The line-by-line radiative code SPARTAN

The numerical code SPARTAN is a Line-by-Line code for the simulation of high-temperature, low-pressure plasma radiation, with an emphasis on radiation from entry plasmas, plasma sources, and Hall effect thrusters.

The code has been developped in MATLAB and FORTRAN languages, and is freely distributed under a GNU General Public License.

The spectral database of the code encompasses over 60 bound, bound-free, and free radiative transitions. This allows simulating high temperature gases and plasmas radiation for Earth (Air) and Martian-type (CO2-N2) mixtures, with typically 10,000 to 1,000,000 lines and the superposition of several continua. Other gas mixtures are partially implemented, enabling a variety of other simulations in general plasma science.

The current version of the code is SPARTAN v2.6, dated May 2016.

Dor any questions please contact the developper of the code:


Detailed description of the code

The code numerical routines are capable of simulating bound-bound atomic and molecular radiation with fine-structure effects (singlet, doublet and triplet transitions, with Lambda-doubling effects). Bound-free radiation like photodissociation, photoionization and photodetachment transitions can be accounted for according to available cross-sections from the literature, regardless of whether they are cross-sections integrated over specific temperature ranges, or state-specific cross-sections. Free-free transitions like Bremsthrahlung are also accounted for, using the most popular theoretical and semi-empirical expressions found in the literature.

The Voigt line profile routine is able to account for Doppler broadening, typically the dominant broadening process in low-pressure plasmas, but also Lorentz collisional broadening processes which can be important for higher pressures or higher electron densities (Stark broadening). The line profile routine has been specifically tailored for allowing fast and accurate spectral simulations of about a million of lines, through the application of an innovative algorithm which has recently been developed (2007). The line calculation accuracy is also fully customizable by the user, allowing to chose application-specific compromises between results accuracy, for a larger number of line points, and speed of calculation, for a lower number of points. The numerical efficiency of the line calculation routine is the main factor that enables the application of the code SPARTAN to large-scale spectral simulations with millions of lines (with a particularly relevance for CO2 IR radiation, which can be simulated through the more detailed line-by-line method).

The numerical code has been built with the maximum concern for flexibility. The spectral database is fully decoupled from the numerical routines, being handled in the form of ASCII text files. The code provides a graphical interface, useful for quick spectral simulations, but this merely works as an additional layer, as all the inputs-outputs of the code SPARTAN are handled through text-files. The SPARTAN code can be therefore be utilized coupled to an hydrodynamic and a radiative transfer code, provided that the former provides inputs in text-file format, and the latter accepts outputs in the same format. Finally, the code has been programmed in two separate blocks: An excitation module, which provides the populations of the atomic and molecular species internal levels, and a radiative module, which calculates the emission and absorption coefficients from the levels handled by the excitation routine. The excitation routine currently calculates the internal levels populations considering multitemperature (Tr,Tv,Texc) Boltzmann distributions, but will be able to take into account nonequilibrium populations through a new Quasi-Steady-State (QSS) routine which is currently being developed for air. The excitation routine can even be bypassed, with the direct supply of internal levels populations from an external hydrodynamic/state-to-state code.

Spectral database of the code

CO2 Bound Transitions

CO2 Infrared

H2 Bound Transitions

H2 Lyman bands, H2 Werner bands

C2 Bound Transitions

C2 Swan, C2 Philips, C2 Mulliken, C2 Deslandres-D’Azambuja, C2 Fox-Herzberg, C2 Ballik-Ramsay

CN Bound Transitions

CN Violet, CN Red

CO Bound Transitions

CO Infrared, CO 4th Positive, CO Angstrom, CO 3rd Positive, CO Triplet, CO Asundi

CO+ Bound Transitions

CO+ B-A, CO+ B-X, CO+ Comet Tail

N2 Bound Transitions

N2 1st Positive, N2 2nd Positive

N2+ Bound Transitions

N2+ 1st Negative

NO Bound Transitions

NO gamma, NO beta, NO delta, NO epsilon, NO beta’, NO gamma’

O2 Bound Transitions

O2 Schumann-Runge, O2 Schumann-Runge Continuum

Atomic Lines

H, C, C+, N, N+, O, O+, Ar, Ar+, Hg, Xe, Xe+

Atomic Photoionization

H, C, C+, N, N+, O, O+, Ar, Ar+

Molecular Photoionization

CO2, CO, CN, C2, N2, O2, NO


N, O, N2, O2


C-, N-, O-

Associated packages

The SPARTAN code includes a database routine (RKR-SCH) which is capable of producing accurate transition probabilities from spectroscopic constants and transition moments found in the literature. The code works as follows: Spectroscopic constants from different bibliographical resources are imputed in a numerical routine which reconstructs the potential curves for the transition electronic states using an RKR method and calculates the upper and lower states wavefunctions solving the radial Schrodinger equation. Such wavefunctions are then coupled to accurate electronic transition moments from the literature, to yield appropriate Einstein coefficients.

The SPARTAN code has an associated radiative transfer routine (SPARTAN-RT)* which utilizes the ray-tracing method for the calculation of the radiative fluxes impacting a surface (such as a spacecraft thermal protections or a facility radiation detector). This routine is capable of running in a parallelized fashion in multiprocessor computers, and handling the very fine spectral grids (several million points) obtained using the SPARTAN code. Radiative transfer is therefore fully calculated resorting to the line-by-line method. The radiative transfer routine has insofar successfully been applied to the simulation of the radiative fluxes of a Martian atmospheric entry in the case of two different missions: the NASA PHOENIX mission, and the upcoming ESA ExoMars mission.

* Currently not included in the production version

Example of a Ray-tracing calculation of the heat fluxes impacting a point in the back of a spacecraft entering Mars atmosphere.

License and how to obtain a version of the code

The SPARTAN code is distributed under a GNU Lesser General Public License, a free software license allowing researchers and developers to use and/or integrate the SPARTAN code into their own (even proprietary) software.

Any user wishing to use the code, and agreeing to the license terms, should fill the form below in order to request a copy of the latest version of the code. For verification purposes and to avoid spambots, it is also required to fill a CAPTCHA verification at the end of the registration form.

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User's manual of the code

The code user's manual can be downloaded here.

Sample calculations using the SPARTAN Code

Sample calculations using the SPARTAN Code.

Emission coefficient for a 97% CO2- 3% N2 (Martian-type) equilibrium mixture at 1000 K
Absorption coefficient for a 97% CO2- 3% N2 (Martian-type) equilibrium mixture at 1000 K
Emission coefficient for a 97% CO2- 3% N2 (Martian-type) equilibrium mixture at 5000 K
Absorption coefficient for a 97% CO2- 3% N2 (Martian-type) equilibrium mixture at 5000 K
Emission coefficient for a 97% CO2- 3% N2 (Martian-type) equilibrium mixture at 5000 K
Absorption coefficient for a 97% CO2- 3% N2 (Martian-type) equilibrium mixture at 5000 K
Comparison of a synthetical spectra generated by the SPARTAN code and a measured spectra for the CN VIolet Δv=0 System
Comparison of a synthetical spectra generated by the SPARTAN code and a measured spectra for the CN VIolet Δv=-1 System

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