In this article, different electron energy distribution functions (EEDF) for plasma conditions in xenon dielectric barrier discharge (DBD) are explored in plasma modelling. At the beginning, ionization and excitation rates resulting from electron-neutral collisions are discussed. Generally, local-field approximation (LFA) is used for those collisions by assuming electrons gain energy in nanoseconds and reaches equilibrium. For the LFA models, electron energy distribution function is governed by the Boltzmann equation for the primary elastic and inelastic collisions. Although LFA is useful to calculate the primary ionization and excitation rates, diffusion and mobility coefficients, the secondary processes are omitted. These processes can be superelastic collisions, stepwise ionization, electron-ion recombination etc. The models using LFA neglect the secondary processes to reduce the computational cost.
The recent models decouple the mean electron energy from the electric field by replacing E/N to mean electron energy ( ε) which is obtained from the third moment of the Boltzmann equation. The effects of the secondary processes on the mean electron energy can be calculated directly. However, in the models, the distribution function is assumed to be Maxwellian. For DBDs, it is known that the distribution is non-Maxwellian. Therefore, using a Maxwellian EEDF causes an overestimation of the excitation and ionization rates by an order of magnitude at least. To attain a better distribution profile, Maxwellian, bi-Maxwellian, Druyvesteyn and bi-Druyvesteyn functions are used by solving the Boltzmann equation and calculating electronic ionization (α_i ) and excitation rates (α_ex ), diffusion ( D_ex) and mobility ( μ_ex) for xenon DBD.
While comparing, two different energy levels are calculated from the Boltzmann EEDF. The levels are defined to be lower and higher energies with respect to the first excitation energy. For each EEDF achieved by distinct functions, a normalized function is fitted to the Boltzmann solution. Once the energy distribution functions are graphed, the coefficients can be calculated. According to the results, bi-Druyvesteyn is in close agreement with the Boltzmann values for ionization (α_i ) and excitation rates (α_ex ), diffusion ( D_ex) and mobility ( μ_ex). The bi-Maxwellian distribution gives accurate results for the ionization and excitation rates but fails in the electron mobility at low energies. Similarly, a Druyvesteyn EEDF does not match with the values obtained with the Boltzmann equation. On the other hand, the Maxwellian distribution considerably overestimates the values.
As a result, the article proposes an alternative way to evaluate the EEDF in DBD modelling. By using a bi-Druyvesteyn distribution, the energy function and the calculated values would become more realistic in the inclusion of the secondary processes compared to a Maxwellian distribution profile.
Reference: Carman, R. J., and R. P. Mildren. “Electron energy distribution functions for modelling the plasma kinetics in dielectric barrier discharges.” Journal of Physics D: Applied Physics 33, no. 19 (2000): L99.
Course: AME 60637