plasma_dispersion_func

plasmapy.dispersion.dispersion_functions.plasma_dispersion_func(

zeta: complex | ndarray | Annotated[Quantity, Unit(dimensionless)],

) → complex | ndarray | Annotated[Quantity, Unit(dimensionless)]

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:

array_like or Quantity

Raises:

UnitsError – If zeta is a Quantity but is not dimensionless.

See also

None

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)
np.complex128(1.77245385...j)
>>> plasma_dispersion_func(1 + 1j)
np.complex128(-0.36905845...+0.54014504...j)
>>> plasma_dispersion_func([0.3, 0.7 + 2.3j])
array([-0.56526333+1.61990085j, -0.09995023+0.37685142j])