Environmental Engineering Reference
In-Depth Information
Figure 3.3
The electron drift velocity in helium in the regime of low electric field strength. Solid
curve - theory, signs - experiment [32].
One can conclude there is general character of evolution of the electron energy
when an electron travels in an atomic gas in an external electric field, and its en-
ergy exceeds the thermal atom energy
T
significantly. In the first stage of electron
evolution, its energy increases monotonically up to
max
and the equilibrium cor-
responds to this electron energy until criterion (3.32) holds true. In this stage of
electron evolution its distribution function is described by a delta function. Sub-
sequent collisions with gas atoms lead to broadening of the distribution function,
which is given by (3.27).
ε
3.2.3
Electrons in a Gas in the Regime of High Electron Number Density
The regime of electron drift in the limit of high electron number densities is
defined by the inverse criterion with respect to criterion (3.30). In this regime
I
ea
(
f
0
)
0,
which leads to the Maxwell distribution function (3.9). From this, for a motionless
electron gas we have
I
ee
(
f
0
), and the second equation of the set (3.25) gives
I
ee
(
f
0
)
D
m
e
2
exp
3/2
2
m
e
v
f
0
(
)
D '
(
)
D
N
e
,
v
v
π
T
e
2
T
e
wherethisfunctionisnormalizedby(3.1)and
T
e
is the electron temperature. Thus,
the thermodynamic equilibrium takes place inside the electron subsystem in this
limiting case. But since an external electric field violates such an equilibrium in the
total ionized gas, the electron temperature
T
e
differs from the gas temperature
T
.
Using the Maxwell distribution function in the first equation of the set (3.25), we
have
a
m
e
v
T
e
f
0
D
ν
v
f
1
,
