The LisbOn KInetics - LoKI

The LisbOn KInetics tools comprise a suite for plasma chemistry simulations (LoKI) and a Monte Carlo code for electron kinetics simulations (LoKI-MC).

The LoKI tools and data leverage on the scientific heritage in the field of non-equilibrium plasma kinetics of the Portuguese group N-Plasmas Reactive: Modelling and Engineering (N-PRiME), and they were developed / consolidated resorting to well-grounded scientific foundations established years ago.

The LisbOn KInetics (LoKI) is a simulation tool that couples two main calculation blocks:

a Boltzmann solver (LoKI-B) for the electron Boltzmann equation, released as open-source code licensed under the GNU general public license, being freely available here;

a Chemical solver (LoKI-C) for the global kinetic model(s) of pure gases or gaseous mixtures. LoKI-C is under development still, and presently there is no tentative date for its conclusion and/or release.

LoKI 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.
Overall, LoKI provides the combined chemical and transport description of plasma charged/neutral species, both in volume and surface phases, for user-defined working conditions: mixture compositions, pressure, dimensions and excitation features (glow (dc/hf), afterglow, pulsed).

LoKI-B (available as an open-source tool) solves the space independent form of the two-term electron Boltzmann equation (EBE) for non-magnetised non-equilibrium low-temperature plasmas, excited by DC/HF electric fields or time-dependent (non-oscillatory) electric fields (NEW FEATURE introduced in version 2.0.0) from different gases or gas mixtures. The tool addresses glow plasmas, using a stationary description for DC fields, a Fourier time-expansion description for HF fields, and a time-dependent description for time-varying fields.
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 (ionization and attachment) by assuming growth models (temporal or spatial) for the electron density.

LoKI-C solves the system of zero-dimensional (volume average) rate balance equations for the most relevant charged and neutral species in the plasma, receiving as input data the kinetic schemes KIT(s) for the gas/plasma system under study via an intuitive parser-file.
LoKI-C uses several modules to describe the mechanisms (collisional, radiative and transport) controlling the creation / destruction of species, namely various transport models for the charged particles (ambipolar diffusion, effective diffusion, and Liberman and Lee’s low-pressure model) and for the neutral particles (multicomponent diffusion of species following Wilke’s approach, and considering wall recombination). LoKI-C includes also a gas/plasma thermal model, for the self-consistent calculation of the gas temperature (NEW FEATURE introduced in version 3.0.0), and the handling of surface kinetics fully coupled with the volume kinetics (NEW FEATURE included in version 3.1.0, to be released).

LoKI-B includes the following special features:
(i) the prescription of populations to manage the effective momentum-transfer cross section;
(ii) the definition of a generalized Maxwellian EEDF as possible output;
(iii) the calculation of the first anisotropy component of the electron distribution function;
(iv) the possibility of calculating the time-evolution of the EEDF, for excitations promoted by fast-pulsed applied electric fields;
(v) the possibility of considering anisotropic effects in inelastic electron collisions, namely in rotational events, by resorting to momentum-transfer cross sections (included in version 2.2.0, to be released)

The following additional developments of LoKI-B are also pursued.
(i) The development of LoKI-B++, the C++ version of LoKI-B (currently under verification; to be released later);
(ii) The development of special modules and features with LoKI-B, namely:
• an additional heating operator, describing the combined ohmic & stochastic interaction of electrons with the applied electric field;

The following additional developments of LoKI-C are being pursued.
(i) The time-dependent coupling between LoKI-B and LoKI-C.

For more information about LoKI-B, see
A. Tejero-del-Caz, V. Guerra, D. Gonçalves, M. Lino da Silva, L. Marques, N. Pinhão, C. D. Pintassilgo and L. L. Alves, The LisbOn KInetics Boltzmann solver, Plasma Sources Science and Technology 28 043001 (2019), available here.
A Tejero-del-Caz, V Guerra, N Pinhão, C D Pintassilgo and L L Alves, On the quasi-stationary approach to solve the electron Boltzmann equation in pulsed plasmas, Plasma Sources Science and Technology 30 065008 (2021), available here.

After downloading LoKI-B (available here), and especially if you intend to interact with us, you are invited to send a short message
to: loki@tecnico.ulisboa.pt
with subject: LoKI-B
just giving your name and affiliation.

When using LoKI in your work:
- please give proper credits to the main developers, by adding the following citations
Tejero-Del-Caz A et al "The LisbOn KInetics Boltzmann solver" 2019 Plasma Sources Sci. Technol. 28 043001
Tejero-del-Caz A et al "On the quasi-stationary approach to solve the electron Boltzmann equation in pulsed plasmas" 2021 Plasma Sources Sci. Technol. 30 065008
- you are kindly requested to mention the simulation tool in your presentations, using one slide in the packages below
• slides for LoKI-B;
• slides for LoKI-C.

LoKI has being presented in seminars at various research laboratories around the world. See here a copy of the presentation

LoKI-B and LoKI-C can run coupled together or as standalone tools. The scheme below shows the general workflow of LoKI.

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For a given set of discharge parameters (gas pressure and temperature, reduced electric field and excitation frequency, electron density, gas mixture composition), LoKI-B calculates the electron energy distribution function (EEDF) and the electron rate coefficients and transport parameters, from appropriate integrals over the EEDF, using complete sets of validated electron-impact cross sections (provided in a table format compliant with the open-access website LXCat).
The electron parameters are supplied to LoKI-C, to be used in the solution of the 0D rate-balance equations, knowing the kinetic scheme for the plasma/gas system. A test upon charged-particle neutrality calculates a new E/N value, which is introduced in LoKI-B along with the new concentrations of the different heavy-species, in an iterative procedure that continues until convergence. As output, LoKI-C provides the densities of species, the reaction creation / destruction rates, and the self-consistent value of the reduced maintenance electric field.

See here a home video by Duarte Gonçalves on his MSc thesis and the LoKI workflow.

The LisbOn KInetics Monte Carlo (LoKI-MC) solves the electron kinetics for low-temperature plasmas excited by uniform DC electric fields from different gas mixtures, using Monte Carlo techniques. LoKI-MC was released as open-source code licensed under the GNU general public license, being freely available here

LoKI-MC is written in C++, benefiting from a highly-efficient object-oriented structure.

Following the strategy and data organization of the LisbOn KInetics Boltzmann solver (LoKI-B), the code easily addresses any complex mixture of atomic/molecular species, describing electron collisions with any target state (electronic, vibrational and rotational), characterized by any user-prescribed population.
On input, the code requires the working conditions, the gas-mixture composition, the distributions of populations for the levels of the atomic/molecular gases considered, and the relevant sets of electron-scattering cross sections obtained from the open-access website LXCat. On output, it yields the electron energy and velocity distribution functions, the electron swarm parameters, the collision rate-coeffcients, and the electron power absorbed from the electric field and transferred to the different collisional channels.

For more information about LoKI-MC, see
T. C. Dias, A. Tejero-del-Caz, L. L. Alves and V. Guerra, The LisbOn KInetics Monte Carlo solver, Computer Physics Communications 108554 (2022), available here.

After downloading LoKI-MC (available here), and especially if you intend to interact with us, you are invited to send a short message
to: loki@tecnico.ulisboa.pt
with subject: LoKI-MC
just giving your name and affiliation.

When using LoKI-MC in your work please give proper credits to the main developers, by adding the following citation
Dias T C et al "The LisbOn KInetics Monte Carlo solver" 2022 Comput. Phys. Commun. 108554