plasmapy.formulary.permittivity_1D_Maxwellian(omega: Unit(‘rad / s’), kWave: Unit(‘rad / m’), T: Unit(‘K’), n: Unit(‘1 / m3’), particle, z_mean: Unit(dimensionless) = None)

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.



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>