3.2. Simulation results

<sup>I</sup> <sup>¼</sup> <sup>e</sup> U<sup>a</sup> ððð V

118 Plasma Science and Technology - Basic Fundamentals and Modern Applications

expressed as [36].

expressed as

parameter of exponential distribution.

NpW<sup>p</sup> � NeW<sup>e</sup> � NnW<sup>e</sup>

where U<sup>a</sup> indicates the applied voltage, E<sup>a</sup> the applied field, and V the discharging volume. On one hand, the field within the cavity should exceed a critical value so that a discharge may take place. Based on the ignition condition of streamer, the critical field is expressed as follows [35]:

> <sup>760</sup> d<sup>g</sup> � � <sup>þ</sup> <sup>6730</sup>

> > dg

where P is in Torr. After a discharge takes place, electrons and ions accumulate on the dielectric surface. Due to the recombination of charges from gas, surface, and bulk conduction of dielectric, the accumulated surface charges will decay until the next discharge occurs. It is found from our previous experiments that the decaying discipline of surface charges could be

> σp σp0 ¼ e �t

σe σe0 ¼ e �t

tion is much lower in comparison with electron and positive ions.

<sup>τ</sup> <sup>¼</sup> <sup>∞</sup>

(

where σp0 and σe0 indicate initial positive charge and electron density at dielectric surfaces, respectively. η<sup>p</sup> and η<sup>e</sup> equal 312.5 and 568.8 ms, both of which represent the surface charge decay time for positive ions and electrons. The negative ion is neglected because its concentra-

On the other hand, although free electrons from the volume ionization and surface emission are formulated, their supply shows a strong scholastic behavior. Hence, there is usually a time delay between the instant of application of an electric field in excess of the critical field and the onset of breakdown, which is called a discharge time lag (strictly speaking, it is a statistical time lag, but the formative time lag is very short for cavity discharge and could be neglected). In order to simplify the physical process of free electron production, the discharge time lag is introduced to our model. Some experimental and simulation results show that the discharge time lag is not completely random, but is subject to exponential distribution [37, 38], which is

�ln 1ð Þ � P<sup>d</sup> =ζ

where P<sup>d</sup> indicates the discharge probability, which belongs to [0, 1) and is random, ζ the rate

In terms of Eq. (17), the critical field for gas breakdown is calculated, and it equals 67,000 V/cm. In this case, the potential difference across the electrodes is 3130 V. Because the PD mechanism

E<sup>z</sup> < E<sup>b</sup> E<sup>z</sup> ≥ E<sup>b</sup>

Eb <sup>¼</sup> <sup>24410</sup> <sup>P</sup>

� � � <sup>E</sup>adV (16)

<sup>η</sup><sup>p</sup> (18)

<sup>η</sup><sup>e</sup> (19)

(17)

(20)

ffiffiffiffiffiffiffiffiffiffiffi P <sup>760</sup> d<sup>g</sup> q
