add some details to docs

Docs/source/theory/kinetic_fluid_hybrid_model.rst

@@ -48,6 +48,9 @@ integrating over velocity), also called the generalized Ohm's law, is given by:
 
         en_e\vec{E} = \frac{m}{e}\frac{\partial \vec{J}_e}{\partial t} + \frac{m}{e^2}\left( \vec{U}_e\cdot\nabla \right) \vec{J}_e - \nabla\cdot {\overleftrightarrow P}_e - \vec{J}_e\times\vec{B}+\vec{R}_e
 
+where :math:`\vec{U}_e = \vec{J}_e/(en_e)` is the electron fluid velocity,
+:math:`{\overleftrightarrow P}_e` is the electron pressure tensor and
+:math:`\vec{R}_e` is the drag force due to collisions between electrons and ions.
 Applying the above momentum equation to the Maxwell-Faraday equation (:math:`\frac{\partial\vec{B}}{\partial t} = -\nabla\times\vec{E}`)
 and substituting in :math:`\vec{J}` calculated from the Maxwell-Ampere equation, gives,
 
@@ -59,9 +62,11 @@ Plugging this back into the generalized Ohm' law gives:
 
     .. math::
 
-        \left(en +\frac{m}{e\mu_0}\nabla\times\nabla\times\right)\vec{E} = - \frac{m}{e}\left( \frac{\partial\vec{J}_{ext}}{\partial t} + \sum_{s\neq e}\frac{\partial\vec{J}_s}{\partial t} \right) + \frac{m}{e^2}\left( \vec{U}_e\cdot\nabla \right) \vec{J}_e - \nabla\cdot {\overleftrightarrow P}_e - \vec{J}_e\times\vec{B}+\vec{R}_e.
+        \left(en_e +\frac{m}{e\mu_0}\nabla\times\nabla\times\right)\vec{E} =&
+        - \frac{m}{e}\left( \frac{\partial\vec{J}_{ext}}{\partial t} + \sum_{s\neq e}\frac{\partial\vec{J}_s}{\partial t} \right) \\
+        &+ \frac{m}{e^2}\left( \vec{U}_e\cdot\nabla \right) \vec{J}_e - \nabla\cdot {\overleftrightarrow P}_e - \vec{J}_e\times\vec{B}+\vec{R}_e.
 
-If we now further assume electrons are inertialess, the above equation simplifies to,
+If we now further assume electrons are inertialess (i.e. :math:`m=0`), the above equation simplifies to,
 
     .. math::