Function saha_ionization_fraction_kernel 

pub fn saha_ionization_fraction_kernel<R>(
    temperature: Temperature<R>,
    total_number_density: R,
    ionization_energy_ev: R,
    partition_ratio: R,
) -> Result<IonizationFraction<R>, PhysicsError>
where
    R: RealField + FromPrimitive,

Saha-equilibrium ionization fraction α = n_e / n_tot for a singly-ionized gas, from

$$ \frac{n_e n_i}{n_n} = g,\Big(\frac{2\pi m_e k_B T}{h^2}\Big)^{3/2} \exp!\Big(-\frac{E_{ion}}{k_B T}\Big) \equiv K(T) $$

With n_e = n_i = α n_tot and n_n = (1-α) n_tot, this gives α²/(1-α) = K/n_tot, solved as α = (-x + √(x² + 4x))/2, x = K/n_tot. Saha is the full ionization equilibrium — pathway-independent — so it already accounts for electron-impact-produced electrons, not only the associative channel.

Arguments

• temperature — temperature T (K).
• total_number_density — total heavy-particle number density n_tot (m⁻³).
• ionization_energy_ev — ionization energy E_ion (eV).
• partition_ratio — statistical-weight factor g = 2 g_i / g_n.

References

• Gupta, Yos, Thompson & Lee, NASA RP-1232 (1990), eq. 5b (papers/gupta_1990_nasa_rp1232.pdf).