plasma_dispersion_func
- plasmapy.dispersion.dispersion_functions.plasma_dispersion_func(zeta: complex | ndarray | Quantity) complex | ndarray | Quantity [source]
Calculate the plasma dispersion function.
The plasma dispersion function is defined as:
\[Z(ζ) = π^{-0.5} \int_{-∞}^{+∞} \frac{e^{-x^2}}{x-ζ} dx\]where the argument is a complex number [Fried and Conte, 1961].
- Parameters:
zeta (array_like or
Quantity
) – The real or complex value to be provided as an argument to the plasma dispersion function.- Returns:
The real or complex value of plasma dispersion function evaluated at
zeta
.- Return type:
- Raises:
UnitsError – If
zeta
is aQuantity
but is not dimensionless.
See also
Notes
In plasma wave theory, the plasma dispersion function appears frequently when the background medium has a Maxwellian distribution function. The argument of this function then refers to the ratio of a wave’s phase velocity to a thermal velocity.
Examples
>>> from plasmapy.dispersion import plasma_dispersion_func >>> plasma_dispersion_func(0) 1.7724538509055159j >>> plasma_dispersion_func(1 + 1j) (-0.369...+0.540...j) >>> plasma_dispersion_func([0.3, 0.7 + 2.3j]) array([-0.56526333+1.61990085j, -0.09995023+0.37685142j])