1.3. Numerical modeling
1.3.1. Monte Carlo simulations of electron dynamics
In Janda et al., Acta Physica Slovaca 55 (2005) 507514, we present a free software for modeling the electron dynamics in the uniform electric field named WebEEDF. It provides electron energy distribution function (EEDF), electron drift velocity, electron mobility, and collision frequency of electrons with neutrals as functions of reduced electric flied strength (E/N). EEDF (Fig. 1) enables us to calculate electron mean energy, electron mean free path, rate coefficients (Fig. 2) of electronmolecule collisional processes (e.g. excitation, attachment, ionization), and the branching of the electron energy towards these processes.
Calculated rate coefficients of electroninduced processes can facilitate better understanding of the importance of various reaction pathways leading to the decomposition of air pollutants in various gas mixtures. Despite its simplicity the WebEEDF results are in good agreement with literature. It is also suitable for educational purposes by providing clearer insight in understanding physical and chemical mechanisms in plasma processes.
This electron dynamics modeling was further developed in Janda et al., Eur. J. Phys. D 45 (2007) 309315. Motivated by the decomposition of CO_{2} and the synthesis of amino acids in DC electrical discharges, we investigated the electron dynamics by Monte Carlo simulations in N_{2}/CO_{2} gas mixtures. The results of the simulations include electron mean energy, drift velocity, collision frequency of electrons with neutrals, mean free path of electrons, rate coefficients of selected electronimpact processes, and ionization and attachment coefficients as functions of the reduced electric field strength and the composition of a gas mixture. The knowledge of these parameters is crucial for the understanding of plasma induced chemistry and behavior of electrical discharges in such mixtures.
The applied computational method was proved useful for the calculation of steadystate EEDFs and derived parameters characterizing electrons in homogeneous electric fields in various gaseous mixtures. WebEEDF source code can be downloaded from http://enviro.fmph.uniba.sk/webeedf.
We are currently developing new version which will enable to simulate time evolution of EEDFs, or the relaxation of electrons in electron beams.

Fig. 1. Electron energy distribution functions(EEDF) in air as functions of reduced electric field
strength (E/N). 

Fig. 2. Rate coefficients of the most important
electron impact reactions in N_{2}/CO_{2} mixtures, E/N = 120 Td. 
More details in:
http://enviro.fmph.uniba.sk/webeedf
Janda M., Machala Z., Morvová M., Franček V., Lukáč P.: WEBEEDF: Open Source Software for Modeling the Electron Dynamics, Acta Physica Slovaca 55, 507514 (2005). abstract download citations: 0  Janda M., Hensel K., Martišovitš V., Morvová M.: Theoretical Study of Influence of H2O on Parameters of LowTemperature Plasmas in Humid Mixtures, Czech. J. Phys. 56, B774B780 (2006). abstract download citations: 1  Janda M., Martišovitš V., Morvová M., Machala Z., Hensel K.: Monte Carlo simulations of electron dynamics in N_{2}/CO_{2} mixtures, Eur. Phys. J. D 45 (2), 309315 (2007). abstract download citations: 13 
1.3.2. Plasma kinetics
The modeling of chemical kinetics aiming to calculate the density evolution of all species included
in the kinetic model is an effective tool for complex systems description. In many cases, it is the
most powerful way to solve problems where the complexity inhibits using analytical methods and direct
experimental measurements. It is commonly used not only for modeling of cold plasma chemistry,
but also for description of high temperature steady state arc plasma, nanosecond duration of streamer
propagation, and other problems in plasma physics and chemistry.
We are currently developing chemical kinetic model fitted for the
transient spark (TS) discharge. This
model can be used to determine the evolution of density of various species.
Moreover, this model is able to describe macroscopic parameters such as
plasma conductivity and current density in the plasma channel. The validity of the model was tested by
comparing calculated electron densities with experimental data (Fig. 3).
This model is based on available open source package
ZDPlaskin.
We studied the mechanism
of the streamertospark transition and breakdown in the TS using this model. We assume that the
breakdown mechanism in TS is based on the gas density (N) decrease and can be summarized as follows:
heating of the channel → increase of the pressure → hydrodynamic expansion → decrease of N in
the core of the channel → increase of E/N → acceleration of ionization processes. However, this
mechanism is influenced by species accumulated due to previous TS pulses at higher TS repetition
frequencies. Sensitivity analysis focused on major electron loss and production processes indicates
an important role of the amount of O_{2} dissociated by the previous pulses. Lower density of O_{2} means
lower rate of electron attachment, while accumulated atomic oxygen atoms lead to acceleration of
electron detachment processes.
Further research of this memory effect using improved
version of our kinetic model simulating sequence of pulses is needed to verify this hypothesis.
We further plan to use an improved version of our model to study generation of various reactive species by TS discharge.

Fig. 3. Comparison of measured and calculated electron densities during the spark phase of the transient spark discharge, repetition frequency around 1 kHz. 
More details in:
Dvonč L., Janda M.: Study of transient spark discharge properties using kinetic modeling, IEEE Trans. Plasma Phys. 43 (8), 25622570 (2015). abstract download citations: 2  Janda M., Machala Z., Dvonč L., Lacoste D.A., Laux C.O.: Selfpulsing discharges in preheated air at atmospheric pressure, J. Phys. D: Appl. Phys. 48, 035021 (2015). abstract download citations: 12  Janda M., Martišovitš V., Dvonč L., Hensel K., Machala Z.: Measurement of the electron density in transient spark discharge, Plasma Sources Sci. Technol. 23, 065016 (2014). abstract download citations: 16 
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