SPARTAN 2.6 User's Manual M´arioLino da Silva, Bruno Lopez, and Susana Espinho May 5, 2016 Contents Introduction1 1 Getting Started3 1.1 Launching the SPARTAN code...................4 1.1.1 Running the Graphical User Interface (GUI) of the SPAR- TAN code...........................4 1.1.2 How the Graphical User Interface works..........6 1.1.3 Other user-defined parameters...............6 1.1.4 Running the SPARTAN code without the Graphical User Interface............................6 1.2 Recorded data............................6 1.3 Sample comparisons.........................7 1.4 Stepping a little further.......................7 2 Physical Models9 2.1 Discrete radiation models......................9 2.1.1 Selection rules........................9 2.1.2 Line positions and intensities................ 13 2.1.3 Broadening mechanisms................... 20 2.2 Continuum radiation models.................... 23 2.2.1 Transition intensities..................... 24 2.2.2 Special cases......................... 25 2.3 Generalized Kirchhoff–Planck Law for radiative transfer..... 26 2.3.1 Discrete transitions...................... 26 2.3.2 Photoionization transitions................. 26 2.3.3 Photodissociation transitions................ 27 2.3.4 Bremsstrahlung transitions................. 27 3 Detailed Description of the Code 29 3.1 Introduction.............................. 29 3.2 Summary of the capabilities of the SPARTAN code........ 31 3.3 Units used in the SPARTAN code................. 32 3.4 Core routines............................. 32 3.5 The Lineshape calculation routine................. 34 3.5.1 Calculation of a Voigt lineshape.............. 38 3.5.2 Handling and Overlay of Individual Lineshapes...... 42 4 Modifying the Code Spectral Database 45 4.1 Introduction.............................. 45 4.2 Building spectral datafiles for diatomic transitions........ 46 4.2.1 Guidelines for the selection of appropriated spectral con- stants............................. 46 4.2.2 Step-by-step instructions.................. 50 4.2.3 Special case for Homonuclear/Fermion transitions.... 55 4.2.4 Testing your files....................... 55 4.3 Datafiles for diatomic species partition functions calculations.. 56 4.3.1 Approximations considered in the population routine... 57 4.3.2 File structure......................... 58 4.4 Building spectral datafiles for other transitions.......... 59 4.4.1 Atomic discrete and continuum transitions........ 59 4.4.2 Linear polyatomic discrete transitions........... 60 4.4.3 Molecular continuum transitions.............. 62 4.5 Linking new spectral datafiles to the SPARTAN database.... 63 4.6 Summary............................... 66 A References for the SPARTAN Spectral Database 67 B H¨onl{LondonFactors 71 B.1 Applied approximations....................... 72 B.1.1 Neglecting line spin-splitting effects for satellite lines in- volving Σ states....................... 72 B.1.2 Neglecting weaker rotational branches........... 72 B.2 First Rotational Lines intensities.................. 74 B.3 Intermediary a{b case H¨onl-LondonFactors............ 74 C Potential Energies and Wavefunctions Reconstruction 81 C.1 Theory................................. 81 C.1.1 Recalculating potentials for an arbitrary rotational exci- tation............................. 83 C.1.2 Expressions for Radiative transition probabilities..... 84 C.1.3 Numerical Routines Description............... 85 D Other Auxiliary Routines 87 Bibliography 88 E Code Versions Log 95 E.1 Next Version updates........................ 95 E.2 Code Regressions........................... 95 E.3 Code Run Times........................... 97 F Selected Published Works 99 Introduction The SPARTAN code (Simulation of PlasmARadiation in ThermodynAmic Nonequilibrium) is a line-by-line numerical code which calculates the spectral- dependent emission and absorption coefficients of a gas which can be either in thermodynamic equilibrium or not. In it's present version, the code is writ- ten in the MATLAB language. A FORTRAN version of the code is in the works. The numerical code has been initially focused for the simulation of low- pressure, high-temperature plasma applications in aerospace applications (sim- ulation of planetary atmospheric entry radiation). However, the code can and has been applied to a variety of different applications, as for example the simu- lation of radiation from atmospheric and low-pressure plasma sources. Last but not least, the code can be applied to the simulation of atmospheric opacities, the simulation of radiation from combustion processes, or even other applications. The code can be operated in two different fashions: coupled to a fluid dynamics code, which calculates the local macroscopic • properties of the flow, and handles them to the SPARTAN code. The SPARTAN code is in turn coupled to a radiative transfer code, which accounts for the calculated spectral dependent emission and absorption coefficients of the gas, and calculates radiative transfer. stand-alone for the simulation of the local spectral properties of gases and • plasmas, or for the comparison with experimentally determined spectra, providing information on the species temperatures/energy levels distribu- tion functions. The second standalone application is by far the most common one, and this program manual is primarily intended at providing support with the setup of such kind of simulations. This manual is divided in four Chapters: Chapter1 gives a quick overview on how to quickly start using the code • for calculating spectra, using the supplied database of the code. Chapter2 describes the physical models available in the code. • 2 Chapter3 provides a more detailed description of the numerical algorithms • inserted in the code. Chapter4 provides an in-depth description of the file structure of the • SPARTAN spectral database, and explains how the database can be cus- tomized by the user. AppendixA references the spectral database of the SPARTAN code (ex- • cept for Bound Diatomic transitions). AppendixB presents the expressions for the H¨onl{Londonfactors that • have been inserted in the code. AppendixC describes the companion RKR_SCH routine that can be used • for the calculation of the full set of rovibronic states for a specific elec- tronic configuration of a diatomic molecule, and the calculation of Einstein coefficients for bound diatomic transitions. AppendixD describes the other auxiliary routines of the SPARTAN code. • Copyright Notice The SPARTAN code is distributed under the terms of the GNU Lesser Public License (LGPL) as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later versions. The LGPL license allows utilizing the SPARTAN code linked to closed-source/proprietary codes. This program is distributed to the scientific and general community in the hope that it will be useful, but without any warranty. Community involvement in the development of the SPARTAN code itself, or its associated database, is an important endeavor for the developers and main- tainers of the code. As such, we would be grateful if you would be willing to take back a little of your time and share with us any improvements of the code and/or its spectral database so that they can be further distributed among the community of SPARTAN code users. This is something that sometimes tends to be overlooked by the academic community, as much as it can avoid spurious duplication of efforts by different research teams. As such, any sort of feedback would be welcomed by the team, who also man- ages an online repository of spectral data (the GASPAR database, available at http://esther.ist.utl.pt/gaspar). If you wish to have any spectroscopic data added to this ever growing open-access repository (with nearly 1,000 dif- ferent sets of data), feel free to contact us. The latest version of the SPARTAN code is maintained at the following address: http://esther.ist.utl.pt/spartan. Chapter 1 Getting Started This Chapter describes how the SPARTAN code can be quickly used by first-time users, relying on the provided spectroscopic database and using the default line calculation settings. 4 Getting Started 1.1 Launching the SPARTAN code Upon starting MATLAB, the user should select the SPARTAN code direc- tory as a working directory. Then, in the line command, one can type one of the two following instructions to start the SPARTAN code: >> SPARTAN or >> SPARTAN_noGUI The first command launches the graphical user interface (GUI) of the code, whereas the second command launches the application directly, without using the GUI. 1.1.1 Running the Graphical User Interface (GUI) of the SPARTAN code This section will focus on the SPARTAN GUI, which provides a useful in- terface allowing the main calculation parameters to bet set and calculations to be launched without major efforts. Upon launching the application, the GUI window is opened (see Fig. 1.1). Figure 1.1: Graphical User Interface of the SPARTAN Code The interface provides the following items which can be defined by the user: 1.1 Launching the SPARTAN code 5 1. Apparatus function: Here, the user can define a Gaussian apparatus function of a given FWHM in A˚ for the simulation of experimentally mea- sured spectra. this FWHM is added to the calculated Voigt FWHM. Setting this option to 0 reproduces the \physical" spectra, for given local conditions. 2. Rotational temperature: The user defines here the rotational temper- ature for the overall species1. For the calculation of broadening mecha- nisms, the species translational temperature