"""Functions to calculate plasma density parameters."""
__all__ = [
"critical_density",
"mass_density",
]
__aliases__ = ["rho_"]
import numbers
from typing import Optional
import astropy.units as u
import numpy as np
from astropy.constants.si import e, eps0, m_e
from plasmapy.particles import Particle, ParticleLike
from plasmapy.utils.decorators import validate_quantities
__all__ += __aliases__
[docs]
@validate_quantities(
omega={"can_be_negative": False},
validations_on_return={
"units": [u.m**-3],
},
)
def critical_density(omega: u.Quantity[u.rad / u.s]) -> u.Quantity[u.m**-3]:
r"""Calculate the plasma critical density for a radiation of a given frequency.
Parameters
----------
omega: `~astropy.units.Quantity`
The radiation frequency in units of angular frequency.
Returns
-------
n_c : `~astropy.units.Quantity`
The plasma critical density.
Notes
-----
The critical density for a given frequency of radiation is
defined as the value at which the electron plasma frequency equals
the frequency of the radiation.
The critical density is given by the formula
.. math::
n_{c}=\frac{m_{e}\varepsilon_0\omega^{2}}{e^{2}}
where :math:`m_{e}` is the mass of an electron,
:math:`\varepsilon_0` is the permittivity of free space, :math:`\omega`
is the radiation frequency, and :math:`e` is the elementary charge.
Examples
--------
>>> import astropy.units as u
>>> critical_density(5e15 * u.rad / u.s)
<Quantity 7.85519457e+27 1 / m3>
"""
n_c = m_e * eps0 * omega**2 / (e**2)
return n_c.to(u.m**-3, equivalencies=u.dimensionless_angles())
[docs]
@validate_quantities(
density={"can_be_negative": False}, validations_on_return={"can_be_negative": False}
)
def mass_density(
density: (u.m**-3, u.kg / (u.m**3)),
particle: ParticleLike,
z_ratio: Optional[numbers.Real] = 1,
) -> u.Quantity[u.kg / u.m**3]:
r"""
Calculate the mass density from a number density.
.. math::
\rho = \left| \frac{Z_{s}}{Z_{particle}} \right| n_{s} m_{particle}
= | Z_{ratio} | n_{s} m_{particle}
where :math:`m_{particle}` is the particle mass, :math:`n_{s}` is a number
density for plasma species :math:`s`, :math:`Z_{s}` is the charge number of
species :math:`s`, and :math:`Z_{particle}` is the charge number of
``particle``. For example, if the electron density is given for :math:`n_s`
and ``particle`` is a doubly ionized atom, then :math:`Z_{ratio} = -1 / 2`\ .
Parameters
----------
density : `~astropy.units.Quantity`
Either a particle number density (in units of m\ :sup:`-3` or
equivalent) or a mass density (in units of kg / m\ :sup:`3` or
equivalent). If ``density`` is a mass density, then it will be passed
through and returned without modification.
particle : `~plasmapy.particles.particle_class.Particle`
The particle for which the mass density is being calculated for. Must
be a `~plasmapy.particles.particle_class.Particle` or a value convertible to
a `~plasmapy.particles.particle_class.Particle` (e.g., ``'p+'`` for protons,
``'D+'`` for deuterium, or ``'He-4 +1'`` for singly ionized helium-4).
z_ratio : `int`, `float`, optional
The ratio of the charge numbers corresponding to the plasma species
represented by ``density`` and the ``particle``. For example, if the
given ``density`` is and electron density and ``particle`` is doubly
ionized ``He``, then ``z_ratio = -0.5``. Default is ``1``.
Raises
------
`~astropy.units.UnitTypeError`
If the ``density`` does not have units equivalent to a number density
or mass density.
`TypeError`
If ``density`` is not of type `~astropy.units.Quantity`, or convertible.
`TypeError`
If ``particle`` is not of type or convertible to
`~plasmapy.particles.particle_class.Particle`.
`TypeError`
If ``z_ratio`` is not of type `int` or `float`.
`ValueError`
If ``density`` is negative.
Returns
-------
`~astropy.units.Quantity`
The mass density for the plasma species represented by ``particle``.
Examples
--------
>>> import astropy.units as u
>>> mass_density(1 * u.m**-3, "p+")
<Quantity 1.67262...e-27 kg / m3>
>>> mass_density(4 * u.m**-3, "D+")
<Quantity 1.33743...e-26 kg / m3>
>>> mass_density(2.0e12 * u.cm**-3, "He")
<Quantity 1.32929...e-08 kg / m3>
>>> mass_density(2.0e12 * u.cm**-3, "He", z_ratio=0.5)
<Quantity 6.64647...e-09 kg / m3>
>>> mass_density(1.0 * u.g * u.m**-3, "")
<Quantity 0.001 kg / m3>
"""
if density.unit.is_equivalent(u.kg / u.m**3):
return density
if not isinstance(particle, Particle):
try:
particle = Particle(particle)
except TypeError as e:
raise TypeError(
f"If passing a number density, you must pass a plasmapy Particle "
f"(not type {type(particle)}) to calculate the mass density!"
) from e
if not isinstance(z_ratio, (float, np.floating, int, np.integer)):
raise TypeError(
f"Expected type int or float for keyword z_ratio, got type {type(z_ratio)}."
)
return abs(z_ratio) * density * particle.mass
rho_ = mass_density
"""Alias to `~plasmapy.formulary.densities.mass_density`."""