The problem has been solved throughout the years by many different research groups around the world, that developed EBE solvers as standalone codes or as routines embedded into other numerical models. The electron kinetics can be described in detail by solving numerically the electron Boltzmann equation (EBE) for LTPs, usually written under an approximation framework that expands the electron distribution function in powers of some quantity around the equilibrium, assuming that the thermal velocities are larger than the drift velocities resulting from the combined anisotropic effects of electromagnetic applied forces and pressure gradients. Detailed knowledge of the electron energy distribution is essential also to obtain quantitative information for use in fluid/global predictive models or in the analysis of experimental diagnostics, by calculating quantities such as rate coefficients, transport parameters and fractional average powers, hereafter termed electron macroscopic parameters. Therefore, it becomes paramount to control the energy distribution of the electrons, tailoring it as to fine-tune the energy transferred to the heavy species. Electrons are key in this strategy, as they convey the energy available to the heavy species through various collisional channels that stimulate the reactivity of the plasma. These features open the way to develop plasma-based technologies that use different energy distribution scenarios, through efficient channeling of the energy to targeted species, both in volume and in plasma-facing substrates. Low-temperature plasmas (LTPs) are highly-energetic highly-reactive environments, exhibiting a low density of charged particles (ionisation degrees ), high electron temperature (∼1 eV) and variable heavy-species characteristic temperatures, ranging from 300 K to ∼10 4 K.
This topical review presents LoKI-B and gives examples of results obtained for different model and real gases, verifying the tool against analytical solutions, benchmarking it against numerical calculations, and validating the output by comparison with available measurements of swarm parameters. LoKI-B is developed with flexible and upgradable object-oriented programming under MATLAB ®, to benefit from its matrix-based architecture, adopting an ontology that privileges the separation between tool and data. On output, it yields the isotropic and the anisotropic parts of the electron distribution function (the former usually termed the electron energy distribution function), the electron swarm parameters, and the electron power absorbed from the electric field and transferred to the different collisional channels. On input, LoKI-B defines the operating work conditions, the distribution of populations for the electronic, vibrational and rotational levels of the atomic/molecular gases considered, and the relevant sets of electron-scattering cross sections obtained from the open-access website LXCat ( ). LoKI-B includes electron-electron collisions, it handles rotational collisions adopting either a discrete formulation or a more convenient continuous approximation, and it accounts for variations in the number of electrons due to non-conservative events by assuming growth models for the electron density.
LoKI-B was developed as a response to the need of having an electron Boltzmann solver easily addressing the simulation of the electron kinetics in any complex gas mixture (of atomic/molecular species), describing first and second-kind electron collisions with any target state (electronic, vibrational and rotational), characterized by any user-prescribed population. The LisbOn KInetics Boltzmann (LoKI-B) is an open-source simulation tool ( ) that solves a time and space independent form of the two-term electron Boltzmann equation, for non-magnetised non-equilibrium low-temperature plasmas excited by DC/HF electric fields from different gases or gas mixtures.
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