cold_plasma_permittivity_SDP¶

plasmapy.formulary.
cold_plasma_permittivity_SDP
(B: Unit(‘T’), species, n, omega: Unit(‘rad / s’))¶ Magnetized cold plasma dielectric permittivity tensor elements.
Elements (S, D, P) are given in the “Stix” frame, i.e. with \(B ∥ \hat{z}\).
The \(\exp(i ω t)\) timeharmonic convention is assumed.
 Parameters
B (
Quantity
) – Magnetic field magnitude in units convertible to tesla.species (
list
ofstr
) – List of the plasma particle species, e.g.:['e', 'D+']
or['e', 'D+', 'He+']
.n (
list
ofQuantity
) –list
of species density in units convertible to per cubic meter The order of the species densities should follow species.omega (
Quantity
) – Electromagnetic wave frequency in rad/s.
 Returns
Notes
The dielectric permittivity tensor is expressed in the Stix frame with the \(\exp(i ω t)\) timeharmonic convention as \(ε = ε_0 A\), with \(A\) being
\[\begin{split}ε = ε_0 \left(\begin{matrix} S & i D & 0 \\ +i D & S & 0 \\ 0 & 0 & P \end{matrix}\right)\end{split}\]where:
\[ \begin{align}\begin{aligned}S = 1  \sum_s \frac{ω_{p,s}^2}{ω^2  Ω_{c,s}^2}\\D = \sum_s \frac{Ω_{c,s}}{ω} \frac{ω_{p,s}^2}{ω^2  Ω_{c,s}^2}\\P = 1  \sum_s \frac{ω_{p,s}^2}{ω^2}\end{aligned}\end{align} \]where \(ω_{p,s}\) is the plasma frequency and \(Ω_{c,s}\) is the signed version of the cyclotron frequency for the species \(s\).
References
T.H. Stix, Waves in Plasma, 1992.
Examples
>>> from astropy import units as u >>> from numpy import pi >>> B = 2*u.T >>> species = ['e', 'D+'] >>> n = [1e18*u.m**3, 1e18*u.m**3] >>> omega = 3.7e9*(2*pi)*(u.rad/u.s) >>> permittivity = S, D, P = cold_plasma_permittivity_SDP(B, species, n, omega) >>> S <Quantity 1.02422...> >>> permittivity.sum # namedtuplestyle access <Quantity 1.02422...> >>> D <Quantity 0.39089...> >>> P <Quantity 4.8903...>