# ionization_balance¶

plasmapy.formulary.ionization_balance(n: Unit("1 / m3"), T_e: Unit("K")) -> Unit(dimensionless)

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.

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

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

Aliases: Z_bal_

Parameters: T_e (Quantity) – The electron temperature. n (Quantity) – The electron number density of the plasma. UnitsWarning – If units are not provided, SI units are assumed. TypeError – The T_e or n is not a Quantity and cannot be converted into a ~astropy.units.Quantity. UnitConversionError – If the T_e or n not in appropriate units.

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 number of ions in each state are equal. Quantity