# ionization_balance

plasmapy.formulary.ionization.ionization_balance(n: Unit('1 / m3'), T_e: Unit('K'))

Return the average ionization state of ions in a plasma assuming that the numbers of ions in each state are equal.

Z_bal is the estimate average ionization level of a plasma in thermal equilibrium that balances the number density of ions in two different ionization states. Z_bal is derived from the Saha equation with the assumptions that the atoms are of a single species, are either hydrogenic or completely ionized, and that there is a balance between ionization and recombination, meaning that the number of atoms in either state are equal. The Saha equation and therefore Z_bal are more accurate when the plasma is at a high density and temperature.

$Z\_bal = \sqrt{\frac{k_B T_e}{E_H}} \sqrt{\ln{\frac{1}{4 n a_{0}^3} (\frac{k_B T_e}{π E_H})^{3/2}}} - \frac{1}{2}$

Where $$k_B$$ is the Boltzmann constant, $$a_0$$ is the Bohr radius, and $$E_H$$ is the ionization energy of Hydrogen

Aliases:

Parameters
Warns

UnitsWarning – If units are not provided, SI units are assumed.

Raises

Examples

>>> import astropy.units as u
>>> T_e = 5000 * u.K
>>> n = 1e19 * u.m ** -3
>>> ionization_balance(n, T_e)
<Quantity 0.274...>
>>> T_e = 50 * u.eV
>>> n = 1e10 * u.m ** -3
>>> ionization_balance(n, T_e)
<Quantity 12.615...>

Returns

Z – The average ionization state of the ions in the plasma assuming that the numbers of ions in each state are equal.

Return type

Quantity