Detailed plasma 4

documentation/source/physics-models/detailed_physics.md

@@ -79,7 +79,84 @@ $$
 ---------------------
 
 ### Larmor Frequency | `calculate_larmor_frequency()`
-
+ 
 $$
 f_{\text{Larmor}} = \frac{Z_ieB}{2\pi m_i}
-$$
+$$
+
+--------------------
+
+### Upper Hybrid Frequency | `calculate_upper_hybrid_frequency()`
+
+$$
+f_{\text{UH}} = \sqrt{\omega_{p}^2+ \omega_{\text{Larmor}}^2}
+$$
+
+--------------------
+
+### Reduced mass of two particles | `calculate_reduced_mass()`
+
+$$
+m_{\text{reduced}} = \frac{m_1 m_2}{m_1+m_2}
+$$
+
+-----------------
+
+### Relative average velocity | `calculate_average_relative_velocity()`
+
+$$
+v_{\text{rel}} = \sqrt{v_1^2+v_2^2}
+$$
+
+-----------------
+
+### Electron-electron collision time | `calculate_electron_electron_collision_time()`
+
+For $T_\text{e}$ in eV
+
+$$
+\tau_{\text{ee}} = \frac{12\sqrt{2}\pi^{\frac{3}{2}}\epsilon_0^2 \sqrt{m_{\text{e}}}T_{\text{e}}^{\frac{3}{2}}}{\ln \Lambda_{\text{ee}}\text{e}^4 n_{\text{e}}}
+$$
+
+-------------------
+
+### Electron-ion collision time | `calculate_electron_ion_collision_time()`
+
+For $T_\text{e}$ in eV.
+
+This method takes the ion density $n_i$ (`nd_plasma_ions`). For a quasi-neutral single-species plasma,
+
+$$
+n_{\text{e}} = Z_i n_i
+$$
+
+so the standard form written in terms of electron density,
+
+$$
+\tau_{\text{ei}} = \frac{12 \pi^{\frac{3}{2}}\epsilon_0^2 \sqrt{m_{\text{e}}}T_{\text{e}}^{\frac{3}{2}}}{\sqrt{2} Z_i^2 \ln \Lambda_{\text{ei}} \text{e}^4 n_{\text{e}}}
+$$
+
+is equivalent to the form used with ion density,
+
+$$
+\tau_{\text{ei}} = \frac{12 \pi^{\frac{3}{2}}\epsilon_0^2 \sqrt{m_{\text{e}}}T_{\text{e}}^{\frac{3}{2}}}{\sqrt{2} Z_i^3 \ln \Lambda_{\text{ei}} \text{e}^4 n_i}
+$$
+--------------------
+
+### Spitzer ion slowing down time | `calculate_spitzer_ion_slowing_down_time()`
+
+For $T_\text{e}$ in eV
+
+$$
+\tau_{\text{spitzer}} = \frac{3 (2\pi)^{\frac{3}{2}}\epsilon_0^2 \sqrt{m_{\text{e}}} m_{\text{i}} T_{\text{e}}^{\frac{3}{2}}}{Z_i^2 \ln \Lambda_{\text{ei}} \text{e}^4 n_{\text{e}}}
+$$
+
+--------------------
+
+### Spitzer resistivity | `calculate_spitzer_resistivity()`
+
+For $T_\text{e}$ in eV
+
+$$
+\eta_{\text{spitzer}} = \frac{4 \sqrt{2 \pi}}{3 }\frac{Z_i e^2 \sqrt{m_{\text{e}}} \ln \Lambda_{\text{ei}}}{\left(4 \pi \epsilon_0 \right)^2 T_{\text{e}}^{\frac{3}{2}}}
+$$