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the mean and the fluctuated fields:
E µ = E + E 1 ,
B µ = B + b 1 ,
where E and B are the macroscopic electric and magnetic fields averaged over
the volumes with many particles. Field fluctuations are described with the
terms E 1 and b 1 result in fluctuations in the particle movement presented in
(1.7) by the collision integral. The E and B fields determine the Lorentz force
(1.8) that is to be substituted into (1.7) for charged particles.
Let ρ ext and j ext are the densities of the charge and current produced by
external drivers. Then Maxwell's equations for the plasma with the external
sources are given by
c
α
1
c
E
∂t + 4 π
c j ext + 4 π
×
B =
j ( α ) ,
1
c
B
∂t ,
×
E =
E =4 πρ ext +4 π
α
·
ρ α ,
·
B =0 ,
(1.9)
where
ρ α ( r ,t )= q α f α ( r , V ,t )d V ,
j ( α ) ( r ,t )= q α V f α ( r , V ,t )d V .
(1.10)
Hydrodynamic Equations
A treatment of the distribution function and the kinetic equations can be
found in a series of handbooks on plasma physics. The complete system of ki-
netic and field equations is extremely complicated and may not always be prac-
tically used. However, the physical pattern of phenomena, and often proper
quantity results as well, may be found using an essentially simpler theory. Fol-
lowing Chapman and Cowling [3], we call it an elementary theory. Numerous
phenomena related to velocity distribution, for instance, Landau damping,
and all the kinetic instabilities in the partially ionized plasma are neglected
in the elementary theory. A plasma state is characterized by the directed ve-
locities of an 'mean' electron v e , ion v ( α ) of species α , neutral particle v ( β ) of
species β and by their mean temperatures T e ,T α ,T β . The electron T e and
ion temperatures T α are defined as
W e = 3
W α = 3
2 kT α ,
where W e and W α denote the energy of chaotic motions of the 'mean' electron
and α ion.
2 kT e ,
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