Fluid Theory
Plasma fluid equations are obtained by taking loworder velocityspace moments of the kinetic equation [18].
The loworder moments of the distribution function, , all have simple physical interpretations.
First, we have the particle number density,

(2.2) 
and the mean flow velocity,

(2.3) 
Next, we have the pressure tensor,

(2.4) 
and the heat flux,

(2.5) 
Here,

(2.6) 
The trace of the pressure tensor measures the ordinary (or scalar) pressure,

(2.7) 
The (kinetic) temperature is defined as

(2.8) 
The loworder velocityspace moments of the collision operator also have simple interpretations.
The friction force density takes the form

(2.9) 
whereas the collisional heating rate density (in the species rest frame) is written

(2.10) 
The zeroth, first, and contracted second velocityspace moments of the kinetic equation, (2.1),
yield the following set of fluid equations for species [18]:
Here,

(2.14) 
is the wellknown convective derivative, and
we have written
where is the unit (identity) tensor, and
is the viscosity tensor. Obviously, Equation (2.11) is a particle conservation
equation for species, Equation (2.12) is a momentum conservation equation, and Equation (2.13) is an energy conservation equation [18].