Environmental Engineering Reference
In-Depth Information
average electron energy
ε
D
3
T
e
/2
1
m
e
M
d
dt
D
T
T
e
2
eEw
e
h
v
ν
i
.
Accounting for the electron drift velocity being established in a time of approxi-
mately 1/
) being required for establishment
of the electron temperature, we take the equilibrium value of the drift velocity in
this equation. Assuming the difference
T
0
ν
and a time of approximately
M
/(
m
e
ν
T
e
between the equilibrium and cur-
rent electron temperatures to be relatively small, we have this equation in the form
d
dt
D
3
dT
e
2
dt
D
m
e
M
T
T
0
(
T
e
2
T
0
)
h
v
ν
i
.
Therefore, if we reduce this equation to the form
dT
e
dt
D
ν
ε
(
T
e
T
0
),
the energy relaxation rate
ν
ε
is given by
2
m
e
3
M
T
T
0
h
v
2
ν
ε
D
ν
i
.
(3.40)
As is seen, at large electric field strengths this relaxation rate along with a small
parameter
m
e
/
M
contains one more small parameter,
T
/
T
e
.
3.2.4
Conductivity of an Ionized Gas and a Plasma
The selective action of an external field on electrons of an ionized gas determines
the behavior of the ionized gas in an external electric field. The field energy is
transmitted first from the field to electrons and then it is transferred to gas atoms
through their collisions with electrons. Because of a strong action of the electric
field on electrons and a weak action on atoms, atoms have the Maxwell distribution
function for energies, whereas the electron distribution function for energies may
differ remarkably from the Maxwell one.
Electrons of a weakly ionized gas determine the electric properties of the gas, and
the gas conductivity
is defined as the proportionality factor for the relationship
between the electric current density
i
and the electric field strength
E
in Ohm's law:
Σ
i
D
Σ
E
.
The electric current is a sum of the electron and ion currents:
i
D
eN
e
w
e
C
eN
i
w
i
,
where
N
e
and
N
i
are the electron and ion number densities and
w
e
and
w
i
are
the electron and ion drift velocities. Since
w
e
w
i
, the main contribution to the
