Preparing Cross Sections

There are a variety of ways to specify cross sections with the ThunderBoltz interface. In the Quick Start Guide, we used a built-in Helium cross section model. A more general approach to preparing cross sections is with the CrossSections object.

Initializing the CrossSections Object

There are three main ways to initialize a CrossSections object:

With cross section data from another ThunderBoltz run

from thunderboltz import CrossSections
# Just specify the path to the simulation directory of a
# different ThunderBoltz run.
cross_sections = CrossSections(input_path="path/to/thunderboltz_sim_dir")

Refer to the CrossSections section of the API Reference to ensure the simulation data is set up correctly for interpretation by CrossSections.

By reading from an LXCat text file extract.
```
from thunderboltz import CrossSections
# First initialize an empty cross sections object
cross_sections = CrossSections()
# Then reference a text file extract from LXCat
cross_sections.from_LXCat("path/to/LXCat_data.txt")
```
Note

For now, the LXCat parser assumes two species electron-gas systems where all processes are between electrons and gas macroparticles. If you wish to use LXCat data for other purposes, you can alter the species indices to your liking via CrossSections.table after loading in LXCat data.

By programmatically generating cross section data in python.

This approach involves the Process object.

from thunderboltz import CrossSections
from thunderboltz import Process

# Initialize an empty cross sections object
cross_sections = CrossSection()

# Next make a few processes

# You can pass arbitrary tabulated data like so
elastic_data = [
  # [eV], [m^2]
    [0.0, 2e-20],
    [0.001, 2.1e-20],
    [.01, 3e-20],
    [10.0, 1e-19],
    [1000, 1e-18],
    [10000, 2e-19],
]
elastic_process = Process(
    "Elastic", # The type of process
    r1=0, # The first reactant species index
    r2=1, # The second reactant species index
    p1=0, # The first product species index
    p2=1, # The second product species index
    cs_data=elastic_data,
    # This will determine the name of the
    # written cross section file and ideally should
    # be unique.
    name="elastic_example",
)
# You can also pass data frames, or ndarrays if that is
# preferable

# Or, use an analytic form defined with a python
# function.
import numpy as np # Import math functionality
def inelastic_model(energy, parameter):
    # It's okay to have conditional statements
    if energy < 5:
        return parameter

    # And nonlinear functions
    return parameter*np.log(energy)/energy

# You can parameterize your model
cs_mod_1 = lambda e: inelastic_model(e, 1e-20)
cs_mod_2 = lambda e: inelastic_model(e, 2e-20)
cs_mod_3 = lambda e: inelastic_model(e, 3e-20)

# And create multiple cross sections
inelastic_1 = Process(
    "Inelastic", threshold=1., cs_func=cs_mod_1, name="inelastic1")
inelastic_2 = Process(
    "Inelastic", threshold=1., cs_func=cs_mod_2, name="inelastic2")
inelastic_3 = Process(
    "Inelastic", threshold=1., cs_func=cs_mod_3, name="inelastic3")

# Finally, you can create processes with differential cross section
# models, if they are available in your ThunderBoltz version.
ionization = Process("Ionization", threshold=10.,
    cs_func=lambda e: 1e-19*np.log(e)/e,
    # This, for example, will add the equal energy sharing condition
    differential_process="equal",
    name="ionization")


# You can add your process to the CrossSections object one at a time
cross_sections.add_process(elastic_process)
# Or all at once
cross_sections.add_processes(
    [inelastic_1, inelastic_2, inelastic_3, ionization]
)

Note

It is important to explicitly specify threshold values for inelastic and superelastic processes because their values will not be inferred from the cross section data.

Viewing Your Cross Sections

When parsing data from external sources, it is important to ensure that the correct data is being used in the intended context for the simulation. You can view the reaction table for the model by printing out the table attribute.

print(cross_section.table)

And you can view the cross section data associated with each process by printing out the data attribute.

print(cross_section.data)

To view a plot of the cross section data, use the plot_cs() method.

cross_section.plot_cs()

# Remember to show the plot at the end of plotting scripts
# Make sure to include the import statement "import matplotlib.pyplot as plt"
plt.show()

See the API reference for plotting related quantities with the plot_cs() method.

Attaching the CrossSections Object

Finally, attach the CrossSections object to the main ThunderBoltz object using the cs keyword to use the cross section model within it.

calc = ThunderBoltz(
    # ...
    cs=cross_sections,
    # ...
)

calc.run()
# ...