# Data Needs for Modeling Low-Temperature Non-Equilibrium Plasmas: The LXCat Project, History, Perspectives and a Tutorial

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## Abstract

**:**

Contents | ||||

1 | Introduction | 2 | ||

2 | Data Needs for Modeling LTPs | 4 | ||

2.1 | Kinetic Models: Cross-Sections ............................................................................................................................... | 5 | ||

2.2 | Fluid Models: Transport Coefficients and Reaction Rate Coefficients ............................................................... | 6 | ||

2.3 | Additional Needs for Modeling Non-Equilibrium Plasmas ................................................................................ | 8 | ||

3 | History and Statistics | 9 | ||

3.1 | Origins ....................................................................................................................................................................... | 9 | ||

3.2 | LXCat 10 Years Later ................................................................................................................................................ | 9 | ||

3.3 | Data for Modeling of Plasmas (DMP) Association ............................................................................................... | 11 | ||

4 | What Is Available on LXCat? | 11 | ||

4.1 | List of Data Groups, Databases and Species ......................................................................................................... | 11 | ||

4.1.1 | Differential Scattering Cross-Sections ....................................................................................................... | 12 | ||

4.1.2 | Electron-Scattering Cross-Sections ............................................................................................................ | 12 | ||

4.1.3 | Swarm/Transport Data for Electrons ......................................................................................................... | 14 | ||

4.1.4 | Ion-Scattering Cross-Sections ..................................................................................................................... | 16 | ||

4.1.5 | Interaction Potentials ................................................................................................................................... | 17 | ||

4.1.6 | Swarm/Transport Data for Ions .................................................................................................................. | 18 | ||

4.2 | List of Species ........................................................................................................................................................... | 19 | ||

4.3 | Staging Areas on LXCat .......................................................................................................................................... | 19 | ||

5 | Tutorial: Online Calculations, Data Retrieval and Use | 21 | ||

5.1 | Video Tutorial .......................................................................................................................................................... | 21 | ||

5.2 | Comparison of Data ................................................................................................................................................ | 21 | ||

5.3 | LXCat Online Boltzmann Solver and Swarm Parameters Comparison ............................................................ | 22 | ||

5.4 | Definitions, Guidelines, and Best Practices .......................................................................................................... | 24 | ||

6 | LXCat under the Hood | 27 | ||

6.1 | The Exchange Format and Choice for a Database Type ..................................................................................... | 28 | ||

6.2 | Framework Implementation .................................................................................................................................. | 30 | ||

6.3 | Afternote .................................................................................................................................................................. | 30 | ||

7 | Recent Developments and Perspectives | 31 | ||

8 | Conclusions | 32 | ||

A | How to Cite Data Retrieved from LXCat and Online Calculations | 33 | ||

B | Referencing and Redistribution of Data | 33 | ||

References | 34 |

## 1. Introduction

The integrity of the results obtained from numerical modeling depends […] on the identification of a physical model appropriate for addressing the problem of interest, on a good choice and proper implementation of the numerical solution techniques, and on the availability of reliable input data.

Apart from the obvious advantages that open data could bring for reproducibility and scientific integrity–although there is devil in the detail of how to implement this–one argument in favour of data sharing is that having more pairs of eyes on data may lead to new discoveries and faster scientific progress.

## 2. Data Needs for Modeling LTPs

#### 2.1. Kinetic Models: Cross-Sections

**cross-sections**${\sigma}_{j}$, each characterizing the probability of a given collision process j on a (microscopic) particle level.

#### 2.2. Fluid Models: Transport Coefficients and Reaction Rate Coefficients

**rate coefficients**of different electron-impact processes, for example, can be computed from the corresponding cross-sections via the following integral:

**drift velocity**$\overrightarrow{W}$ and the

**diffusion coefficient**D. The drift velocity is proportional to the electric field, $\overrightarrow{W}=\pm \mu \overrightarrow{E}$, with a coefficient of proportionality $\mu $ called

**mobility**and ± the sign of the particle charge. These transport coefficients can be measured in swarm experiments (as functions of $E/N$), hence they are known as “swarm parameters”. They can also be calculated from an appropriate set of cross-sections by solving the Boltzmann equation for a simple particle swarm system with a uniform electric field and no boundaries, or, alternatively, by Monte Carlo simulation of such a system [7,26].

**Townsend coefficients**for ionization, $\alpha $, and for electron attachment, $\eta $, defined as the inverse characteristic length of spatial growth or decay of a steady-state electron swarm. The net electron production rate per unit volume can be calculated by multiplying $(\alpha -\eta )$ by the electron flux density in the drift direction.

**electron mean energy**as a function of $E/N$,

#### 2.3. Additional Needs for Modeling Non-Equilibrium Plasmas

_{2}and N

_{2}

^{+}molecular band emissions [34]. For determining the population rates by electron impact, so-called optical emission cross-sections are measured experimentally. Knowledge of the detailed excitation pathways is also needed when one is interested in the production of specific excited states. For example, metastable species in noble gases are frequently of interest. Predicting the formation of these states requires state-to-state models which track the multitude of excited states which can exist. Similarly, in the case of plasma medicine, the production and destruction of particular reactive species can require immense reaction sets. The choice of detail for a particular plasma model requires careful consideration about quantities of interest while balancing the model’s complexity.

## 3. History and Statistics

#### 3.1. Origins

#### 3.2. LXCat 10 Years Later

#### 3.3. Data for Modeling of Plasmas (DMP) Association

- encourage the exchange and open access of fundamental data via the Internet;
- develop tools to facilitate the exchange of online data;
- contribute to the collection and evaluation of data;
- communicate with the international scientific community to increase the visibility of fundamental data available online;
- communicate with specialists via forums such as the French Cold Plasma Network;
- encourage open access to numerical tools for the generation and analysis of data as well as for modeling plasmas;
- contribute to the standardization of formats for storing and exchange of data.

## 4. What Is Available on LXCat?

#### 4.1. List of Data Groups, Databases and Species

**present data “as-is” after generation by the LXCat online tools to illustrate the functionalities of the website**.

#### 4.1.1. Differential Scattering Cross-Sections

_{2}[47,50]. The ANU database was introduced in October 2016, and contains a significant number of species, namely He [51], Ne [52], Ar [39], Kr [53,54], Xe [55], CF

_{2}[56], CH

_{4}[57], C

_{2}F

_{4}[58], C

_{2}H

_{4}[59], C

_{4}F

_{8}[60], C

_{4}H

_{8}O [61], C

_{4}H

_{8}O

_{2}[62], C

_{6}H

_{6}[63,64], C

_{6}F

_{6}[64], CO [65], CO

_{2}[66], SF

_{6}[67], H

_{2}[68], H

_{2}O [69], H

_{2}S [70], HCOOH [71], O

_{2}[72], N

_{2}[73,74], N

_{2}O [75], NH

_{3}[76,77], NO [78], and SO

_{2}[79]. The database is a compilation of experimental data from researchers at the Australian National University and their collaborators.

#### 4.1.2. Electron-Scattering Cross-Sections

**complete set**, i.e., a set accounting in a consistent manner for the complete electron energy losses and momentum losses due to collisions. For electron-scattering cross-sections, LXCat recognizes 5 distinct processes that each relate back to a particular collision model used in solutions of the Boltzmann equation.

- Elastic: elastic momentum-transfer process.
- Excitation: electron-scattering process where part of its kinetic energy is transferred into electronic excitation of atoms or molecules. Similarly, excitation of rotational and vibrational levels of molecules are electron-impact excitation processes.
- Ionization: ionization process, inelastic collision in which a new electron is created.
- Attachment: an electron is lost in the collisional process. This can be either due to formation of negative ions but also electron-ion recombination.
- Effective: momentum transfer including all electron-scattering with a given target particle species. This is equal to the sum of the elastic momentum transfer and the total cross-sections for all inelastic and ionization processes. For historical reasons, this is included instead of elastic momentum transfer in some data sets.

- Biagi [80]: data transcribed by the LXCat team from S.F. Biagi’s FORTRAN code, MagBoltz, versions 8.9 and later [81,82], the exact version depending on the species as listed in the database. The database contains cross-sections for rare gases He, Ne, Ar, Kr, and Xe, and molecules H
_{2}, D_{2}, N_{2}, O_{2}, CO_{2}and SF_{6}. The transcription of data for other gases is in progress. These data were compiled for use with a Monte Carlo simulation (or multi-term Boltzmann code), but their use in a 2-term Boltzmann solver gives reasonably accurate results in most cases. Please note that the LXCat data tables do not have the same energy grid as the original data in the MagBoltz code. - Biagi-v7.1 [83]: This database contains cross-sections for the rare gases He, Ne, Ar, Kr, and Xe, transcribed by the LXCat team from the Magboltz code version 7.1 by Stephen Biagi [81,82]. The excitation cross-sections are grouped into a few effective excitation levels. These cross-sections were compiled for use in a Monte Carlo (or multi-term Boltzmann) code.
- BSR [43]: The results in this database are from a semi-relativistic Breit-Pauli B-spline R-matrix (close-coupling) calculations [41,42]. It contains data for the species Ne, Ar, Kr, Xe, Be, C, N and F. Compared to 2016 the Ar data were extended with 469 records [87] and Be (201 records), C [88] (1178 records), N [89] (353 records), and F [90] (384 records) were added.
- CCC [91]: Cross-sections obtained by calculations using the convergent close-coupling method [44,45,46,47]. To the already present species H, He, D
_{2}^{+}, DT^{+}, H_{2}^{+}, HD^{+}, HT^{+}, and T_{2}^{+}, data for the following species have been added since 2016: H_{2}, HD, HT, D_{2}, DT, and T_{2}[47,92,93,94]. - FLINDERS [99]: A compilation of cross-sections uploaded to LXCat by Laurence Campbell of Flinders University, containing data for the species CO
_{2}, N_{2}, NO, and O_{2}. - Hayashi [100]: These data sets were derived by comparing calculated swarm parameters, using as input the cross-sections sets in this database, with measurements. It contains data for the species Ar, Xe, C
_{2}H_{2}, C_{2}H_{4}, C_{2}H_{6}, CCl_{2}F_{2}, CCl_{4}, CF_{4}, CH_{4}, CO_{2}, H_{2}O, HCl, N_{2}O, NH_{3}, NO, Si_{2}H_{6}, SiH_{4}, and SO_{2}. - IST-Lisbon [35]: This database contains data compiled from the literature from different authors, resulting in complete sets of cross-sections, validated against measured swarm parameters by solving the two-term homogeneous electron Boltzmann equation [101]. To improve predictions at low E/N, some sets need to be completed with rotational cross-sections, also available in the database. The following species are represented: He (replaced since 2016 [102]), Ar, CH
_{4}, H, H_{2}, N (replaced since 2016 [103]), N_{2}, O_{2}, and added since 2016: CO [104], CO_{2}[105], O [106], and O_{2}vibrational states [107]. - Morgan (Kinema Research & Software) [110]: Cross-section sets suited for use with 2-term Boltzmann solvers assembled by W.L. Morgan for the species He, Ne, Ar, Xe, Kr, C, C
_{2}H_{2}, C_{2}H_{4}, C_{2}H_{6}, C_{3}H_{8}, CF_{4}, CH, CH_{2}, CH_{3}, CH_{4}, Cl_{2}, CO, CO_{2}, F_{2}, H, H_{2}, H_{2}O, HCl, N, N_{2}, NH_{3}, NO, O, O_{2}, O_{3}, SF_{6}, and SiH_{4}. - NGFSRDW [111]: A set of excitation cross-section to individual fine-structure levels of Ar and Kr (a collection of 148 records added since 2016) calculated by Al Stauffer and co-workers.
- Phelps [112]: A compilation of atomic and molecular data, assembled and evaluated by A.V. Phelps and collaborators, including the species He, Ne, Ar, Xe, CO, CO
_{2}, H_{2}, H_{2}O, Mg, N_{2}, Na, NO, O_{2}, and SF_{6}. - Puech [113]: Cross-section sets assembled by V. Puech and colleagues in late 1980s and 1990s for the species Ne, Ar, Xe, C
_{2}H_{4}, and C_{3}H_{6}. - QUANTEMOL [114]: Data calculated and published by Quantemol Ltd. and associated researchers using Quantemol-N software/expert system [115]. This database includes the species BF
_{3}, C_{2}, C_{2}H_{2}, C_{2}OH_{6}, C_{3}, C_{3}H_{4}, C_{3}N, CaF, CF, CF_{2}, CF_{4}, CH, CH_{4}, CNH, CO, CO_{2}, CONH_{3}, COS, CS, F_{2}O, H_{2}, H_{2}O, H_{2}S, CH_{4}, HBr, HCHO, HCN, HCP, Kr, N_{2}, N_{2}O, NH_{3}, NO_{2}, O_{2}, O_{3}, PH_{3}, SiF_{2}, SiH_{4}, SiO, and SO_{2}. - SIGLO [116]: A compilation of data used in-house by the group GREPHE at LAPLACE in Toulouse, taken from different sources and including the species He, Ne, Ar, Xe, Kr, Cl
_{2}, CO_{2}, Cu, F_{2}, HCl, Hg, N_{2}, SF_{6}, and SiH_{4}. - TRINITI [117]: Cross-sections retrieved from the EEDF software package for calculations of the electron energy distribution function [118], for the species He, Ne, Ar, Xe, BCl, BCl
_{2}, BCl_{3}, CF_{3}I, CF_{4}, CH_{4}, CO, CO_{2}, Cs, F_{2}, H, H_{2}, H_{2}O, HCl, N_{2}, Na, NF_{3}, O, O_{2}, and SF_{6}. All data except O_{2}have been uploaded to LXCat since 2016.

_{2}

^{+}[126] and BeH

^{+}[127,128] already uploaded. The Laporta database is a compilation of vibrationally resolved cross-sections for electron-molecule scattering based on R-Matrix calculations. It currently contains data for vibrationally resolved dissociative excitation and attachment for the NO [129,130] and O

_{2}[131] molecules.

#### 4.1.3. Swarm/Transport Data for Electrons

_{6}) and IST-Lisbon [35] (data for Ar, CH

_{4}, H

_{2}, He, and N

_{2}) databases also contain electron-scattering cross-sections and were already briefly described in Section 4.1.2. The following were already described in [38]:

- ETHZ [134]: Data obtained with pulsed Townsend experiments at the High Voltage Laboratory of ETH Zurich, Switzerland. It contains data for the species Ar, CO
_{2}, N_{2}, and the gas mixtures 2−C_{4}F_{8}with Ar, CO_{2}, and N_{2}, and c-C_{4}F_{8}O with Ar, CO_{2}, and N_{2}. Since 2016 the following species and gas mixtures have been added: CO_{2}(second set) [135], O_{2}[136], CH_{3}CN, N_{2}O [137], C_{3}HF_{5}[138], C_{4}F_{7}N [139], C_{5}F_{10}O [140], SF_{5}CF_{3}[141], CF_{3}−O−CF=CF_{2}, HFC227ea [142], HFO1234ze [143], and the gas mixtures C_{3}HF_{5}with CO_{2}and N_{2}[138], C_{4}F_{7}N with CO_{2}, CO_{2}:O_{2}, and N_{2}[139,144], C_{5}F_{10}O with CO_{2}, CO_{2}:O_{2}, N_{2}, and N_{2}:O_{2}[140], CO_{2}with N_{2}and O_{2}[145], HFC227ea with CO_{2}and N_{2}[142], HFO1234ze with Ar, CO_{2}, N_{2}, and SF_{6}[143,146,147], HFPO with CO_{2}and N_{2}[148], N_{2}:O_{2}[136], SF_{5}CF_{3}with CO_{2}and N_{2}[141]. - LAPLACE [149]: Collection of data from after 1975 or not appearing in the Dutton compilation [133] digitized by S. Chowdhury from LAPLACE, Toulouse. It includes the gases Ar, C
_{2}F_{6}, C_{2}H_{4}, C_{2}H_{6}, C_{3}F_{8}, C_{3}H_{6}(cyclopropane and propene), C_{3}H_{8}, CF_{3}I, CF_{4}, CH_{4}, CHF_{3}, CO, CO_{2}, H_{2}, H_{2}O, He, Kr, n-C_{4}F_{10}, N_{2}, N_{2}O, Ne, O_{2}, Xe, Air, and the gas mixtures Air:H_{2}O, CO_{2}:Ar, H_{2}:Ne, He:H_{2}, N_{2}:Ar, N_{2}O:Ar, O_{2}:Ar, Xe:H_{2}, and Xe:N_{2}. - UNAM [150]: Electron-swarm data derived from pulsed Townsend experiments for the gases Ar, C
_{2}F_{4}, C_{2}F_{6}, CF_{3}I, CHF_{3}, CO_{2}, N_{2}, SF_{6}, and gas mixtures C_{2}F_{4}with Ar and Xe, C_{2}F_{6}with Ar and N_{2}, CF_{3}I with N_{2}and SF_{6}, CHF_{3}with Ar and N_{2}, and SF_{6}with Ar, CF_{4}, CHF_{3}, CO_{2}, He, N_{2}, N_{2}O, O_{2}, and Xe.

- CDAP (State-to-state electron-impact excitation rate coefficients) [151]: State-to-state electron-impact excitation rate coefficients between argon neutral or xenon ionic states obtained by combination of plasma experiments and theoretical calculations. In particular, the data are used for collisional-radiative modeling and examined in the afterglow plasma of argon (CDAP method) or examined in the different regions of electric propulsion devices using xenon. Rate coefficients for both atoms and ions are given here, and can be used for plasma modeling and optical emission spectroscopy (OES) [152,153].
- Heidelberg [154]: database of electron transport parameters measured at the University of Heidelberg in the years 1978 to 1996. Different electron-swarm experiments were setup by Bernhard Schmidt and co-workers which allowed to measure electron transport parameters in pure electric and perpendicular crossed electric and magnetic fields. This database contains only those data for B=0. Additional swarm data for non-zero B fields will be made available in tabular and graphical form when resources become available. The following gases and gas mixtures are present: C
_{2}H_{4}, C_{2}H_{6}, C_{2}H_{6}O, C_{3}H_{6}, C_{3}H_{8}, CH_{4}, CO_{2}, D_{2}, H_{2}, N_{2}, Ar:C_{2}H_{6}O, C_{4}H_{10}:Ar, C_{4}H_{10}:He, CO_{2}:Ar, CO_{2}:Ne, H_{2}:Ar, H_{2}:Kr, H_{2}:Xe, and N_{2}:Ar. These data were collected by Malte Hildebrandt, presently at the Paul Scherrer Institute in Switzerland, from publications and theses in the Heidelberg group and were made available to the LXCat team for inclusion in LXCat.

#### 4.1.4. Ion-Scattering Cross-Sections

^{+}and He

^{+}in their parent gases taken from the Phelps database. The Phelps database also contains data for Xe

^{+}in its parent gas and in Ne. In July 2017, the second database providing this type of data was introduced, namely the Viehland database [158]. This database contains data for ions of all elements highlighted in Figure 6 (excluding P) in the noble gases [159]. Viehland provides angular scattering information in the form of angle moments of the total differential scattering cross-sections. He calculated these from the ion-neutral interaction potentials which are also present in the Viehland database.

#### 4.1.5. Interaction Potentials

_{2}resulting in 660 potentials.

#### 4.1.6. Swarm/Transport Data for Ions

^{+}, Ne

^{+}, Ar

^{+}, N

^{+}, and N

_{2}

^{+}in their respective parent gases [112]. The UNAM database contains mobility parameters for CF

_{3}

^{+}in CF

_{4}, CHF

_{2}

^{+}in CHF

_{3}, and C

^{+}in Ar [161]. The Viehland database is transcribed in part from the Gaseous Ion Transport and Rate Coefficient Database developed by Viehland [159]. In this database are several additional parameters derived from theory following high-order moments expansion of the Boltzmann equation. Data for 424 positively or negatively charged atomic and molecular ions is available for a wide variety of elements across the periodic table of elements (see also Figure 6). Some of the notable changes and extensions since 2016 in the Viehland database involve ions of C [162,163], Co, Cr, and Ni [164], Gd [165], K [166,167], Mg [168,169,170,171], O [172,173], S [174], and Si [175].

#### 4.2. List of Species

#### 4.3. Staging Areas on LXCat

**BOLSIG+**is a user-friendly Windows application for the numerical solution of he Boltzmann equation for electrons in weakly ionized gases in uniform electric fields, conditions which typically appear in the bulk of collisional low-temperature plasmas. Under these conditions the electron energy distribution is determined by the balance between acceleration in the electric field and momentum and energy loss in collisions with neutral gas particles [27,179]. An improved description of Coulomb collisions was developed by Hagelaar and is included in the more recent versions of BOLSIG+ [180].**ZDPlasKin**: Zero-Dimensional Plasma Kinetics solver ZDPlasKin is a Fortran 90 module designed to follow the time evolution of the species densities and gas temperature in a non-thermal plasma with an arbitrarily complex chemistry [21]. BOLSIG+ is integrated in this package.**EEDF**is a user-friendly program for the numerical solution of Boltzmann equation for the Electron Energy Distribution Function in low-ionized plasma in an electric field. It is used for calculations of electron transport and kinetic coefficients in gas mixtures. EEDF comes with Data Bank, several files containing data on cross-sections for the electron-scattering from atoms and molecules [118] compatible with EEDF program. These cross-section data can be found in the TRINITI database on LXCat.**BOLOS**: This package provides a pure Python library for the solution of the Boltzmann equation for electrons in a non-thermal plasma. It is a multi-platform, open-source implementation compatible with the LXCat cross-section input format [181].**PumpKin**: (pathway reduction method for plasma kinetic models) is a tool for post-processing of results from zero-dimensional plasma kinetics solvers. The goal is to analyze the production and/or destruction mechanisms of selected species of interest, as well as to reduce complex plasma chemistry models. Only once the user is required to solve first the full chemical reaction system. The output is then used as an input for PumpKin. The PumpKin package analyzes the full chemical reaction system, and automatically determines all significant pathways in the system, i.e., all pathways with a rate above a user-specified threshold [182,183].**METHES**is an open-source Monte Carlo collision code written in MATLAB for the simulation of electron transport in arbitrary gas mixtures in the presence of electric fields. For steady-state electron transport in a uniform electric field, the program provides the transport coefficients, reaction rates and the electron energy distribution function. The program is compatible with the electron-scattering cross-section files from LXCat. Temporal studies of electron transport are possible by tracking position, velocity and number of electrons [184,185].**MultiBolt**is a multi-term Boltzmann equation model for calculating electron kinetic phenomena in electron swarms and low-temperature plasmas. MultiBolt uses a combined electron density gradient and spherical harmonics decomposition of the electron phase space in the Boltzmann equation. From this, macroscopic rate and transport coefficients (flux and bulk) are calculated. MultiBolt has been demonstrated to be consistent with other popular kinetic models (BOLSIG+, METHES, and others), and is also in excellent agreement with other published models when calculating rate and transport coefficients for model gases, such as the Reid ramp model gas and the Lucas-Saelee attachment-ionization model gas. See also, J. Stephens, “A multi-term Boltzmann equation benchmark of electron-argon cross-sections for use in low-temperature plasma models” [186].**LoKI-B**: The LisbOn KInetics Boltzmann solver (LoKI-B), available as MATLAB open-source tool, solves the time and space independent form of the two-term electron Boltzmann equation, for non-magnetized non-equilibrium low-temperature plasmas excited by DC/HF electric fields from different gases or gas mixtures, considering growth models for the electron density to describe non-conservative events. LoKI-B can easily simulate 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 [187].**THERMCAT**: A fast and robust online tool for simulation of different modes of axially symmetric current transfer from high-pressure arc-discharge plasmas to cylindrical thermionic cathodes, created and maintained by Mikhail Benilov and co-workers. The code computes both the diffuse mode of current transfer and modes with axially symmetric spots and can be used in a wide range of arc currents, plasma-producing gases, and cathode materials and dimensions. The tool also serves as a tutorial that can help to make physicists and engineers working in the field comfortable with multiple solutions describing different modes of current transfer to electrodes in low-temperature plasmas [188,189].**ELEM**: A code for evaluation of the field to thermo-field to thermionic electron emission current density. The code is based on an accurate and computationally efficient method of evaluation of the Murphy-Good formalism [190].**MOBION**: A code for evaluation of the mobility and temperature of ions in a weakly ionized gas as functions of reduced electric field and gas temperature. The code is based on the two-temperature displaced-distribution theory [191].

## 5. Tutorial: Online Calculations, Data Retrieval and Use

#### 5.1. Video Tutorial

#### 5.2. Comparison of Data

_{2}currently present on LXCat. One can see an overall good agreement between the different databases.

#### 5.3. LXCat Online Boltzmann Solver and Swarm Parameters Comparison

**BOLSIG+ database**from the online Boltzmann solver, which is a temporary database created, when requested, by the user following execution of the online Boltzmann solver. The contents of this database include swarm/transport parameters versus E/N calculated after selecting a complete dataset for each species considered in the calculation.

**(see Figure Figure 10 for an example of selected datasets and some computed quantities)**. The data existing in this temporary database can be plotted along with measured quantities available on the other databases or compared with results from other online calculations in different gas mixtures. This temporary database is deleted when the user exits the LXCat site. A video tutorial was made to show how to perform such calculations online and how to compare the results of the calculations with data available on the website [197].

_{2}gas calculated using the Biagi database [80,198] compared to the experimental data available on LXCat (see the caption under the figure for the references) as a function of reduced electric field. One can see a relative spread of the experimental data (see references in Section 4.1.3) but an overall good agreement in the intermediate reduced field strength range.

#### 5.4. Definitions, Guidelines, and Best Practices

**Historical origins of electron-neutral cross-section sets**

**Definition of complete set**

**Mixing cross-sections data sets or using incomplete sets**

**Selection of a cross-sections data set**

**The elastic momentum-transfer cross-section and anisotropic scattering**

**Swarm configurations and growth models**

**Piecewise linear interpolation of cross-sections**

**Bulk and flux transport coefficients**

**Temperature range for validity of a given set of cross-sections**

**Treatment of three-body collisions**

**Sorting and filtering target species**

**Accessing and viewing large data sets online**

**Chemistry models and how they affect calculations**

**Formatting for excitation and superelastic processes in a cross-section file**

`->`”, or by a double-head arrow “

`<->`” (e.g., “

`Ar->Ar*`”, or “

`Ar<->Ar*`”, where “

`Ar`” is the target state, and “

`Ar*`” is the excited state). The latter case is used to denote that the excitation is a reversible process, with the reverse process corresponding to a superelastic collision (i.e. the electron gain energy after the collision). In the double-head arrow format, the online Boltzmann solver will automatically define and additionally use the corresponding superelastic collision in its kinetic computation.

## 6. LXCat under the Hood

- The data exchange format, the data model and the choice for a database type;
- The overall framework design.

#### 6.1. The Exchange Format and Choice for a Database Type

`NULL`values in the table. These are necessary for species where a particular coupling scheme is not applicable. In this case, neither e nor Ar${}^{*}$ are described by the LS coupling scheme. The larger, implicit problem is that the addition of each new optional parameter affects the entire table, even those entries for which the parameter is not relevant. These issues suggest the need to reconsider the LXCat backend to better serve the community. Although some techniques exist to ameliorate these issues (e.g., table indirection), they do not solve the fundamental problem which is that table-based databases are not well suited for heterogeneous data sets.

#### 6.2. Framework Implementation

#### 6.3. Afternote

## 7. Recent Developments and Perspectives

## 8. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A. How to Cite Data Retrieved from LXCat and Online Calculations

## Appendix B. Referencing and Redistribution of Data

**1**) anyone willing to contribute data to the site can request a password and set up a database; the contents and maintenance of the databases remain the responsibility of the individual contributors. (

**2**) The site is open access and data can be downloaded without registering or paying a fee. (

**3**) The databases are dynamic and contributors are free to make changes as they see fit. Consequences of these guidelines are that data for the same processes can be listed in multiple databases and that different versions of the same data can be accessed on the website. Hence users are strongly encouraged to reference data downloaded from LXCat in all publications making use of the data.

- Third parties should direct their users to the LXCat website to obtain data. Before downloading data, visitors to the site are asked to click to confirm that “Yes. I understand the LXCat policy and I agree to properly reference these data”. The header in downloaded files contains reference information that should be included in all publications making use of LXCat data and further guidelines for proper referencing are given in Appendix A.
- The LXCat team can provide customized interfaces to institutional members of the non-profit association “Data for Modeling Plasmas” (http://assoc.lxcat.net). This option is useful for code developers who recommend specific LXCat data sets for use in their software; that is, users who access the LXCat website through such a customized interface are directed to the specific data chosen by the code developers.
- In cases where neither of the above options is practical, third parties can include data from LXCat in their packages under the following conditions:
- Explicit written permission must be obtained from the owner of the database (the contributor) whose data is being included in the third-party package.
- LXCat must be notified in advance and a Memorandum Of Understanding (MOU) must be prepared between the LXCat team, the contributors who agree to have their data set redistributed within a software or any other shareable format and the MOU must be signed by all parties.
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1 | As will be seen later, the velocity distribution function of electrons is frequently non-Maxwellian. However, the term ‘temperature’ is often used where ‘mean energy’ would be more appropriate. |

2 | |

3 | There exists also a second Townsend coefficient, characterizing the yield of electrons from a cathode bombarded by positive ions which helps sustaining a discharge. |

4 | For the interested reader: we have built a framework for the compilation of the schema files from elementary building blocks in JavaScript/TypeScript, which also can host chemical (non-electronic) processes in a future database release. |

**Figure 1.**Example of a “traditional way” of retrieving data from a physically printed plot of a paper by Biberman et al. [14] which was itself scanned in the present case from a printed journal volume (courtesy from J. van Dijk, TU/e).

**Figure 2.**Geographic location of the countries currently contributing to the LXCat project. Please note that this map reflects on the location of direct contributors to the project and not necessarily on the countries from which the data originally came from.

**Figure 3.**Statistics about LXCat: (

**a**) Number of citations of the LXCat website per year in scientific publications according to Google Scholar research engine up to 3 December 2020. (

**b**) Number of visits and downloads per week over the last three years (January 2017–November 2020).

**Figure 4.**Differential scattering cross-section for elastic and inelastic scattering processes with argon ground state. (

**a**) Experimental measurement of elastic electron/Ar collisions from ANU database [39,40] for different electron-impact energies with label from 1 to 8: 1 eV, 1.5 eV, 2 eV, 3 eV, 3.14 eV, 5 eV, 7.5 eV and 10 eV; Theoretical calculations from the BSR database [41,42,43] using the R-matrix method of differential cross-sections for electrons with ground state Ar: (

**b**) elastic collision; (

**c**) electronic excitation from ground state to Ar${}^{*}4{s}^{\prime}{[1/2]}_{1}$ state; (

**d**) electronic excitation from ground state to Ar${}^{*}4s{[3/2]}_{2}$ state.

**Figure 5.**Ion-scattering cross-sections from the Phelps database [112]: backscattering (curve 1) and isotropic scattering (curve 2) of Ar

^{+}ion in Argon; backscattering (curve 3) and isotropic scattering (curve 4) of He

^{+}ion in Helium.

**Figure 8.**Sample of different types of swarm parameters taken from Viehland’s database plotted for some different ions in different background gases as a function of the reduced electric field E/N in Td [158]. (

**a**) Product of gas number density and ion diffusion coefficient in the perpendicular ($N{D}_{x}$) (curves 1–2) and parallel ($N{D}_{z}$) directions to the electric field (curves 3–5) for 2 different temperatures of 100 and 500 K (curves 2 and 4 for the latter) [176]. (

**b**) Ion drift velocity of Xe

^{+}ions in He at 100 K (curve 1) and 500 K (curve 2) [176]. (

**c**) Ion mobility in different background gases at 300 K [177,178]: (1) O

_{2}

^{+}in air, (2) O

_{2}

^{−}in He, (3) O

_{2}

^{−}in air, (4) SF

_{3}

^{+}in SF

_{6}, (5) He

_{2}

^{+}in He, (6) O

_{2}

^{+}in He, (7) O

_{2}

^{−}in He.

**Figure 10.**(

**a**) Input cross-sections data from the Morgan database [110,196]: cross-sections 1–13 belong to CO

_{2}and 14–38 to N

_{2}datasets) and computed quantities for a 0.5–0.5 CO

_{2}/N

_{2}gas mixture as a function of reduced electric field E/N in Td; (

**b**) electron energy distribution function (EEDFs); (

**c**) mean electron energy; (

**d**) EEDF anisotropy.

**Figure 11.**Swarm parameters calculated using the online Boltzmann solver for a pure CO${}_{2}$ gas using the Biagi database [80,198] and comparison with experimental swarm measurements [133,135,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219] from Dutton [132], ETHZ [134], Heidelberg [154], LAPLACE [149] and UNAM [150] databases as a function of reduced electric field. The computed quantities are: (

**a**) characteristic electron energy, (

**b**) product of the gas number density and electron diffusion coefficient, (

**c**) product of the gas number density and electron mobility coefficient, (

**d**) Townsend coefficients.

**Figure 12.**The argon excitation cross-section from the Phelps database [112] (excerpt).

**Figure 13.**Using a collection of documents instead of a table is a lot more suited to heterogeneous data. Meanwhile, object structure can be controlled by defining a JSON Schema document that all entries should adhere to.

**Figure 14.**Schematic representation of the current (

**a**) and proposed (

**b**) framework implementations. Currently, the website is directly coupled to the database. The proposed implementation adds an API layer that can serve multiple frontends through a set of well-defined endpoints

**Table 1.**Different state entries in the LXCat database can have divergent requirements when it comes to their description, e.g., Ar${}^{*}$ vs Ar(${}^{1}{S}_{0}$). Such heterogeneous data can lead to a lot of

**NULL**values.

Particle | Charge | e | S | L | Parity | J |
---|---|---|---|---|---|---|

e | −1 | NULL | NULL | NULL | NULL | NULL |

Ar | 0 | * | NULL | NULL | NULL | NULL |

Ar | 0 | NULL | 0 | 0 | Even | 0 |

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## Share and Cite

**MDPI and ACS Style**

Carbone, E.; Graef, W.; Hagelaar, G.; Boer, D.; Hopkins, M.M.; Stephens, J.C.; Yee, B.T.; Pancheshnyi, S.; van Dijk, J.; Pitchford, L. Data Needs for Modeling Low-Temperature Non-Equilibrium Plasmas: The LXCat Project, History, Perspectives and a Tutorial. *Atoms* **2021**, *9*, 16.
https://doi.org/10.3390/atoms9010016

**AMA Style**

Carbone E, Graef W, Hagelaar G, Boer D, Hopkins MM, Stephens JC, Yee BT, Pancheshnyi S, van Dijk J, Pitchford L. Data Needs for Modeling Low-Temperature Non-Equilibrium Plasmas: The LXCat Project, History, Perspectives and a Tutorial. *Atoms*. 2021; 9(1):16.
https://doi.org/10.3390/atoms9010016

**Chicago/Turabian Style**

Carbone, Emile, Wouter Graef, Gerjan Hagelaar, Daan Boer, Matthew M. Hopkins, Jacob C. Stephens, Benjamin T. Yee, Sergey Pancheshnyi, Jan van Dijk, and Leanne Pitchford. 2021. "Data Needs for Modeling Low-Temperature Non-Equilibrium Plasmas: The LXCat Project, History, Perspectives and a Tutorial" *Atoms* 9, no. 1: 16.
https://doi.org/10.3390/atoms9010016