Energy Degradation

When a precipitating electron collides with a neutral atom or molecule, it can lose energy through several processes. AURORA tracks these energy transfers to build the source term $Q$ that feeds lower-energy bins.

Processes

Electron-electron collisions

Energetic electrons also lose energy through Coulomb collisions with the thermal electron population. This continuous energy loss is modelled using the Swartz & Nisbet (1971) formula and transfers energy from bin $iE$ to bin $iE-1$.

\[L_e(E, z) = \frac{3.0271 \times 10^{-10} \, n_e(z)^{0.97}}{E^{0.44}} \left(\frac{E - E_e(z)}{E - 0.53\,E_e(z)}\right)^{2.36} \frac{1}{v(E)}\]

with thermal electron energy

\[E_e(z) = \frac{k_B}{q_e} T_e(z)\]

where $L_e$ is the suprathermal-electron energy loss rate [eV m⁻¹], $n_e$ is the ambient electron density [m⁻³], $T_e$ is the thermal electron temperature [K], and $v(E)$ is the speed of an electron with energy $E$.

Inelastic scattering

An electron excites a neutral to a higher electronic, vibrational, or rotational state, losing a discrete amount of energy equal to the excitation threshold. The scattered electron continues at reduced energy with a new pitch angle determined by the differential cross section.

Ionization

An electron ionizes a neutral, producing:

1. A secondary electron — ejected from the neutral. Secondary electrons are emitted isotropically over all pitch angles, i.e. they are redistributed uniformly across all beams weighted by their solid angle. Their energy distribution is species-dependent and evaluated from a species-dependent analytic law before being rebinned onto the simulation energy grid.
2. A degraded primary — the incident electron, which continues at reduced energy (reduced by the ionization potential plus the energy given to the secondary) and in the same pitch-angle beam as the original electron. Its lower-energy redistribution is obtained from the pre-computed cascading transfer matrices.

Both the secondary and degraded primary electrons contribute to the source term for lower energy bins.