plasmapy.formulary.dielectric.permittivity_1D_Maxwellian(omega: Unit("rad / s"), kWave: Unit("rad / m"), T: Unit("K"), n: Unit("1 / m3"), particle, z_mean: Unit(dimensionless) = None) -> Unit(dimensionless)

The classical dielectric permittivity for a 1D Maxwellian plasma. This function can calculate both the ion and electron permittivities. No additional effects are considered (e.g. magnetic fields, relativistic effects, strongly coupled regime, etc.)

  • omega (Quantity) – The frequency in rad/s of the electromagnetic wave propagating through the plasma.
  • kWave (Quantity) – The corresponding wavenumber, in rad/m, of the electromagnetic wave propagating through the plasma. This is often modulated by the dispersion of the plasma or by relativistic effects. See for ways to calculate this.
  • T (Quantity) – The plasma temperature - this can be either the electron or the ion temperature, but should be consistent with density and particle.
  • n (Quantity) – The plasma density - this can be either the electron or the ion density, but should be consistent with temperature and particle.
  • particle (str) – The plasma particle species.
  • z_mean (str) – The average ionization of the plasma. This is only required for calculating the ion permittivity.

chi – The ion or the electron dielectric permittivity of the plasma. This is a dimensionless quantity.

Return type:



The dielectric permittivities for a Maxwellian plasma are described by the following equations [1]

\[ \begin{align}\begin{aligned}\chi_e(k, \omega) = - \frac{\alpha_e^2}{2} Z'(x_e)\\\chi_i(k, \omega) = - \frac{\alpha_i^2}{2}\frac{Z}{} Z'(x_i)\\\alpha = \frac{\omega_p}{k v_{Th}}\\x = \frac{\omega}{k v_{Th}}\end{aligned}\end{align} \]

\(chi_e\) and \(chi_i\) are the electron and ion permittivities respectively. \(Z'\) is the derivative of the plasma dispersion function. \(\alpha\) is the scattering parameter which delineates the difference between the collective and non-collective Thomson scattering regimes. \(x\) is the dimensionless phase velocity of the EM wave propagating through the plasma.


[1]J. Sheffield, D. Froula, S. H. Glenzer, and N. C. Luhmann Jr, Plasma scattering of electromagnetic radiation: theory and measurement techniques. Chapter 5 Pg 106 (Academic press, 2010).


>>> from astropy import units as u
>>> from numpy import pi
>>> from astropy.constants import c
>>> T = 30 * 11600 * u.K
>>> n = 1e18 ***-3
>>> particle = 'Ne'
>>> z_mean = 8 * u.dimensionless_unscaled
>>> vTh = parameters.thermal_speed(T, particle, method="most_probable")
>>> omega = 5.635e14 * 2 * pi * u.rad / u.s
>>> kWave = omega / vTh
>>> permittivity_1D_Maxwellian(omega, kWave, T, n, particle, z_mean)
<Quantity -6.72809...e-08+5.76037...e-07j>