Kinetic Description of the Electrons

VELOCITY Distribution Function and Velocity Space Averages 

The distribution of the electrons with respect to their velocity space t at the coordinate space position x and at time t is described by the velocity distribution 

If the velocity distribution F(5, x, t) is known, important macroscopic properties of the electrons can be calculated by appropriate velocity space averaging over the distribution. To give some examples, the density n(x, t), the density of the mean energy u (x, t) and the vectorial particle current density j x, t) of the electrons are given by the averages (Desloge, 1966) 

In the introduction of the velocity distribution and the examples, Eqs. (5) to (7), of macroscopic quantities, the usual normalization of the velocity distribution on the electron density has been used. In special conditions, e.g., in steady-state or in time-dependent conditions with only conservative electron collision processes included, the electron density becomes a constant and can easily be separated from the velocity distribution. Especially in these cases, a normalization of the velocity distribution on one electron is often used. 

The different microphysical processes—the field action and the various binary collision processes—in which the electrons are involved in a weakly ionized plasma lead to a complex redistribution of the electrons in their phase space, i.e., their combined coordinate and velocity space. 

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