permittivity_1D_Maxwellian

plasmapy.physics.dielectric.permittivity_1D_Maxwellian(omega, kWave, T, n, particle, z_mean=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.)

Parameters
  • 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 em_wave.py 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.

Returns

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

Return type

Quantity

Notes

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.

References

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).

Example

>>> from astropy import units as u
>>> from plasmapy.constants import pi, c
>>> T = 30 * 11600 * u.K
>>> n = 1e18 * u.cm**-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 -6.72809257e-08+5.76037956e-07j>