# permittivity_1D_Maxwellian¶

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.)

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. chi – The ion or the electron dielectric permittivity of the plasma. This is a dimensionless quantity. 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 numpy import pi
>>> from astropy.constants import 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 -6.72809...e-08+5.76037...e-07j>