Abstract
The LisbOn KInetics Boltzmann (LoKI-B) is an open-source simulation tool (https://github.com/IST-Lisbon/LoKI) 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. 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. 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. 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 (http://lxcat.net/). 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. 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. 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.
Highlights
Low-temperature plasmas (LTPs) are highly-energetic highlyreactive environments, exhibiting a low density of charged particles, high electron temperature (∼1 eV) and variable heavy-species characteristic temperatures, ranging from 300 K to ∼104 K
The electron kinetics can be described in detail by solving numerically the electron Boltzmann equation (EBE) for LTPs [1], 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
A recent topical review [1], integrated in the collection Foundations of low-temperature plasmas and their applications published by Plasma Sources Science and Technology, gives a summary of the essentials of the EBE, when written for an electron distribution function expanded in Legendre polynomials Pl around the angle θ, defining the spatial orientation of the velocity vector with respect to the polar direction of the total anisotropy
Summary
Low-temperature plasmas (LTPs) are highly-energetic highlyreactive environments, exhibiting a low density of charged particles (ionisation degrees ~10-6 - 10-3), high electron temperature (∼1 eV) and variable heavy-species characteristic temperatures, ranging from 300 K to ∼104 K. The Monte-Carlo codes, BOLSIG+ and MultiBolt further calculate transverse and longitudinal bulk/flux swarm parameters, by adopting a density-gradient expansion, and they allow for an electron density growth under steadystate Townsend (SST) or Pulsed Townsend (PT) conditions, by prescribing the energy sharing between the primary and the secondary electrons resulting from ionisation events (METHES), or by taking the limiting cases of no-sharing and/or equal-energy-sharing (BOLSIG+ and MultiBolt) In principle, all these codes can solve the EBE for a mixture of gases chosen by the user, taking into account electron collisions of first and second kind with electronic-like excited levels, but this feature is not available (or is difficult to extend) to the subset of vibrational levels within an electronic level and the subset of rotational levels within a vibrational level.
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