Observation of electron runaway in a tip-plane air gap under negative nanosecond pulse voltage by PIC/MCC simulation

Abstract

The initial stage of the gas breakdown with the generation of the runaway electrons was investigated by particle-in-cell/Monte Carlo collision simulations. The parameters of the solved problem are 1-mm long and atmospheric air gap between the tip-plane electrodes applied with the nanosecond pulse voltage. The pulse is 5.2 ns in rising time (10%-90%), 10 ns in pulse width (FWHM) and 40 kV in amplitude. The cathode is a cone-shaped electrode whose tip is defined by the elliptic equation (the major axis is 4 mm and the minor axis is 1 mm), and the minimum radius of curvature is 0.125 mm. Since it is found in the simulation that the development of discharge channel from the cathode to the anode only takes about tens to hundreds of picoseconds, especially at high over-voltages with runaway electrons, it was assumed that the gap voltage applied in such a short time is nearly constant. Depending on the voltage at the breakdown, the different behavior of the energetic electrons was observed. When the voltage is low, about 12 kV, energetic electrons are produced only in the tip cathode layer where the electric field is highest; No runaway electrons leading the discharge channel are observed. When the voltage is higher, about 15 kV, the energetic electrons begin to run away at the head of the discharge channel where the electric field is high enough. When the voltage is further higher, the energetic electrons run away even at the beginning of the discharge and from the cathode to the anode. The pre-ionization of the gas ahead of the discharge channel by the runaway electrons was observed, which may play an important role in the fast breakdown of the gas under the nanosecond short pulse.

Effect of photoionisation on initial discharge in air under nanosecond pulse voltage

“…The average development speed of the main discharge channel in both cases is about 9 mm/ns, which is reasonable under high overvoltage and has been analysed in detail in Ref. [19]. The results of such simulations may be analysed from the theoretical differences between the energetic electrons and the photoionisation.…”

“…It should be noted here that due to the reduced collision set in electron reaction, the ideal threshold of electron runaway in this model is about 200 kV/cm [19], which is slightly lower than the 240 kV/cm calculated using a more complete reaction set by G. Diniz et al. [20].…”

“…Besides the reactions in Ref. [19], additional reactions considered in this work, listed in Table 1, are considered to implement the photoionisation. Photoionisation of oxygen is considered by absorption of photons emitted by N 2 ( b 1 Π v = 0‐14 ) and N 2 ( b 1 Σ v = 0‐H ) with a wavelength of 98–102 nm [29].…”

“…Then, the calculation method of the ideal threshold of electron runaway is briefly introduced. For the reaction set used in the numerical model, Equations () and () can be used to precisely calculate the effective frictional force F ( ε ) [19, 20]: $$$F(\varepsilon )=\sum\limits _{i,j}\left[{N}_{i}\cdot {\sigma }_{i,j}(\varepsilon )\cdot {\delta }_{i,j}\right]$$$ $$${\delta }_{i,\mathrm{i}\mathrm{o}\mathrm{n}}(\varepsilon )={\varepsilon }_{i,\mathrm{i}\mathrm{o}\mathrm{n}}+\frac{\overline{\varepsilon }}{2\,\mathrm{arctan}\frac{\varepsilon -{\varepsilon }_{i,\mathrm{i}\mathrm{o}\mathrm{n}}}{2\overline{\varepsilon }}}\mathrm{ln}\left[1+{\left(\frac{\varepsilon -{\varepsilon }_{i,\mathrm{i}\mathrm{o}\mathrm{n}}}{2\overline{\varepsilon }}\right)}^{2}\right]$$$ where N i is the partial density per gas composition i (O 2 , N 2 ), σ i,j and δ i,j are the cross section and energy loss of a particular collision process, j, respectively (see Table 1 of this paper and Ref. [19]), δ i, ion is the mean energy loss of the incident electron due to collision ionisation, the constants $$\overline{\varepsilon }$$ are 17.5 eV for O 2 and 13 eV for N 2 , and ε i, ion is the ionisation energy.…”

“…Other details of the numerical model and related theory can be found in Ref. [19]. It must be added that 3D PIC simulation is much closer to reality than 2D PIC simulation.…”