XENON: A matriX-based dispErsioN relatiON solver for plasma physics

XENON is a collection of matrix-based plasma dispersion relation (DR) solvers written in Python 3. Currently, electrostatic/electromagnetic multifluid plasmas, and electrostatic kinetic plasmas are supported. The algorithms are extended from [1] and [2] pioneered by Dr. Huasheng Xie.

The motivation of this work is to facilitate multifluid and Vlasov simulations using the Gkeyll v2 code.

For a quick taste, following is a snippet to compute the DR for the Bump-on-tail instability:

species = np.array([
    # parameters of each species
    # q, m, n,   v,     p
    [-1, 1, 0.9, 0,     0.9],  # background electron
    [-1, 1, 0.1, 7.071, 0.1],  # beam electron
])
params = dict(epsilon0=1)  # other parameters
ks = np.linspace(0.0001, 0.6, 50)  # an array of wavenumbers
# for each wavenumber, compute the complex frequencies
ws = xenon.vlasov.k2w_es1d(ks, species, params)

fig, axs = plt.subplots(2, 1, figsize=(10, 5), sharex=True)
xenon.common.plot_dr(ks, ws, ax0=axs[0], ax1=axs[1])

For more examples, refer to demos.
For the complete API, see https://liangwang0734.github.io/xenon/

How does xenon work?

• The linearized fluid or Vlasov equations are transformed into a matrix form, and complex frequencies [w1, w2, w3, ...] are computed as eigenvalues of this coefficient matrix for each wavenumber k.
• In this matrix-based method, no initial guess is necessary, and all solutions, including eigenvectors, are captured.
• If you prefer Matlab over Python, please consider the original implementation, BO, by Dr. Huasheng Xie.

Does xenon rely on other softwares to work?

• Required: Modern numpy and scipy are required for computation.
• Optional: matplotlib is required for using the builtin visualization tools.

How do I load xenon?

Currently, the package is in development stage and is provided only as is. One option to use the package is to make Python aware of its path:

import sys
sys.path.append("/path/to/parent/folder/of/xenon/")
import xenon

PyPI and Anaconda distributions will be used starting release 0.2.0.

What are the folders/files for?

• fluid: Multifluid dispersion relation solver supporting anisotropic pressure. ES1D, ES3D, and EM3D version are implemented.
• vlasov: Vlasov dispersion relation solver for a warm plasma. ES1D and ES3D versions are implemented.
• common: Coefficient generator, convenience tools for visulization, etc.
• demos: Demos compiled as markdown documents. This folder is being consolidated.

How do I use xenon like an expert?

• For the complete API, see https://liangwang0734.github.io/xenon/
• For examples with both computation and visualization, refer to demos, which will be consolidated in the future.

References

[1] Xie, Hua-sheng. "PDRF: A general dispersion relation solver for magnetized multi-fluid plasma." Computer Physics Communications 185.2 (2014): 670-675.
[2] Xie, Huasheng, and Xiao, Yong. "PDRK: A general kinetic dispersion relation solver for magnetized plasma." Plasma Science and Technology 18.2 (2016): 97.

Funding support

• Air Force Office of Scientific Research Grant No. FA9550-15-1-0193.