def plasma_dispersion_func_lite(zeta):
r"""
The :term:`lite-function` version of
`~plasmapy.dispersion.dispersionfunction.plasma_dispersion_func`.
Performs the same calculation as
`~plasmapy.dispersion.dispersionfunction.plasma_dispersion_func`,
but is intended for computational use and, thus, has all data
conditioning safeguards removed.
Parameters
----------
zeta : :term:`numpy:array_like` of real or complex values
Argument of the plasma dispersion function. ``zeta`` is
dimensionless.
Returns
-------
Z : :term:`numpy:array_like` of complex values
Value of plasma dispersion function.
See Also
--------
~plasmapy.dispersion.dispersionfunction.plasma_dispersion_func
"""
return 1j * np.sqrt(np.pi) * Faddeeva_function(zeta)
def plasma_dispersion_func(
zeta: Union[complex, int, float, np.ndarray, u.Quantity]
) -> Union[complex, float, np.ndarray, u.Quantity]:
r"""
Calculate the plasma dispersion function.
Parameters
----------
zeta : complex, int, float, ~numpy.ndarray, or ~astropy.units.Quantity
Argument of plasma dispersion function.
Returns
-------
Z : complex, float, or ~numpy.ndarray
Value of plasma dispersion function.
Raises
------
TypeError
If the argument is of an invalid type.
~astropy.units.UnitsError
If the argument is a `~astropy.units.Quantity` but is not
dimensionless.
ValueError
If the argument is not entirely finite.
See Also
--------
plasma_dispersion_func_deriv
Notes
-----
The plasma dispersion function is defined as:
.. math::
Z(\zeta) = \pi^{-0.5} \int_{-\infty}^{+\infty}
\frac{e^{-x^2}}{x-\zeta} dx
where the argument is a complex number [fried.conte-1961]_.
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.
References
----------
.. [fried.conte-1961] Fried, Burton D. and Samuel D. Conte. 1961.
The Plasma Dispersion Function: The Hilbert Transformation of the
Gaussian. Academic Press (New York and London).
Examples
--------
>>> plasma_dispersion_func(0)
1.7724538509055159j
>>> plasma_dispersion_func(1j)
0.757872156141312j
>>> plasma_dispersion_func(-1.52+0.47j)
(0.6088888957234254+0.33494583882874024j)
"""
if not isinstance(zeta, (int, float, complex, np.ndarray, u.Quantity)):
raise TypeError("The argument to plasma_dispersion_function "
"must be one of the following types: complex, float, "
"int, ndarray, or Quantity.")
if isinstance(zeta, u.Quantity):
if zeta.unit == u.dimensionless_unscaled:
zeta = zeta.value
else:
raise u.UnitsError("The argument to plasma_dispersion_function "
"must be dimensionless if it is a Quantity")
if not np.all(np.isfinite(zeta)):
raise ValueError("The argument to plasma_dispersion_function is "
"not finite.")
Z = 1j * np.sqrt(np.pi) * Faddeeva_function(zeta)
return Z
def Z(xi):
return 1j * np.sqrt(np.pi) * Faddeeva_function(xi)