solrat.atom_model.multi_term_atom_model_lte.statistical_equilibrium_equations module

class solrat.atom_model.multi_term_atom_model_lte.statistical_equilibrium_equations.MultiTermAtomSEELTE(level_registry: LevelRegistry)

Bases: BaseSEE

Statistical Equilibrium Equations within Multi-Term atom model - an LTE implementation. This class will always output an LTE-distributed Rho tensor.

Parameters:

level_registry – LevelRegistry instance for the multi-term atom under study.

This is needed to be able to use SEELTE directly in nonLTE Radiative Transfer Equations.

property atmosphere_parameters: AtmosphereParameters

classmethod from_model_config(config: MultiTermAtomConfig) → Self

Constructor from the model config.

fill_all_equations(atmosphere_parameters: AtmosphereParameters, radiation_tensor_in_magnetic_frame: RadiationTensor)

Loop through all equations to construct the complete system of equations for rho.

Parameters:

• atmosphere_parameters – AtmosphereParameters instance carrying the magnetic field and other variables.

• radiation_tensor_in_magnetic_frame – RadiationTensor instance

get_solution() → Rho

Return LTE Rho solution.

Assume Zeeman splitting does not cause energy shifts so large that they affect populations.

Then:

\[ \begin{align}\begin{aligned}\rho^K_Q(J,Jʹ) &\sim \delta_{J,Jʹ}\delta_{K,0}\delta_{Q,0} \sqrt{2J+1} \mathrm{exp}(-E_J/kT)\\Tr[\rho^K_Q(J,Jʹ)] &= \Sigma \sqrt{2J+1} \rho^0_0(J,Jʹ) = 1\end{aligned}\end{align} \]

Reference: (LL04 3.108) (LL04 10.118)