This package calculates the roots to the electrostatic dispersion relation given by
where g(u) is the 1D distribution function, here assumed to be a Maxwell-Boltzmann.
To install, after activating your environment, run
pip3 install -e git+https://github.com/ergodicio/plasmadisp.git#egg=plasmadispThen, you can get the complex root to the dispersion relation by
from plasmadisp import electrostatic
kk = 0.3
answer = electrostatic.get_roots_to_electrostatic_dispersion(wp_e=1.0, vth_e=1.0, k0=kk)
print(answer)where the temperature and density of the plasma can be inserted by varying the plasma frequency and thermal velocity.
This will print a complex number where the real part is the frequency of the least damped resonant mode and the imaginary part is the Landau damping rate of that mode.
For more on all of this, please refer to an introductory plasma physics textbook like Chen [2] or Bellan [3].
The results of this solver are tested against the values published in Canosa1973 [1]
This uses scipy's optimize functionality as well as it's Fadeeva special function to represent the plasma dispersion.
Please start an issue if you have any questions or would like to make contributions. At the moment, this package is intentionally limited in scope.
[1]: Canosa, José. “Numerical Solution of Landau’s Dispersion Equation.” Journal of Computational Physics 13, no. 1 (September 1973): 158–60. https://doi.org/10.1016/0021-9991(73)90131-9.
[2]: Chen, Francis F. Introduction to Plasma Physics and Controlled Fusion. Boston, MA: Springer US, 1984. https://doi.org/10.1007/978-1-4757-5595-4.
[3]: Bellan, P. M. Fundamentals of Plasma Physics. Vol. 173, n.d. https://doi.org/10.2277/0521821169.