# IonizationState¶

class plasmapy.particles.ionization_state.IonizationState(particle: plasmapy.particles.particle_class.Particle, ionic_fractions=None, *, T_e: Unit("K") = <Quantity nan K>, kappa: numbers.Real = inf, n_elem: Unit("1 / m3") = <Quantity nan 1 / m3>, tol: Union[float, int] = 1e-15)

Bases: object

Representation of the ionization state distribution of a single element or isotope.

Parameters: particle (str, integer, or Particle) – A str or Particle instance representing an element or isotope, or an integer representing the atomic number of an element. ionic_fractions (ndarray, list, tuple, or Quantity; optional) – The ionization fractions of an element, where the indices correspond to integer charge. This argument should contain the atomic number plus one items, and must sum to one within an absolute tolerance of tol if dimensionless. Alternatively, this argument may be a Quantity that represents the number densities of each neutral/ion. T_e (Quantity, keyword-only, optional) – The electron temperature or thermal energy per particle. n_elem (Quantity, keyword-only, optional) – The number density of the element, including neutrals and all ions. tol (float or integer, keyword-only, optional) – The absolute tolerance used by isclose when testing normalizations and making comparisons. Defaults to 1e-15. AtomicError – If the ionic fractions are not normalized or contain invalid values, or if number density information is provided through both ionic_fractions and n_elem. InvalidParticleError – If the particle is invalid.

Examples

>>> states = IonizationState('H', [0.6, 0.4], n_elem=1*u.cm**-3, T_e=11000*u.K)
>>> states.ionic_fractions[0]  # fraction of hydrogen that is neutral
0.6
>>> states.ionic_fractions[1]  # fraction of hydrogen that is ionized
0.4
>>> states.n_e  # electron number density
<Quantity 400000. 1 / m3>
>>> states.n_elem  # element number density
<Quantity 1000000. 1 / m3>


Notes

Calculation of collisional ionization equilibrium has not yet been implemented.

Attributes Summary

 T_e Return the electron temperature. Z_mean Return the mean integer charge Z_most_abundant Return a list of the integer charges with the highest ionic fractions. Z_rms Return the root mean square integer charge. atomic_number Return the atomic number of the element. base_particle Return the symbol of the element or isotope. element Return the atomic symbol of the element. equil_ionic_fractions Return the equilibrium ionic fractions for temperature T_e or the temperature set in the IonizationState instance. integer_charges Return an array with the integer charges. ionic_fractions Return the ionic fractions, where the index corresponds to the integer charge. ionic_symbols Return the ionic symbols for all charge states. isotope Return the isotope symbol for an isotope, or None if the particle is not an isotope. kappa Return the kappa parameter for a kappa distribution function for electrons. n_e Return the electron number density assuming a single species plasma. n_elem Return the total number density of neutrals and all ions. number_densities Return the number densities for each state. tol Return the absolute tolerance for comparisons.

Methods Summary

 equilibrate(T_e) Set the ionic fractions to collisional ionization equilibrium for temperature T_e. info(minimum_ionic_fraction) Print quicklook information for an IonizationState instance. normalize() Normalize the ionization state distribution (if set) so that the sum becomes equal to one.

Attributes Documentation

T_e

Return the electron temperature.

Z_mean

Return the mean integer charge

Z_most_abundant

Return a list of the integer charges with the highest ionic fractions.

Examples

>>> He = IonizationState('He', [0.2, 0.5, 0.3])
>>> He.Z_most_abundant
[1]
>>> Li = IonizationState('Li', [0.4, 0.4, 0.2, 0.0])
>>> Li.Z_most_abundant
[0, 1]

Z_rms

Return the root mean square integer charge.

atomic_number

Return the atomic number of the element.

base_particle

Return the symbol of the element or isotope.

element

Return the atomic symbol of the element.

equil_ionic_fractions

Return the equilibrium ionic fractions for temperature T_e or the temperature set in the IonizationState instance. Not implemented.

integer_charges

Return an array with the integer charges.

ionic_fractions

Return the ionic fractions, where the index corresponds to the integer charge.

Examples

>>> hydrogen_states = IonizationState('H', [0.9, 0.1])
>>> hydrogen_states.ionic_fractions
array([0.9, 0.1])

ionic_symbols

Return the ionic symbols for all charge states.

isotope

Return the isotope symbol for an isotope, or None if the particle is not an isotope.

kappa

Return the kappa parameter for a kappa distribution function for electrons.

The value of kappa must be greater than 1.5 in order to have a valid distribution function. If kappa equals inf, then the distribution function reduces to a Maxwellian.

n_e

Return the electron number density assuming a single species plasma.

n_elem

Return the total number density of neutrals and all ions.

number_densities

Return the number densities for each state.

tol

Return the absolute tolerance for comparisons.

Methods Documentation

equilibrate(T_e: Unit("K") = <Quantity nan K>)

Set the ionic fractions to collisional ionization equilibrium for temperature T_e. Not implemented.

info(minimum_ionic_fraction: numbers.Real = 0.01) → None

Print quicklook information for an IonizationState instance.

Parameters: minimum_ionic_fraction (Real) – If the ionic fraction for a particular ionization state is below this level, then information for it will not be printed. Defaults to 0.01.

Example

>>> He_states = IonizationState(
...     'He',
...     [0.941, 0.058, 0.001],
...     T_e = 5.34 * u.K,
...     kappa = 4.05,
...     n_elem = 5.51e19 * u.m ** -3,
... )
>>> He_states.info()
IonizationState instance for He with Z_mean = 0.06
----------------------------------------------------------------
He  0+: 0.941    n_i = 5.18e+19 m**-3
He  1+: 0.058    n_i = 3.20e+18 m**-3
----------------------------------------------------------------
n_elem = 5.51e+19 m**-3
n_e = 3.31e+18 m**-3
T_e = 5.34e+00 K
kappa = 4.05
----------------------------------------------------------------

normalize() → None

Normalize the ionization state distribution (if set) so that the sum becomes equal to one.