Ionization state data structures

The ionization state (or charge state) of a plasma refers to the fraction of an element that is at each ionization level. For example, the ionization state of a pure helium plasma could be 5% He⁰⁺, 94% He¹⁺, and 1% He²⁺.

The ionization state of a single element

We may use the IonizationState class to represent the ionization state of a single element, such as for this example.

>>> from plasmapy.particles import IonizationState
>>> ionization_state = IonizationState("He", [0.05, 0.94, 0.01])

The ionization state for helium may be accessed using the ionic_fractions attribute. These ionic fractions correspond to the integer_charges attribute.

>>> ionization_state.ionic_fractions
array([0.05, 0.94, 0.01])
>>> ionization_state.integer_charges
array([0, 1, 2])

The Z_mean attribute returns the mean integer charge averaged over all particles in that element.

>>> ionization_state.Z_mean
0.96

The Z_rms attribute returns the root mean square integer charge.

>>> ionization_state.Z_rms
0.9899...

The Z_most_abundant attribute returns a list of the most abundant ion(s). The list may contain more than one integer charge in case of a tie.

>>> ionization_state.Z_most_abundant
[1]

The summarize method prints out the ionic fraction for the ions with an abundance of at least 1%.

>>> ionization_state.summarize()
IonizationState instance for He with Z_mean = 0.96
----------------------------------------------------------------
He  0+: 0.050
He  1+: 0.940
He  2+: 0.010
----------------------------------------------------------------

The number density of the element may be specified through the n_elem keyword argument.

>>> import astropy.units as u
>>> ionization_state = IonizationState(
...     "He", [0.05, 0.94, 0.01], n_elem = 1e19 * u.m ** -3,
... )

The n_e attribute provides the electron number density as a Quantity.

>>> ionization_state.n_e
<Quantity 9.6e+18 1 / m3>

The number_densities attribute provides the number density of each ion or neutral.

>>> ionization_state.number_densities
<Quantity [5.0e+17, 9.4e+18, 1.0e+17] 1 / m3>

Ionization states for multiple elements

The IonizationStateCollection class may be used to represent the ionization state for multiple elements. This can be used, for example, to describe the various impurities in a fusion plasma or the charge state distributions of different elements in the solar wind.

>>> from plasmapy.particles import IonizationStateCollection

The minimal input to IonizationStateCollection is a list of the elements or isotopes to represent. Integers in the list will be treated as atomic numbers.

>>> states = IonizationStateCollection(["H", 2])

To set the ionic fractions for hydrogen, we may do item assignment.

>>> states["H"] = [0.9, 0.1]

We may use indexing to retrieve an IonizationState instance for an element.

>>> states["H"]
<IonizationState instance for H>

The ionization states for all of the elements may be specified directly as arguments to the class.

>>> states = IonizationStateCollection(
...     {"H": [0.01, 0.99], "He": [0.04, 0.95, 0.01]},
...     abundances={"H": 1, "He": 0.08},
...     n0 = 5e19 * u.m ** -3,
... )

The ionic fractions will be stored as a dict.

>>> states.ionic_fractions
{'H': array([0.01, 0.99]), 'He': array([0.04, 0.95, 0.01])}

The number density for each element is the product of the number density scaling factor n0 with that element’s abundance. The number density for each ion is the product of n0, the corresponding element’s abundance, and the ionic fraction.

>>> states.n0
<Quantity 5.e+19 1 / m3>
>>> states.abundances
{'H': 1.0, 'He': 0.08}
>>> states.number_densities["H"]
<Quantity [5.00e+17, 4.95e+19] 1 / m3>

The corresponding element’s abundance, and the ionic fraction.

>>> states.n0
<Quantity 5.e+19 1 / m3>
>>> states.abundances
{'H': 1.0, 'He': 0.08}
>>> states.number_densities["H"]
<Quantity [5.00e+17, 4.95e+19] 1 / m3>

The corresponding element’s abundance, and the ionic fraction.

>>> states.n
<Quantity 5.e+19 1 / m3>
>>> states.abundances
{'H': 1.0, 'He': 0.08}
>>> states.number_densities["H"]
<Quantity [5.00e+17, 4.95e+19] 1 / m3>

The summarize method may also be used to get a summary of the ionization states.

>>> states.summarize()
----------------------------------------------------------------
H  1+: 0.990    n_i = 4.95e+19 m**-3
----------------------------------------------------------------
He  0+: 0.040    n_i = 1.60e+17 m**-3
He  1+: 0.950    n_i = 3.80e+18 m**-3
----------------------------------------------------------------
n_e = 5.34e+19 m**-3
T_e = 1.30e+04 K
----------------------------------------------------------------