jaxrts.saha.gen_saha_equation

jaxrts.saha.gen_saha_equation(gi: float, gj: float, T_e: Quantity, n_e: Quantity, energy_diff: Quantity, chem_pot: Quantity) → Quantity[source]

Generic Saha equation, using jaxrts.plasma_physics.chem_pot_sommerfeld_fermi_interpolation() calculate the chemical potential which is plugged into the equation

Returns the value n_j / n_i * n_e

\[\frac{n_{i+1}n_e}{n_i} = 2\frac{g_j}{g_i} \exp\left({\frac{-\Delta E - \mu}{k_B T_e}}\right)\]

Note

Since the free electron number \(n_e\) is an input to this function, solving the gen_saha_equation has to be done iteratively, until the result is self-consistent.

Parameters:

gi (float) – The statistical weight of the lower-energy state.
gj (float) – The statistical weight of the upper-energy state, often g_{i+1}.
T_e (Quantity) – The electron temperature.
n_e (Quantity) – The free electron density.
energy_diff – The difference in energy levels.

Returns:

n_j / n_i * n_e (Quantity) – The ratio of the population of the two states, multiplied with the free-electron density.