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The particle distribution function
is defined
so that the total number of particles in a differential sixdimensional
phase space element
is equal to
.
The
particle number density (number of particles per unit volume)
is

(3.1) 
Other physical quantities are obtained by taking moments, where
the
moment of quantity
is defined by

(3.2) 
Using (3.2), the following physical quantities are
defined for particle species :

Fluid velocity:

(3.3) 

Mean thermal velocity:

(3.4) 

Mass density:

(3.5) 

Mean mass velocity:

(3.6) 

Velocity of particle relative to mean mass velocity:

(3.7) 

(3.8) 

The pressure tensor
is defined in terms of
:

(3.9) 
The equilibrium velocity distribution function is a Maxwellian, with

(3.10) 
Other distributions are often detected in space plasmas; for example,
biMaxwellians with different temperatures in directions parallel
and perpendicular to the background magnetic field, and generalized
Lorentzian (or Kappa)
distributions which depart from the Maxwellian functional form
at high energies and obey a power law.
Next: Basic equations
Up: Fluid & MHD Theory
Previous: Fluid & MHD Theory
Iver Cairns
19990809