makes sense to remove the reactive part as it does no work and is purely geometrical. For a capacitively coupled plasma the real power is divided by the area exposed to the plasma. If the return electrode is large like a grounded wall, use only the area of the driven electrode. The units would be watts/cm^2. The work piece area should not be used unless it is acting as an electrode or extending the area of the electrode.
An inductively coupled plasma is a different case and there is no standard way to define this, I would probably work with an power per unit volume and derive an area from that. Or as Renato has suggested an energy density would be more appropriate is this type of plasma.