cold_plasma_permittivity_LRP¶

plasmapy.formulary.
cold_plasma_permittivity_LRP
(B: Unit(‘T’), species, n, omega: Unit(‘rad / s’))¶ Magnetized cold plasma dielectric permittivity tensor elements.
Elements (L, R, P) are given in the “rotating” basis, i.e. in the basis \((\mathbf{u}_{+}, \mathbf{u}_{}, \mathbf{u}_z)\), where the tensor is diagonal and with \(B ∥ z\).
The \(\exp(i ω t)\) timeharmonic convention is assumed.
 Parameters
B (
Quantity
) – Magnetic field magnitude in units convertible to tesla.species (
list
ofstr
) – 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
In the rotating frame defined by \((\mathbf{u}_{+}, \mathbf{u}_{}, \mathbf{u}_z)\) with \(\mathbf{u}_{\pm}=(\mathbf{u}_x \pm \mathbf{u}_y)/\sqrt{2}\), the dielectric tensor takes a diagonal form with elements L, R, P with:
\[ \begin{align}\begin{aligned}L = 1  \sum_s \frac{ω_{p,s}^2}{ω\left(ω  Ω_{c,s}\right)}\\R = 1  \sum_s \frac{ω_{p,s}^2}{ω\left(ω + Ω_{c,s}\right)}\\P = 1  \sum_s \frac{ω_{p,s}^2}{ω^2}\end{aligned}\end{align} \]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) >>> L, R, P = permittivity = cold_plasma_permittivity_LRP(B, species, n, omega) >>> L <Quantity 0.63333...> >>> permittivity.left # namedtuplestyle access <Quantity 0.63333...> >>> R <Quantity 1.41512...> >>> P <Quantity 4.8903...>