tberlok/plasma-dispersion

Dispersion solver for homogeneous plasmas with a gyrotropic distribution function.

About this software

This is a dispersion solver for homogeneous plasmas with a gyrotropic distribution function. The theory underlying the code is described in detail in my PhD thesis. See in particular Chapters 6, 7 and 12.

Some details

The calculation of the conductivity tensor has been implemented in Cython in order to have optimal performance.

The Vlasov-Fluid (kinetic ions described by the collisionless Vlasov equation and zero-mass electrons described as a fluid) dispersion relation has been implemented as a class which can, given the frequency and the wavenumber, return the determinant of the dispersion tensor.

This code is still work in progress but so far it can reproduce most of the figures in the HYDROS paper, "A linear dispersion relation for the hybrid kinetic-ion/fluid-electron model of plasma physics" by D. Told, J. Cookmeyer, P. Astfalk and F. Jenko. Notable exceptions are the plot for the oblique firehose instability and the fastwave which I still need to figure out.

The code presented here does not yet include resistivity but it is not limited to a single ion species. At some point I also hope to add support for drifting distribution functions.

It might also prove useful to reproduce some of the plots in the paper Comparative study of gyrokinetic, hybrid-kinetic and fully kinetic wave physics for space plasmas.

The code uses scipy's Newton-Raphson method which, however, falls back to the secant method when the derivative of the function is not provided. I intend to add the derivative of the lambda tensor which will hopefully aid in the solver being a bit less sensitive to the initial guess for the frequency.

Requirements

Assuming you already have Python 3 installed you can install the rest of the requirements using:

$ pip install -r requirements.txt

How to use

Compilation can be done using

$ make

It is also a good idea to the directory to your python path. On my computer this would be

$ export PYTHONPATH=$PYTHONPATH:/Users/berlok/projects/plasma-dispersion

All the examples can be run by simply doing

$ make figures