The Saha equation is a thermodynamic realtionship between the ionisation levels of an element, their energy differences and temperature. This equation can be used to compare the ratios of the multiple ionisation levels of given elements.
The goal of this repository is to provide a python solver for the Saha equation that can take a state (total densities of the elements as well as the temperature of the system) and return the exact densities of each ionised state of these elements.
Given that the code will be mainly used for solar studies, the input data will be assumed to be in CGS units (cm-g-s) and the temperature is assumed in Kelvin. The code will then convert it into natural units (hbar = c = kb = 1). It is important to stick to these units because some of the computations include mass which is provided in the code dictionary in natural units (1Da = 9.3289e8 eV).
Here are some shortcuts to convert:
1eV = 1.78e-33 g ; 1eV^-1 = 1.97e-5 cm
1g = 0.5618e33 eV ; 1cm = 0.5076e5 eV^-1
1 g/cm^3 = 4.2955e18 eV^4
Here the task is simple. You just have to download the code and have the appropriate packages installed on your machine. These packages are listed in the virtual_env.yml file along with their versions.
If you use Anaconda/Miniconda, you can automate this process by using the env create command in this folder:
conda env create -f virtual_env.yml
Once this is done the code should run without any issues.
The default way to run the code is to give it the elements you are interested in, their densities, and the temperature of the system. This can be done directly from the terminal as follows
python main.py -e H He -d 1662424176 719087680 -t 1.549e+09
The example above is solving a system of Hydrogen and Helium, with respective densities of 1662424176 and 719087680 eV^4, at a temperature of 1.549e+09 eV.
The output here is descriptive (given that its just one computation).
Temperature: 133482.49224845882 eV
Total Number Densities: [7.595260026104078e+18, 8.272280373370961e+17] eV3
Number Densities of Ionised States: [7.540700734348527e+18, 5.4559291755552696e+16, 8.037987768016884e+17, 2.3261011402521604e+16, 168249132885872.66] eV3
Maximum Electron Number Density: 9.24971610077827e+18 eV3
Actual Electron Number Density: 7.815680142384608e+16 eV3
The total ionization in the system is: 0.8 %
--- 0.15461421012878418 seconds ---
Another way of running this program is by using a Solar Model file (or any other model). Such a file should contain rows of different temperatures and densities. A sample model can be found here https://wwwmpa.mpa-garching.mpg.de/~aldos/SSM/AGSS09/model_agss09.dat
To run the code you have to still give it the element symbols you want, with the filename of the model and the position of the temperature and respective element columns. Here is an example
python main.py -e H He -s solar_data.txt -p 2 6 7 -f results.txt
Which means that we want to solve for Hydrogen and Helium, and that the third column is the temperature data, and the 7th and 8th are the respective densities of the elements. We also include the name of the file to save the results to.
The command output will be just the time elapsed. The actual solver results will go into the file with the specified name above. They will be comma seperated and in the following order
[T(eV), nH(eV3), nHe(eV3), ..., nH0(eV3), nH1(eV3), nHe0(eV3), ..., nE_Max(eV3), nE(eV3)]
Below is the list of items included in the code dictionary, and their corresponding symbol.
- Hydrogen (H)
- Helium (He)
- Helium 3 Isotope (He3)
- Carbon (C)
- Nitrogen (N)
- Oxygen (O)
- Neon (Ne)
- Silicon (Si)
- Iron (Fe)
If you face any issues or errors while working with this code, do not hesitate to post it on "https://github.com/jelkuweiss/many-ion-saha-equation/issues" and I will get back to it ASAP.
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