**5. Discussion**

The deduced space charge effect in the corona discharge development process of both polarities are concluded and compared, to further discuss the PD mechanisms.

For initial streamer stage, space charge effect is weak. Streamers develops when *E* of tiny region reaches *E*0. The development degree of streamers is low, so *V* is low and Δ*t* is short. Discharges are relatively random.

Then space charges begin to retain, and actions play a main role. At transition stage of positive PD, the action group weaken the internal electric field while strengthen the external one. But *E* of the weaken regions are not even. In central axial region, electric field is the strongest and still higher than *E*0 after being weakened. While *E* of regions around is not, so streams develop toward these regions are stopped earlier. Thus, two forms of streamer occur.

At Trichel discharge stage of negative PD, the action layer strengthen the internal electric field while weaken the external one. Actions are more dispersive and intensive, and are closer to the needle tip. Because of the strengthen effect, from needle tip to action layer, electric field decreases little, or even increase. While the *E*'s outside cation layers are basically lower than *E*0, which stops streamers in a similar degree and causes unchanged *V*. The electric field inside cation layer is high, flat, and linear, and grows with the increase of applied voltage, so some Δ*t*–*V* has an approximate proportional relationship. Recovery times are short and stable, so *n* rises in a linear fashion. Discharges inside the cation layer are strong. More anions are transformed and gradually become close to cations at the later stage.

Because actions are more intensive and closer to the needle tip on negative polarity, its effects are more obvious, which reflects on the variations of parameters, especially *n*, *q*.

Next, retained space charges increase to a certain level, electric effects are obvious. At glow-like discharge stage of positive PD, the effect of actions are more obvious because of higher density. The streamers are basically limited inside action group and cause unchanged *V*. Notice that PD parameter rules of this stage are similar to that of Trichel discharges in negative polarity. So it can be concluded that the electric field distribution of discharge regions are similar at two stages. The phenomenon delay and are not so obvious on negative polarity because of the different effects of actions. At the later transition stage, because cation group expands and becomes sparse, its effect is weakened and streamers in some regions are not limited, discharge form is transforming to breakdown streamer.

At the glow-discharge stage of negative PD, intensive anions occur close to the outer edge of cation layer, and plasma layer is formed. Stable glow discharges occur inside plasma layer, which does not produce a PD pulse without instantaneous space charge variations. In a few regions of the cation layer and plasma layer, some intermittent streamers occur. Because the regions are tiny and *E* is relatively weak, the PD is weak. Within a certain voltage range, the increase of applied voltage only causes the expanding of cation layer, so negative polarity glow discharge stage lasts long.

At last, streamers with few limitation occur gradually and cause breakdown. At breakdown streamer stage of positive PD, the cations group is far from the needle tip and its density decreases. Its effects are reduced, and the streamers are almost not limited and become strong. While at breakdown streamer stage of negative PD, cation layer and plasma layer still work. When the plasma layer is close

to the plate, the high *E* regions in peripheral regions of plasma expand, the negative streamers 'restart' and develop without much limitation. As such, the negative streamers are relatively weak, and cause a breakdown sooner because they start near the plate.

The statistic rules of PD parameters in this paper and others support each other in some aspects [10–14]. The mechanism explanations are based on the classical theories and well-founded. The deduced result can be interpreted in perspective of previous studies, for example, space charge and plasma distribution at some stages can be verified by luminescent image [19]. In follow-up research, we are hopeful the deduced space charge effects and electric field distributions will be verified by a simulation on the basis of the corona discharge fluid model mentioned previously [17].

The statistical analysis method and some deduced rules may also be effective in other gas PD under an uneven electric field, with DC voltage and AC voltage with low frequency, where space charges have enough time to retain.
