plasma_dispersion_func¶
-
plasmapy.dispersion.
plasma_dispersion_func
(zeta: Union[complex, int, float, numpy.ndarray, astropy.units.quantity.Quantity]) → Union[complex, float, numpy.ndarray, astropy.units.quantity.Quantity]¶ Calculate the plasma dispersion function.
Parameters: zeta (complex, int, float, ndarray, or Quantity) – Argument of plasma dispersion function.
Returns: Z – Value of plasma dispersion function.
Return type: Raises: TypeError
– If the argument is of an invalid type.UnitsError
– If the argument is aQuantity
but is not dimensionless.ValueError
– If the argument is not entirely finite.
See also
Notes
The plasma dispersion function is defined as:
\[Z(\zeta) = \pi^{-0.5} \int_{-\infty}^{+\infty} \frac{e^{-x^2}}{x-\zeta} dx\]where the argument is a complex number [1].
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
[1] Fried, Burton D. and Samuel D. Conte. 1961. The Plasma Dispersion Function: The Hilbert Transformation of the Gaussian. Academic Press (New York and London). ISBN 9781483261737 Examples
>>> plasma_dispersion_func(0) 1.7724538509055159j >>> plasma_dispersion_func(1j) 0.757872156141312j >>> plasma_dispersion_func(-1.52+0.47j) (0.6088888957234254+0.33494583882874024j)