Interaction cross section in recharge model¶

See Effective cross section.

Notation:

\(a_0\) (a_0) is bohr_radius.
\(\mathrm{IE}_\text{H}\) (IE_h) is hydrogen_ionization_energy.
\(k_\text{B}\) (k_B) is boltzmann_constant.
\(e\) (e) is elementary_charge.

cross_section¶: cross_section of interaction of particles.

Symbol:: sigma
Latex:: \(\sigma\)
Dimension:: area

ionization_energy¶: Ionization energy of the particles.

Symbol:: E_i
Latex:: \(E_\text{i}\)
Dimension:: energy

molecular_mass¶: mass of a single gas particle.

Symbol:: m
Latex:: \(m\)
Dimension:: mass

pressure¶: Gas pressure.

Symbol:: p
Latex:: \(p\)
Dimension:: pressure

temperature¶: Gas temperature.

Symbol:: T
Latex:: \(T\)
Dimension:: temperature

electric_field_strength¶: electric_field_strength.

Symbol:: E
Latex:: \(E\)
Dimension:: voltage/length

law¶

sigma = pi * a_0^2 * IE_h / E_i * log(sqrt(3 * k_B * T / m) * sqrt(E_i / IE_h) * sigma * p * m / (2 * k_B * T * e * E))^2

Latex:: \[\sigma = \pi a_0^{2} \frac{\mathrm{IE}_\text{H}}{E_\text{i}} \log \left( \sqrt{\frac{3 k_\text{B} T}{m}} \sqrt{\frac{E_\text{i}}{\mathrm{IE}_\text{H}}} \frac{\sigma p m}{2 k_\text{B} T e E} \right)^{2}\]