Benchmark Testing

There are three benchmark tests available in the repository. These benchmark simulations are described in detail in Sect. III of the ThunderBoltz paper. The resulting calculations and figures from these benchmark tests can be compared directly to the figures given in the paper. Each can be imported from the run.py python module.

Onsager Relation

The Onsager relation [1] predicts the kinetic rates of the following chemical reactions between arbitrary heavy particles,

\[A \rightleftarrows B \rightleftarrows C \rightleftarrows A.\]

Based on the equilibrium condition, \(n_i k_{ij}=n_jk_{ji}\), the rate constants \(k_{ij}\) have the analytic solution

\[k(T) = d^2\sqrt{\frac{8 \pi k_{\textrm{B}}T}{m_r}} e^{-E_a/k_{\textrm{B}}T}.\]

To run this system in in ThunderBoltz, run the prepared function either in a python script:

# Run this from within the repository root
import run
run.onsager_relation()

or directly from the command line:

python -c "import run; run.onsager_relation()"

The resulting calculation will automatically run in the directory simulations/onsager_relation.

Once the simulation has finished, run the following on the command line (or in a python script) to view a time evolution of the species densities, reaction rates, and absolute rates.

python -c "import visualize; visualize.plot_onsager()"

This will automatically save a pdf of the plot in the simulations directory.

Ikuta-Sugai

The Ikuta-Sugai benchmark problem tests electron transport in crossed electric and magnetic fields.

To run this system in ThunderBoltz and compare it to the analytic theory presented by Ness [2], run the prepared function either in a python script of directly from the command line:

python -c "import run; run.ikuta_sugai()"

Once the simulation has finished, run the following command to view the effect of the magnetic field on the average velocity moments and mean energy of the particles in comparison to Ness:

python -c "import visualize; visualize.plot_ikuta_sugai()"

This will automatically save a pdf of the plot in the simulations directory.

He Transport

Here we generate comparisons of bulk and flux electron mobility, \(\mu N\), and Townshend ionization coefficient, \(\alpha / N\), at various reduced fields. We compare ThunderBoltz results to the two-term Boltzmann equation solver, BOLSIG, as well as some swarm experiments.

To simulate this system in ThunderBoltz run the prepared function either in a python script or directly from the command line:

python -c "import run; run.He_transport()"

Once the simulation has finished, run the following command to view the reduced Townshend ionization coefficient and the reduced electron mobility as a function of reduced electric field:

python -c "import visualize; visualize.plot_He_transport()"

This will automatically save a pdf of the plot in the simulations directory. To view a plot comparing the individual reaction rate coefficients of ThunderBoltz and BOLSIG, run the following:

python -c "import visualize; visualize.rate_comp()"