ionization_balance¶

plasmapy.formulary.
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:
Z_bal_
 Parameters
 Warns
UnitsWarning
– If units are not provided, SI units are assumed. Raises
TypeError – If either of
T_e
orn
is not aQuantity
and cannot be converted into aQuantity
.UnitConversionError – If either of
T_e
orn
is 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 numbers of ions in each state are equal.
 Return type